document_title: List of Indian states by life expectancy at birth

question_text: which state of india has highest life expectancy at birth

root

text:
States and union  territories of India  ordered by
Area
Population

Abbreviations
Capitals
Child Nutrition
Crime rate
Electricity penetration
Fertility rate
Forest cover
GDP (per capita)
Highest point
HIV awareness
HDI
Home ownership
Household size
Human Trafficking
Institutional delivery
Life expectancy at birth
Literacy rate
Media exposure
Number of Vehicles
Number of voters
Obesity
Open defecation
Origin of name
Places of worship
Poverty
Power capacity
Safe Drinking Water
Safety of Women
School Enrollment Rate
Sex ratio
Suicides
Tax revenues
TV ownership
Toilet availability
Transport network
Underweight people
Unemployment
Vaccination coverage
vte

text: This is a list of Indian states by Life expectancy at birth. The figures come from the Human Development Index Report, published in 2011, by United Nations Development Programme (UNDP) India[3] and Sample Registration Survey (SRS) based life table 2010-14.[4][5]

tag: p

text: The report provides life expectancy at birth for years 2002-06 and 2010-14. In 2002-6, Punjab had the second highest life expectancy. Kerala had the highest life expectancy among the states in India, while Assam had the lowest. The figures for North-Eastern States were unavailable.[5]

text:
Rank
State
Life expectancy at birth

(2010-14)[5]
(2002-06)[6]

1
Kerala
74.9
74.0

2
Delhi
73.2
-

3
Jammu and Kashmir
72.6
-

4
Uttarakhand
71.7
60.0

5
Himachal Pradesh
71.6
67.0

5
Punjab
71.6
69.4

5
Maharashtra
71.6
67.2

8
Tamil Nadu
70.6
66.2

9
West Bengal
70.2
64.9

10
Karnataka
68.8
65.3

11
Gujarat
68.7
64.1

12
Haryana
68.6
66.2

13
Andhra Pradesh (includes Telangana)
68.5
64.4

14
Bihar
68.1
61.6

*
India
67.9
63.5

15
Rajasthan
67.7
62.0

16
Jharkhand
66.6
58.0

17
Odisha
65.8
59.6

18
Chhattisgarh
64.8
58.0

19
Madhya Pradesh
64.2
58.0

20
Uttar Pradesh
64.1
60.0

21
Assam
63.9
58.9


document_title: Bethany Hamilton

question_text: where did the girl get her arm bitten off

text: Bethany Hamilton

text: Surfing career[edit]

text:
Placings in surf competitions

Year
Event
Place
Country

1998
Rell Sun Menehune
1st
USA

2002
Open Women's Division of the NSSA
1st
USA

2004
NSSA National Competition
1st
Australia

2005
NSSA National Competition
1st
USA

2005
O'Neill Island Girl Junior Pro tournament
1st
USA

2006
NSSA National Championship: 18-and-under Finalist
5th
USA

2006
Hawaii Team Highlights
4th
5th*
USA

2007
NSSA Regionals
1st
USA

2007
T & C Pipeline Women's Pro
1st
USA

2008
US Open of Surfing—Huntington Beach, California
5th
USA

2008
Roxy Pro Surf Festival—Phillip Island
3rd
Australia

2009
Rio Surf International in Rio de Janeiro
3rd
Brazil

2009
Billabong ASP World Junior Championship
2nd
Australia

2014
Surf 'n' Sea Pipeline Women's Pro
1st
USA

2015
Swatch Women's Pro[1]
13th
USA

2016
Fiji Women's Pro[2]
3rd
Fiji

tag: table

text: Shark attack and recovery[edit]

text: On October 31, 2003, Hamilton, aged 13 at the time, went for a morning surf along Tunnels Beach, Kauai, with best friend Alana Blanchard, Alana's father, Holt, and brother Byron. Around 7:30 a.m., with numerous turtles in the area, she was lying on her surfboard with her left arm dangling in the water, when a 14-foot-long (4.3 m) tiger shark attacked her,[3] severing her left arm just below the shoulder. The Blanchards helped paddle her back to shore, then Alana's father fashioned a tourniquet out of a surfboard leash and wrapped it around the stump of her arm. She was rushed to Wilcox Memorial Hospital. By the time she arrived there she had lost over 60% of her blood and was in hypovolemic shock. A doctor living in a hotel nearby raced to the rescue. Her father, who was scheduled to have knee surgery that morning, was already there, but she took his place in the operating room. She spent a week in recovery before being released. During subsequent media interviews, she confirmed that she felt normal when she was bitten and did not feel much pain from the bite at the moment of the disaster, but felt numb on the way to the hospital.

text: When the news broke out of the shark attack, a family of fishermen led by Ralph Young presented to investigators photos of a 14-foot-long (4.3 m) tiger shark they had caught and killed about one mile from the attack site. It had surfboard debris in its mouth. When measurements of its mouth were compared with those of Hamilton's broken board, it matched. In late 2004, the police officially confirmed that it was the one that attacked her.

text: Despite the trauma of the incident, Hamilton was determined to return to surfing.[4] One month after the attack, she returned to her board.[5]

text: Initially, she adopted a custom-made board that was longer and slightly thicker than standard and had a handle for her right arm, making it easier to paddle, and she learned to kick more to make up for the loss of her left arm. After teaching herself to surf with one arm, on January 10, 2004, she entered a major competition. She now uses standard competitive performance short-boards.[6] The shark-bitten surfboard that Hamilton was riding during the attack, as well as the bathing suit she was wearing at the time, a gift from ocean photographer Aaron Chang, are on display at the California Surf Museum in Oceanside, California.[7][8]

text: Media[edit]

text: Since the attack, she has appeared as a guest on numerous television shows. Her manager, Roy "Dutch" Hofstetter, who went on to produce the film Soul Surfer, managed her rise through the media from shark attack victim to inspirational role model. The television shows she has appeared on include The Biggest Loser, 20/20, Good Morning America, Inside Edition, The Oprah Winfrey Show, The Ellen DeGeneres Show, The Today Show, and The Tonight Show, as well as in magazines People, Time, and American Girl. Additionally, she was the cover story in the premier issue of niNe magazine.[9]

text: In 2004, she won the ESPY Award for Best Comeback Athlete[10] and also received the Courage Teen Choice Award.[11]

text: In 2004, MTV Books published Hamilton's book, Soul Surfer: A True Story of Faith, Family, and Fighting to Get Back on the Board (ISBN 0-7434-9922-0), which describes her ordeal. Her story is also told in the 2007 short subject documentary film Heart of a Soul Surfer, directed by Becky Baumgartner. Described as a "faith-based documentary," the film addresses her devout Christianity and the courage and faith in Jesus Christ in the aftermath of the shark attack, and follows her quest for spiritual meaning.[12][13]

text: On August 7, 2009, she was a contestant on Are You Smarter Than a Fifth Grader? and won $25,000. On May 16, 2010, she appeared on an episode of ABC's Extreme Makeover: Home Edition. In March 2011, Hamilton appeared in a video for the Christian organization I Am Second, telling of her struggle after the shark attack and how she trusted in God to get her through it.

text: On April 8, 2011, a feature film Soul Surfer, based on her 2004 book, was released in theaters. Hamilton was portrayed by actress AnnaSophia Robb. Hamilton herself performed all the one-armed surfing stunts in it.[14] The movie was released on DVD and Blu-ray on August 2, 2011.

text: On October 11, 2011, she appeared on the TLC series 19 Kids and Counting, in the episode titled "Duggars Under the Sea," when the Duggar family visited her, in Atlanta, Georgia.

text: Hamilton plays herself in the film Dolphin Tale 2, which revolves around the baby dolphin Hope's story. Filming began in Clearwater, Florida, on October 7, 2013. It was released on September 12, 2014.[15] Hamilton and her husband, Adam Dirks, competed as a team on the 25th season of The Amazing Race, finishing in third place. Filmed in June 2014, it premiered on September 26 on CBS.[16]

text: Personal life[edit]

text: Hamilton was home-schooled from 6th grade and went back to school for high school. Bethany is a Christian.[4] She is the youngest of three siblings.[17] In early 2012, Hamilton met youth minister[18] Adam Dirks through mutual friends.[19] They became engaged in April 2013.[20][21] The couple were married on August 18, 2013, in front of 300 friends and family members at a secluded 130-acre estate on Kauai's north shore, near where she grew up.[22][23] She and Adam competed on The Amazing Race 25 where they placed in the top 3. In 2015, Hamilton gave birth to a son.[24]


document_title: Corporal

question_text: when was the rank of corporal established in the marine corps

question_tokens: when was the rank of corporal established in the marine corps

text: Corporal

text: Etymology[edit]

text: The word is derived from the medieval Italian phrase capo corporale ("head of a body").[1] It may also be derived from an appointment as an officer's bodyguard,[citation needed] originally being an adjective pertaining to the word "body".

text: Argentina[edit]

text: All three branches of the Armed Forces of the Argentine Republic use two or three ranks of corporal, or cabo. Corporals in the Argentine military are considered suboficiales subalternos (subaltern sub-officers/lower non-commissioned officers), superior only to all ranks of Volunteers (enlisted members of the Army and Air Force) and Seamen (enlisted members of the Navy).

text: In the Argentine Army, there are two ranks of corporal, junior and senior: Cabo ("corporal") and cabo primero ("first corporal").

text: While the Argentine Navy has three corporal ranks, from junior to senior: Cabo segundo (corporal second class), Cabo primero (corporal first class) and cabo principal (principal corporal), which is equal to the army rank of sargento (sergeant). The Air Force has the same number of corporal ranks as the navy, and keeps the same titles, with the exception of cabo (corporal) instead of the navy's cabo segundo (corporal second class).

text: The rank is also used by the Argentine National Gendarmerie and the Argentine Federal Police, which use the rank in the same manner as the Army, as well as the Argentine Naval Prefecture.

text: Australia[edit]

text: Corporal is the second lowest of the non-commissioned officer ranks in the Australian Army, falling between lance-corporal and sergeant. A corporal is usually appointed as a section commander, and is in charge of 7-14 soldiers of private rank. They are assisted by a second-in-command, usually a lance-corporal or senior private. A Corporal within Artillery is known as a bombardier. Corporal is also a rank of the Royal Australian Air Force, being equal to both the Australian Army and Royal Air Force rank of corporal.

text: Belgium[edit]

text: With the exception Belgian Naval Component, the branches of the Belgian Armed Forces use three ranks of corporal: corporal (Dutch: korporaal, French: caporal), master corporal (Dutch: korporaal-chef, French: caporal-chef) and 1st master corporal (Dutch: 1ste korporaal-chef, French: 1e caporal-chef). Corporal is equivalent to NATO Rank Code OR-3, whereas master corporal and 1st master corporal are equivalent to OR-4. The rank immediately below corporal is 1st private and the rank directly above 1st master corporal is sergeant.

text: Units with a cavalry, artily or Logistic Corps (Transport unit) tradition replace Corporal by “Brigadier”.

text: The equivalent of these ranks in the Naval Component are quartermaster, chief quartermaster and 1st chief quartermaster.

text: Brazil[edit]

text: Corporal (in Portuguese cabo) is the first NCO rank of the Army, Navy, Air Force and states military police forces. Soldiers who successfully complete the corporal course may be promoted to the rank of corporal should they excel in the course. A corporal in the Brazilian Army will lead the smallest fractions of units as machine gun squads, mortar and infantry squads.

text: Canada[edit]

text: Corporal is an Army and Air Force non-commissioned member rank of the Canadian Forces. Its Naval equivalent is leading seaman. It is senior to the rank of private and its naval equivalent able seaman, and junior to master corporal (caporal-chef) and its equivalent master seaman (matelot-chef). It is part of the cadre of junior non-commissioned officers, and one of the junior ranks. In French, the rank is caporal.

text: The rank insignia of a corporal is a two-bar chevron, point down, worn in gold thread on both upper sleeves of the service dress jacket; in rifle green (army) or dark blue (air force) thread on CADPAT slip-ons for operational dress; in old gold thread on blue slip-ons on other air force uniforms; and in gold metal and green enamel miniature pins on the collars of the army dress shirt and outerwear coats. On army ceremonial uniforms, it is usually rendered in gold braid (black for rifle regiments), on either both sleeves, or just the right, depending on unit custom.

text: Corporal is the first non-commissioned officer rank, and the lowest rank officially empowered to issue a lawful command. Corporals can lead troops if they have the formal qualifications to be promoted to master corporal but have not been promoted yet. However, the rank of corporal was severely downgraded after Unification, along with the attendant responsibilities. A corporal in the Canadian Army in 1967 had the same duties and responsibilities that a sergeant has today. In an infantry section, a corporal will sometimes command an assault team if a master corporal is leading the section or they are pending promotion to master corporal.

text: Another effect of Unification was to delete the appointments of lance-corporal and lance-sergeant (a corporal holding the acting rank of sergeant). The former is still common in other Commonwealth militaries.

text: Corporal is deemed to be the substantive rank of the members carrying the appointment of master corporal. On pay documents, corporal was formerly listed as "Cpl (A)" and master corporal as "Cpl (B)".

text: The rank of corporal in artillery units follows the British convention and is styled bombardier — thus a master corporal is a master bombardier.

text: In rifle regiments, a distinction was historically drawn between a corporal and an acting corporal; The Queen's Own Rifles of Canada had a special insignia to distinguish between the two.

text: Chile[edit]

text: In the Army, Navy, Air Force and Police, there are three grades of Corporal: Corporal, Corporal 2nd. and Corporal 1st. The next level is Sergeant 2nd. grade.

text: People's Republic of China[edit]

text: Corporal (Chinese: 下士, literally junior NCO) is the lowest among the ranks of the non-commissioned officer of the People's Liberation Army. This rank was once replaced by the rank "level one non-commissioned officer" (Chinese:一级士官, 1998–2009), but was re-introduced in 2009.

text: Denmark[edit]

text: In the Danish military, the rank of corporal (korporal in Danish) is the lowest rank of the NCO group. Professional (non-conscripted) soldiers, often those with the rank of "overkonstabel" (somewhat similar to "specialist" in the U.S. Army) may sometimes get selected for the rank of corporal, if they have unique experience or skills. This can't be given as a battlefield appointment and the aspiring corporal has to take a course in order to be promoted (6 weeks in the Army, 3 weeks in the Airforce and Navy). A corporal will often be given a task similar to that of other countries corporals; i.e. ad hoc assistance of squad-commanders. In the homeguard, a private can after completing a 10-day course get promoted to the rank of corporal and function as second in command of an infantry squad. The rank of corporal was phased out but was reintroduced into the Danish Army in October 2008.[2][3]

text: Estonia[edit]

text: In the Estonian Defence Forces, the rank of corporal (kapral in Estonian) is not an NCO rank, but an enlisted one and is equivalent to NATO Rank Code OR-2.

text: Finland[edit]

text: Alikersantti is an OR-4 rank and the lowest NCO rank of the Finnish Defence Forces. Alikersantti carries two-chevron rank insignia. In translations from English to Finnish, the corporal rank is often mistranslated as lance corporal, which is called korpraali in Finnish. In direct translation, the rank name basically means "junior sergeant" or "sub-sergeant". Typical duties of alikersantti are leading the squad or being second-in-command of the squad.

text: France[edit]

text: There are three ranks of corporal (caporal in French). In the French Army, these are not NCO ranks, but enlisted ones. The corporals are called "ranked" (gradés). NCO start at the rank of sergent (OR-5).

text:
"Corporal" (caporal) is a NATO OR-3 level rank. The insignia is two chevrons of wool (vs. the two gold chevrons of a sergeant).
"Master corporal" (caporal-chef) is OR-4. The insignia is two chevrons of wool plus a gold chevron.
"First class master corporal" (caporal-chef de première classe) is intermediate between OR-4 and OR-5. The insignia is one red chevron and two gold chevrons.[citation needed]

tag: ul

text: With the exception of Troupes de Marine, which uses caporaux whether the men are infantry, cavalry or artillery, regiments with a cavalry tradition use brigadier.

text: Germany[edit]

text: Historically, the German army rank of Unteroffizier[4] was the traditional German equivalent to the British Army corporal rank, and this grade has existed as a military rank since at least the 18th century. The German ranks of Gefreiter and Obergefreiter are sometimes considered to be equivalent to a corporal rank in the US and other armies. The deputy to an Unteroffizier usually held the rank of Obergefreiter or Gefreiter (but others in the gruppe—squad/section—could as well) and as such is comparable to a British Army or Royal Marine  lance corporal.[4][5][6] Gefreiter and Obergefreiter ranks are based on experience and not on positions. The additional German rank of Obergefreiter was historically considered a senior lance corporal otherwise second corporal in the foot artillery which replaced the bombardier rank.

text: In modern-day Bundeswehr usage, the German rank of Unteroffizier is classified as OR-5 within the combined NATO-standard rank scale and is considered to be more a US sergeant rank than that of a corporal, with Oberstabsgefreiter and Stabsgefreiter now considered the equivalent ranks to the corporal (OR-4).  The British Army does not use OR 5 and considers sergeants to be OR-6.

text: In the years between 1934 and 1945, there was also a corresponding paramilitary Schutzstaffel (SS) rank grade of Unterscharführer, it was considered equivalent to a Germany Army Unteroffizier rank.

text:
Shoulder strap  SS-Unterscharführer (SS-Junker)

Gorget patches Unterscharführer of the Waffen-SS

Military camouflage Unterscharführer of the Waffen-SS

text: India and Pakistan[edit]

text: These ranks are still used in the Indian Air Force and Pakistan Air Force. it is a rank given to an airman who is senior to leading aircraftsman but junior to a sergeant. A corporal is designated as a Non-Commissioned Officer in the Indian Air Force.

text: Indonesia[edit]

text: In the Indonesian Military, the rank "Corporal" is known as Kopral. In Indonesia, "Corporal" has three levels, which are: Second Corporal (Lance Corporal), First Corporal (Corporal), and Master Corporal. After this rank, the rank: Sergeant is promoted.

text:
Second Corporal/Lance Corporal

First Corporal/Corporal

Master Corporal

text: Iran[edit]

text: Corporal (in Persian سرجوخه Sarjukhe) is one of the lower ranks of the Islamic Republic of Iran Army. A sarjukhe is usually responsible for four or five soldiers.

text: Ireland[edit]

text: Corporal (ceannaire in Irish) is the lowest rank of non-commissioned officer within the Irish Army and Air Corps. The Naval Service equivalent is leading seaman.

text: Army[edit]

text: The main role of an infantry corporal is either to command a section as the section commander or to command the fire support group as the second in command of the section. All corporals are qualified instructors on drill, section weapons, and fieldcraft.

text: In the Artillery Corps, the corporal is normally assigned to a gun detachment as a layer, or a detachment commander. Artillery corporals can also find themselves in charge of the battery signals section.

text: The army rank insignia consists of two winged chevrons (or "stripes"), the dress uniform being red chevrons with a yellow border.

text: Air Corps[edit]

text: Before 1994, the Air Corps was considered part of the army and wore army uniforms with distinct corps badges but the same rank insignia. With the introduction of a unique Air Corps blue uniform in 1994, the same rank markings in a white colour were worn, before the introduction of a new two-chevron badge with wing rank marking.

text: Israel[edit]

text: In the Israel Defense Forces, soldiers are promoted from private to corporal (rav-turai or rabat) after 7–10 months of service (7 for combatants, 8 for combat support and 10 for non-combatants), if they performed their duties appropriately during this time. Soldiers who take a commander's course, are prisoner instructors or practical engineers become corporals earlier. Corporals get a symbolic pay raise of 3.60 NIS and those who are also non-commissioned officers (mashak) are able to command privates in their respective units.

text: A corporal may be promoted to sergeant about 11 or 12 months after becoming a corporal, or to the rank of second lieutenant if they complete an officer's course.

text: Italy[edit]

text: A soldier can be promoted from private (soldato) to corporal rank (caporale) after 3 months of service.[7] The title was use as a senior office in the Italian Kingdom during World War II.

text: Mexico[edit]

text: Corporal (in Spanish "cabo") is one of the lower ranks of the Mexican army.

text: New Zealand[edit]

text: The New Zealand Defence Force awards the corporal rank to soldiers or airmen after 6 or 7 years of service. There is substantial responsibility on the part of a corporal in the New Zealand Army and Royal New Zealand Air Force. They usually command a small team and work closely with their sergeants. A pay increase is also given.

text: Like their British, Canadian and Australian counterparts, they wear two chevrons to distinguish their rank.

text: Corporals have what is termed 'power of arrest', and is impressed on recruits in RNZAF basic training. Basically, this power means that any airman or private disobeying or ignoring an order from a corporal will be subject to military arrest by that individual. Needless to say, power of arrest is used by higher ranks to enforce their orders, corporal in the RNZAF being the lowest rank with this power.

text: Norway[edit]

text: In the Norwegian Armed Forces, promotion to the rank of korporal is an acknowledgement for good service by conscripted personnel. The rank does give some commanding authority, and corporals may be given increased informal responsibilities by senior officers and non-commissioned officers. The rank carries two chevrons and a slight pay increase.

text: All conscripted personnel in the military police are awarded the rank after the five month learning period is over.

text: Poland[edit]

text: In the Polish Land Forces, the rank of kapral is the lowest rank in the NCO corps (OR-3 in NATO code). Most commonly the rank is held by a NCO commanding an infantry squad, tank or gun crew, or a similar unit. The equivalent rank in the Polish Navy is mat.

text: As with many other military ranks, direct comparison between various armies might be misleading. Before World War II, the Polish Army's kapral was more or less equivalent to the British rank of lance corporal, while the British rank of corporal was named plutonowy (lit. platooner). In modern times, the rank is still equivalent to a UK lance corporal or a private first class in the U.S. Army (OR-3), while the British and American rank of corporal (OR-4) is equivalent to the Polish rank of starszy kapral (lit. "senior corporal"), which was introduced in 1971.

text: Historically, the rank was first introduced in Poland in the 17th century, together with mercenary troops of Italian origin. In foreign troops on the royal payroll, a kapral commanded four ranks of musketeers or part of a company of pikemen. In the 20th century, between the world wars, the rank of corporal was held by both conscripted NCOs and professional soldiers alike. This was changed after World War II, when the Polish Army was under Soviet command and the rank of kapral was modified to resemble that of Soviet junior sergeant, reserved for conscripted NCOs. In the modern Polish Army, the rank is exclusively reserved for professional soldiers.

text: The insignia of kapral (worn on shoulder straps or badge above breast pocket) are two bars.

text: Portugal[edit]

text: The Portuguese Navy has the rank of cabo da Armada (corporal of the Navy). All other branches of the Portuguese Armed Forces have several ranks of corporal (cabo in Portuguese). The Portuguese Army and the Portuguese Air Force have the ranks of segundo cabo (second corporal), primeiro cabo (first corporal) and cabo-adjunto (corporal adjudant). The National Republican Guard has the ranks of cabo (corporal), cabo-chefe (chief corporal) and cabo-mor (corporal-major).

text: The several ranks of corporal correspond to the several pay grades, above that of private, that can be reached inside the enlisted rank professional category of the Army, the Air Force and the National Republican Guard. In the Navy, the rank of cabo da Armada is the highest pay grade in the enlisted rank category.

text: Russia[edit]

text: The rank of corporal (Russian: капрал) existed in the Russian Army from 1647 to 1798, when it was replaced with that of non-commissioned officer (Russian: унтер-офицер, from German: unteroffizier, literally "sub-officer"). Soviet and modern Russian armies have the rank of junior sergeant (Russian: младший сержант) that is not equivalent to the rank of corporal, as junior sergeants are assigned as squad leaders.

text: Singapore[edit]

text: Corporal in the Singapore Armed Forces lies between lance corporal and corporal first class.[8] National Servicemen are usually promoted to this rank within the 2nd year of their service.

text: Prior to the mid-1990s, the SAF followed the British model where corporals were non-commissioned officers often holding the appointment of section leader. Today, a corporal is not a specialist (NCO-equivalent). Corporals are usually given higher responsibilities/ appointments as a section 2IC, or 2nd-in-command.[9]

text: In the Singapore Police Force, Singapore Civil Defence Force, Singapore Prison Service, Immigration and Checkpoints Authority and Singapore Customs, a corporal is a rank below sergeant. The rank is also used in uniformed groups for students such as National Police Cadet Corps, National Cadet Corps, National Civil Defence Cadet Corps and St. John Ambulance in Singapore

text: The rank insignia for a corporal (中士) is two chevrons pointing downward with an arc on top.

text:
Singapore Armed Forces enlistee ranks

Insignia
(No insignia)
(No insignia)

Rank
Recruit
Private
Private first class
Lance corporal
Corporal
Corporal first class

Abbreviation
REC
PTE
PFC
LCP
CPL
CFC

text: Spain[edit]

text: In the Spanish Armed Forces, cabo (corporal) is the rank between soldado de primera (first class private) and cabo primero (first corporal). It actually equates to a NATO OR-3, with cabo primero equating to an OR-4 and cabo mayor to an OR-5.

text:
Spanish Army Cabo insignia.

Spanish Navy Cabo insignia.

Spanish Navy Marines Cabo insignia.

Spanish Air Force Cabo insignia.

Civil Guard Cabo insignia.

text: Sweden[edit]

text: In the Swedish Army, Navy and Air Force, the rank of korpral is a rank for soldiers with a specialization, and often in charge of a group six to ten men.

text: Taiwan (Republic of China)[edit]

text: Corporal (Chinese: 下士, literally junior NCO) is the lowest among the ranks of the non-commissioned officer of the Taiwan Army, Marines, Air Force and Military Police. The rank wears an insignia with a broad chevron along with a narrow one, representing the NCO character and the juniority of the rank, respectively.

text: Turkey[edit]

text: In Turkey, the rank of Onbaşı (Corporal) is above the rank of the private. Onbaşı literally translated to "Head of 10"

text: Ukraine[edit]

text: Since 2015, the Corporal (Ukrainian: Капрал, translit. Kapral), a OR4-rank, was introduced in the National Police of Ukraine, that is a special rank of junior quarterdeck. It corresponds to former junior sergeant of militia.

text:
Ukrainian military ranks, Army
Ukrainian police ranks

text: United Kingdom[edit]

text:
The rank of corporal, which falls between lance-corporal and sergeant is used by the British Army, Royal Marines, and Royal Air Force. A corporal is often regarded as a slightly more senior rank in the UK services than in other countries: although British corporals are classified as OR-4 under the NATO system, they usually fill posts held by an OR-5 equivalent
in other countries, such as section leader.

text: The badge of rank is a two-bar chevron (also known as "stripes", "tapes", or "hooks"). A corporal's role varies between regiments; but, in the standard infantry role, a corporal commands a section, with a lance-corporal as second-in-command (2ic). When the section is split into fire teams, they command one each. In the Royal Armoured Corps, a corporal commands an individual tank. Their duties therefore largely correspond to those of staff sergeants in the United States Army and corporals are often described as the "backbone" of the British Army.

text: In the Household Cavalry, all non-commissioned ranks are designated as different grades of corporal up to regimental corporal major (who is a warrant officer class 1). There is no effective actual rank of corporal, however, and the ranks progress directly from lance-corporal to lance-corporal of horse (who is effectively equivalent to a corporal; technically, a lance-corporal of horse holds the rank of corporal but is automatically give the appointment of lance-corporal of horse). Similarly, in the Foot Guards and in the Honourable Artillery Company, every Corporal is appointed as a lance-sergeant meaning they wear three chevrons rather than the regular two, with a lance-corporal wearing two chevrons instead of one: this is sometimes said to have originated with Queen Victoria who did not like "her own guardsmen" having only one chevron.[citation needed]

text: Royal Artillery corporals are called bombardiers; although, until 1920, the Royal Artillery had corporals and bombardier was a lower rank. The rank of second corporal existed in the Royal Engineers and Royal Army Ordnance Corps until 1920.

text: A common nickname for a corporal is a "full screw", with lance-corporals being known as "lance-jacks".

text: Corporal is the lowest NCO rank in the Royal Air Force (aside from the RAF Regiment who have lance-corporals), coming between junior technician or Senior aircraftman technician and sergeant in the technical trades, or senior aircraftman and sergeant in the non technical trades. Between 1950 and 1964, corporals in technical trades were known as "corporal technicians" and wore their chevrons point up.

text: In the Royal Navy, the equivalent to corporal is leading hand or leading rate. Although classified as NATO OR-4, British corporals frequently fill OR-5 equivalent posts.

text: The Army Cadet Force, Combined Cadet Force, Air Training Corps, Royal Marines sections of the Sea Cadet Corps and the Combined Cadet Force all have the rank of corporal, reflecting the structure of their parent service; therefore it is the second NCO rank of the ACF, CCF (including the RAF Section, which has the rank of lance corporal) and marine cadets, and the first NCO rank in the ATC.

text:
showvteRatings and other ranks of the British Armed Forces
ServiceRoyal NavyRoyal MarinesArmyRoyal Air Force

OR-1PteAC

OR-2ABMnePteLAC

OR-3Not ApplicableLCplLCplSAC / SAC(T) / LCpl (RAF Regt only)

OR-4LHCplCplCpl

OR-5/OR-6POSgtSgtSgt

OR-7CPOCSgtSSgt / CSgtChf Tech - Flt Sgt

OR-8WO2WO2

OR-9WO1WO1WO1WO / MAcr

text: United States[edit]

text: United States Army[edit]

text: In the U.S. Army, corporal is preceded by the first three forms of private and the rank of specialist.[10] A corporal rank (hard stripe) shares the same pay grade (E-4) as a specialist. Unlike a specialist, however, a corporal is a non-commissioned officer and may direct the activities of other soldiers.[11] A soldier may be promoted to corporal directly from the rank of private first class, laterally promoted from specialist or be demoted to corporal from the rank of sergeant.

text: The typical criterion for promotion to corporal is that the junior enlisted soldier must be serving in a leadership position that would typically be occupied by an NCO such as a sergeant or higher. Normally, these promotions are given latterly to specialists who work in an NCO position but who are prevented promotion to sergeant (E-5) due to not having sufficient promotion points. This promotion is done at the discretion of the unit commander; many specialists serve in NCO positions.

text: For a time, it was not uncommon to find paralegal corporals assigned to the legal assistance branch of a post's staff judge advocate's office, despite often having little or no actual leadership duties. Army Regulation 27-55 Notarial Services conferred (under provisions of 10 U.S.C. §§ 936, 1044a) authority to act as a notary and consul of the United States upon JAG Corps NCOs. Notarisation of powers of attorney and other documents is a "bread-and-butter" task in such offices, which necessitated the presence of either NCOs or state notaries. AR 27-55 was later amended to confer the authority on such paralegal specialists who are so designated by their respective staff judge advocate.

text: It is common for a corporal to lead a fireteam; however, if a soldier is promoted to corporal and there are too many soldiers of that rank, the new corporal will stay in their current position.

text: The rank of corporal was "inherited" from its use in the British Army and American colonial regulars and militia of the several colonies. The corporal has historically been the junior noncommissioned (NCO) rank immediately subordinate to sergeant. Commonly, in the British Army and American colonial forces, there was one corporal for each sergeant with the corporal serving as the junior NCO of the section/squad (the two terms were often used interchangeably).

text: During the American Civil War, the number of corporals was increased to two per sergeant/section and in 1891 the corporal was officially designated as a squad leader, with two squads per section under a sergeant. In 1901, the number of corporals/squads was increased to three per section and in 1917 to four corporals per section. In 1939, with the reorganization from the "square" to the "triangular" division, which eliminated the section in rifle platoons, there were then only three corporals/squads per platoon (with two sergeants in the platoon headquarters).

text: In 1940, corporals became assistant squad leaders while the squad leaders became sergeants (with two staff sergeants in the platoon headquarters). In 1942, with the upgrade of squad leaders to staff sergeants and the assistant squad leaders to sergeants (with a technical sergeant and a staff sergeant in the platoon headquarters), corporals in rifle squads became either an automatic rifleman or a senior rifleman with usually only one or two per squad. In 1948, corporals again became assistant squad leaders under sergeants as squad leaders (staff sergeant having been eliminated and technical sergeant converted to sergeant first class). In 1956, corporals became fire team leaders with two per squad. Finally, in 1958, corporals were effectively eliminated in rifle squads (having been replaced by the rank of specialist third class/specialist four) when squad leaders again became staff sergeants with two sergeants/fire teams per squad. In the 1960s the only corporals found in divisions with assistant gunners in field artillery howitzer crews and Pathfinders (tactical air traffic controllers) in aviation battalions.

text: United States Marine Corps[edit]

text: Corporal is the fourth enlisted rank in the U.S. Marine Corps,[12] ranking immediately above lance corporal and immediately below sergeant. The Marine Corps, unlike the Army, has no other rank at the pay grade of E-4. Corporal is the lowest grade of non-commissioned officer in the U.S. Marine Corps, though promotion to corporal traditionally confers a significant jump in authority and responsibility compared to promotion from private through lance corporal. Marine infantry corporals generally serve as "fire-team leaders", leading a four-man team or weapons crew of similar size (e.g., assault weapons squad, medium machine gun team, or LWCMS mortar squad).

text: In practice, however, the billet of fire team leader is generally held by a lance corporal, while corporals serve in the squad leader billet that would normally be held by a sergeant (E-5) in infantry units. In support units, corporals generally serve in "journeyman" level roles in which they direct the activities of junior Marines and provide technical supervision, on a very limited scope, under the direct supervision of a sergeant or SNCO.

text: Due to its emphasis on small-unit tactics, its infantry-centric ethos, and its tradition of empowering junior NCOs to exercise first-level leadership, the U.S. Marine Corps' Tables of Organization (TOs) usually places corporals (as well as sergeants and staff sergeants) in billets where other services would normally have higher ranking NCOs in authority. For example, the USMC Table of Organization "billet" rank for rifle fire team leader, rifle squad leader, and rifle platoon sergeant is corporal (E-4), sergeant (E-5), and staff sergeant (E-6), respectively. However, the same positions (Table of Organization and Equipment "slots") in US Army infantry units are one grade higher and, except in fire teams (both services with four men in each team), the equivalent Army units are smaller (viz., USMC rifle squad and rifle platoon - 13 men and 43 men, respectively, vice US Army rifle squad and rifle platoon - 9 men and 34 men, respectively). Specifically, for the Army rifle units, the rank of the fire team, squad leader, and platoon sergeant are: sergeant (E-5), staff sergeant (E-6), and sergeant first class (E-7), respectively.[13] Similarly, the term "strategic corporal" refers to the special responsibilities conferred upon a Marine corporal over against the normal responsibilities, and usual authority, of service members in the grade of E-4 in the other branches of the U.S. Armed Forces.[14]

text: Until the mid-to-late 1980s, corporals were the lowest USMC rank eligible for selection as a drill instructor for USMC recruit training.

text: The history of the rank of corporal in the USMC roughly parallels that of the U.S. Army until 1942. From 1775 until WWII, the Marine Corps used essentially the same rank and organizational structure as its common British and colonial forebears with the Army, as well as the later Continental and U.S. armies. In 1942, as the Army modified its triangular division infantry organization to best fight in the European/North African/Middle Eastern Theatre the Marine Corps began modifying the triangular division plan to best employ its amphibious warfare doctrine in the Pacific Theatre. This meant that for the Corps, squad leaders would remain as sergeants and that the rifle squad would be sub-divided into three four-man fire teams each led by a corporal.

text:
showvteUnited States enlisted ranks

Pay grade →Branch of service ↓

E-1

E-2

E-3

E-4

E-5

E-6

E-7

E-8

E-9

Army

PVT

PV2

PFC

 SPC – CPL

SGT

SSG

SFC

 MSG – 1SG

  SGM – CSM – SMA

Marine Corps

Pvt

PFC

LCpl

Cpl

Sgt

SSgt

GySgt

 MSgt – 1stSgt

  MGySgt – SgtMaj – SgtMajMarCor

Navy

SR

SA

SN

PO3

PO2

PO1

CPO

 SCPO – CMDCS

   MCPO – CMDCM – FORCM, FLTCM – MCPON

Air Force

AB

Amn

A1C

SrA

SSgt

TSgt

 MSgt – 1st Sgt

 SMSgt – 1st Sgt

   CMSgt – 1st Sgt – CCM – CMSAF

Coast Guard

SR

SA

SN

PO3

PO2

PO1

CPO

SCPO

   MCPO – CMC – Area CMC, CGRF-CMC – MCPOCG

text: Vietnam[edit]

text: In the Vietnam People's Army, corporal (Hạ sĩ) is the lowest rank in non-commissioned officer. Corporal is below sergeant and above private 2nd class.

text: Corporal in navies[edit]

text: In some navies, a "ship's corporal" is a position used in place of a leading seaman.


document_title: GPS signals

question_text: the encrypted version of the p code is the

question_tokens: the encrypted version of the p code is the

text: GPS signals

text: Common characteristics[edit]

text: The GPS satellites (called space vehicles in the GPS interface specification documents) transmit simultaneously several ranging codes and navigation data using binary phase-shift keying (BPSK). Only a limited number of central frequencies are used; satellites using the same frequency are distinguished by using different ranging codes; in other words, GPS uses code division multiple access. The ranging codes are also called chipping codes (in reference to CDMA/DSSS), pseudorandom noise and pseudorandom binary sequences (in reference to the fact that it is predictable, but statistically it resembles noise).

text: Some satellites transmit several BPSK streams at the same frequency in quadrature, in a form of quadrature amplitude modulation. However, unlike typical QAM systems where a single bit stream is split in two half-symbol-rate bit streams to improve spectral efficiency, in GPS signals the in-phase and quadrature components are modulated by separate (but functionally related) bit streams.

text: Satellites are uniquely identified by a serial number called space vehicle number (SVN) which does not change during its lifetime. In addition, all operating satellites are numbered with a space vehicle identifier (SV ID) and pseudorandom noise number (PRN number) which uniquely identifies the ranging codes that a satellite uses. There is a fixed one-to-one correspondence between SV identifiers and PRN numbers described in the interface specification.[3] Unlike SVNs, the SV ID/PRN number of a satellite may be changed (also changing the ranging codes it uses). At any point in time, any SV ID/PRN number is in use by at most a single satellite. A single SV ID/PRN number may have been used by several satellites at different points in time and a single satellite may have used different SV ID/PRN numbers at different points in time. The current SVNs and PRN numbers for the GPS constellation may be found at NAVCEN.

text: Legacy GPS signals[edit]

text: The original GPS design contains two ranging codes: the coarse/acquisition (C/A) code, which is freely available to the public, and the restricted precision (P) code, usually reserved for military applications.

text: Coarse/acquisition code[edit]

text: The C/A PRN codes are Gold codes with a period of 1,023 chips transmitted at 1.023 Mbit/s, implying a period of 1 ms. They are combined with a navigation message using exclusive or and the resulting bit stream is used for modulation as previously described. These codes only match up, or strongly autocorrelate when they are almost exactly aligned. Each satellite uses a unique PRN code, which does not correlate well with any other satellite's PRN code. In other words, the PRN codes are highly orthogonal to one another.

text: The C/A codes are generated by combining (using "exclusive or") 2 bit streams generated by maximal period 10 stage linear feedback shift registers(LFSR) . Different codes are obtained by selectively delaying one of those bit streams. Thus:

text: where:

text:
The arguments of the functions therein are the number of bits or chips since their epochs, starting at 0. The epoch of the LFSRs is the point at which they are at the initial state; and for the overall C/A codes it the start of any UTC second plus any integer number of milliseconds. The output of LFSRs at negative arguments is defined consistent with the period which is 1,023 chips (this provision is necessary because

B

{\displaystyle B}

 may have a negative argument using the above equation).

text: The delay for PRN numbers 34 and 37 is the same; therefore their C/A codes are identical and are not transmitted at the same time[4] (it may make one or both of those signals unusable due to mutual interference depending on the relative power levels received on each GPS receiver).

text: Precision code[edit]

text: The P-code is also a PRN; however, each satellite's P-code PRN code is 6.1871 × 1012 bits long (6,187,100,000,000 bits, ~720.213 gigabytes) and only repeats once a week (it is transmitted at 10.23 Mbit/s). The extreme length of the P-code increases its correlation gain and eliminates any range ambiguity within the Solar System. However, the code is so long and complex it was believed that a receiver could not directly acquire and synchronize with this signal alone. It was expected that the receiver would first lock onto the relatively simple C/A code and then, after obtaining the current time and approximate position, synchronize with the P-code.

text: Whereas the C/A PRNs are unique for each satellite, the P-code PRN is actually a small segment of a master P-code approximately 2.35 × 1014 bits in length (235,000,000,000,000 bits, ~26.716 terabytes) and each satellite repeatedly transmits its assigned segment of the master code.

text: To prevent unauthorized users from using or potentially interfering with the military signal through spoofing, it was decided to encrypt the P-code. To that end the P-code was modulated with the W-code, a special encryption sequence, to generate the Y-code. The Y-code is what the satellites have been transmitting since the anti-spoofing module was set to the "on" state. The encrypted signal is referred to as the P(Y)-code.

text: The details of the W-code are kept secret, but it is known that it is applied to the P-code at approximately 500 kHz,[5] which is a slower rate than that of the P-code itself by a factor of approximately 20. This has allowed companies to develop semi-codeless approaches for tracking the P(Y) signal, without knowledge of the W-code itself.

text: Navigation message[edit]

text:
GPS message format

Subframe no.
Word no.
Description

1
1–2
Telemetry and handover words
(TLM and HOW)

3–10
Satellite clock,
GPS time relationship

2–3
1–2
Telemetry and handover words
(TLM and HOW)

3–10
Ephemeris
(precise satellite orbit)

4–5
1–2
Telemetry and handover words
(TLM and HOW)

3–10
Almanac component
(satellite network synopsis,
error correction)

text: In addition to the PRN ranging codes, a receiver needs to know detailed information about each satellite's position and the network. The GPS design has this information modulated on top of both the C/A and P(Y) ranging codes at 50 bit/s and calls it the navigation message. The navigation message format described in this section is called LNAV data (for legacy navigation).

text: The navigation message conveys information which can be classified in 3 broad areas:

text:
The GPS date and time, plus the satellite's status and an indication of its health.
The ephemeris: orbital information which allows the receiver to calculate the position of the satellite. Each satellite transmits its own ephemeris.
The almanac data: contains information and status concerning all the satellites; each satellite transmits almanac data for several (possibly all) satellites, depending on which PRN numbers are in use.

text: Whereas ephemeris information is highly detailed and considered valid for no more than four hours, almanac information is more general and is considered valid for up to 180 days.[citation needed] The almanac assists the receiver in determining which satellites to search for, and once the receiver picks up each satellite's signal in turn, it then downloads the ephemeris data directly from that satellite. A position fix using any satellite can not be calculated until the receiver has an accurate and complete copy of that satellite's ephemeris data. If the signal from a satellite is lost while its ephemeris data is being acquired, the receiver must discard that data and start again.

text: The navigation message consists of 1,500 bit long frames. Each frame consists of 5 subframes of 300 bits, numbered 1 to 5. In turn each subframe consists of 10 words of 30 bit each and requires 6 seconds to transmit. Each subframe has the GPS time. Subframe 1 contains the GPS date (week number) and information to correct the satellite's time to GPS time, plus satellite status and health. Subframes 2 and 3 together contain the transmitting satellite's ephemeris data. Subframes 4 and 5 contain components of the almanac but each frame contains only 1/25th of the complete almanac; a receiver must process 25 whole frames worth of data to retrieve the entire 15,000 bit almanac message. At this rate, 12.5 minutes are required to receive the entire almanac from a single satellite. Each of the 25 versions of frames 4 and 5 is called a page and they are numbered 1 to 25.

text: Frames begin and end at the start/end of week plus an integer multiple of 30 seconds. At start/end of week the cycling between pages is reset to page 1.[6]

text: There are 2 navigation message types: LNAV-L is used by satellites with PRN numbers 1 to 32 (called lower PRN numbers) and LNAV-U is used by satellites with PRN numbers 33 to 63 (called upper PRN numbers).[7] The 2 types use very similar formats. Subframes 1 to 3 are the same[8] while subframes 4 and 5 use almost the same format. Both message types contain almanac data for all satellites using the same navigation message type, but not the other type.

text: Each subframe begins with a Telemetry Word (TLM), which enables the receiver to detect the beginning of a subframe and determine the receiver clock time at which the navigation subframe begins. The next word is the handover word (HOW), which gives the GPS time (actually the time when the first bit of the next subframe will be transmitted) and identifies the specific subframe within a complete frame.[9][10] The remaining eight words of the subframe contain the actual data specific to that subframe. Each word includes 6 bits of parity generated using an algorithm based on Hamming codes, which take into account the 24 non-parity bits of that word and the last 2 bits of the previous word.

text: After a subframe has been read and interpreted, the time the next subframe was sent can be calculated through the use of the clock correction data and the HOW. The receiver knows the receiver clock time of when the beginning of the next subframe was received from detection of the Telemetry Word thereby enabling computation of the transit time and thus the pseudorange. The receiver is potentially capable of getting a new pseudorange measurement at the beginning of each subframe or every 6 seconds.[citation needed]

text: Time[edit]

text: GPS time is expressed with a resolution of 1.5 seconds as a week number and a time of week count (TOW).[11] Its zero point (week 0, TOW 0) is defined to be 1980-01-06T00:00Z. The TOW count is a value ranging from 0 to 403,199 whose meaning is the number of 1.5 second periods elapsed since the beginning of the GPS week. Expressing TOW count thus requires 19 bits (219 = 524,288). GPS time is a continuous time scale in that it does not include leap seconds; therefore the start/end of GPS weeks may differ from that of the corresponding UTC day by an integer number of seconds.

text: In each subframe, each hand-over word (HOW) contains the most significant 17 bits of the TOW count corresponding to the start of the next following subframe.[12] Note that the 2 least significant bits can be safely omitted because one HOW occurs in the navigation message every 6 seconds, which is equal to the resolution of the truncated TOW count thereof. Equivalently, the truncated TOW count is the time duration since the last GPS week start/end to the beginning of the next frame in units of 6 seconds.

text: Each frame contains (in subframe 1) the 10 least significant bits of the corresponding GPS week number.[13] Note that each frame is entirely within one GPS week because GPS frames do not cross GPS week boundaries.[14] Since rollover occurs every 1,024 GPS weeks (approximately every 19.6 years; 1,024 is 210), a receiver that computes current calendar dates needs to deduce the upper week number bits or obtain them from a different source. One possible method is for the receiver to save its current date in memory when shut down, and when powered on, assume that the newly decoded truncated week number corresponds to the period of 1,024 weeks that starts at the last saved date. This method correctly deduces the full week number if the receiver is never allowed to remain shut down (or without a time and position fix) for more than 1,024 weeks (~19.6 years).

text: Almanac[edit]

text: The almanac consists of coarse orbit and status information for each satellite in the constellation, an ionospheric model, and information to relate GPS derived time to Coordinated Universal Time (UTC). Each frame contains a part of the almanac (in subframes 4 and 5) and the complete almanac is transmitted by each satellite in 25 frames total (requiring 12.5 minutes).[15] The almanac serves several purposes. The first is to assist in the acquisition of satellites at power-up by allowing the receiver to generate a list of visible satellites based on stored position and time, while an ephemeris from each satellite is needed to compute position fixes using that satellite. In older hardware, lack of an almanac in a new receiver would cause long delays before providing a valid position, because the search for each satellite was a slow process. Advances in hardware have made the acquisition process much faster, so not having an almanac is no longer an issue. The second purpose is for relating time derived from the GPS (called GPS time) to the international time standard of UTC. Finally, the almanac allows a single-frequency receiver to correct for ionospheric delay error by using a global ionospheric model. The corrections are not as accurate as GNSS augmentation systems like WAAS or dual-frequency receivers. However, it is often better than no correction, since ionospheric error is the largest error source for a single-frequency GPS receiver.

text: Structure of subframes 4 and 5[edit]

text:
LNAV-L frames 4 and 5[16]

Subframe no.
Page no.
Description

4
1–2, 6, 11–12,
16, 19–24
Reserved

2–5, 7–10
Almanac data for SV 25–32

13
Navigation message
correction table (NMCT)

14–15
Reserved for system use

17
Special messages

18
Ionospheric correction data
and UTC

25
A-S flags for SV 1–32,
health info. for SV 25–32

5
1–24
Almanac data for SV 1–24

25
Health info. for SV 1–24
almanac reference time

LNAV-U frames 4 and 5[17]

Subframe no.
Page no.
Description

4
1, 6, 10–12,
16, 19–24
Reserved

2–5, 7–9
Almanac data for SV 89–95

13
Navigation message
correction table (NMCT)

14–15
Reserved for system use

17
Special messages

18
Ionospheric correction data
and UTC

25
A-S flags for PRN numbers 33–63,
health info. for SV 89–95

5
1–24
Almanac data for SV 65–88

25
Health info. for SV 65–88
almanac reference time

text: Data updates[edit]

text: Satellite data is updated typically every 24 hours, with up to 60 days data loaded in case there is a disruption in the ability to make updates regularly. Typically the updates contain new ephemerides, with new almanacs uploaded less frequently. The Control Segment guarantees that during normal operations a new almanac will be uploaded at least every 6 days.

text: Satellites broadcast a new ephemeris every two hours. The ephemeris is generally valid for 4 hours, with provisions for updates every 4 hours or longer in non-nominal conditions. The time needed to acquire the ephemeris is becoming a significant element of the delay to first position fix, because as the receiver hardware becomes more capable, the time to lock onto the satellite signals shrinks; however, the ephemeris data requires 18 to 36 seconds before it is received, due to the low data transmission rate.

text: Frequency information[edit]

text: For the ranging codes and navigation message to travel from the satellite to the receiver, they must be modulated onto a carrier wave. In the case of the original GPS design, two frequencies are utilized; one at 1575.42 MHz (10.23 MHz × 154) called L1; and a second at 1227.60 MHz (10.23 MHz × 120), called L2.

text: The C/A code is transmitted on the L1 frequency as a 1.023 MHz signal using a bi-phase shift keying (BPSK) modulation technique. The P(Y)-code is transmitted on both the L1 and L2 frequencies as a 10.23 MHz signal using the same BPSK modulation, however the P(Y)-code carrier is in quadrature with the C/A carrier (meaning it is 90° out of phase).

text: Besides redundancy and increased resistance to jamming, a critical benefit of having two frequencies transmitted from one satellite is the ability to measure directly, and therefore remove, the ionospheric delay error for that satellite. Without such a measurement, a GPS receiver must use a generic model or receive ionospheric corrections from another source (such as the Wide Area Augmentation System or WAAS). Advances in the technology used on both the GPS satellites and the GPS receivers has made ionospheric delay the largest remaining source of error in the signal. A receiver capable of performing this measurement can be significantly more accurate and is typically referred to as a dual frequency receiver.

text: Modernization and additional GPS signals[edit]

text: Having reached full operational capability on July 17, 1995[18] the GPS system had completed its original design goals. However, additional advances in technology and new demands on the existing system led to the effort to "modernize" the GPS system. Announcements from the Vice President and the White House in 1998 heralded the beginning of these changes and in 2000, the U.S. Congress reaffirmed the effort, referred to as GPS III.

text: The project involves new ground stations and new satellites, with additional navigation signals for both civilian and military users, and aims to improve the accuracy and availability for all users. A goal of 2013 has been established with incentives offered to the contractors if they can complete it by 2011.[needs update]

text: General features[edit]

text: Modernized GPS civilian signals have two general improvements over their legacy counterparts: a dataless acquisition aid and forward error correction (FEC) coding of the NAV message.

text: A dataless acquisition aid is an additional signal, called a pilot carrier in some cases, broadcast alongside the data signal. This dataless signal is designed to be easier to acquire than the data encoded and, upon successful acquisition, can be used to acquire the data signal. This technique improves acquisition of the GPS signal and boosts power levels at the correlator.

text: The second advancement is to use forward error correction (FEC) coding on the NAV message itself. Due to the relatively slow transmission rate of NAV data (usually 50 bits per second), small interruptions can have potentially large impacts. Therefore, FEC on the NAV message is a significant improvement in overall signal robustness.

text: One of the first announcements was the addition of a new civilian-use signal, to be transmitted on a frequency other than the L1 frequency used for the coarse/acquisition (C/A) signal. Ultimately, this became the L2C signal, so called because it is broadcast on the L2 frequency. Because it requires new hardware on board the satellite, it is only transmitted by the so-called Block IIR-M and later design satellites. The L2C signal is tasked with improving accuracy of navigation, providing an easy to track signal, and acting as a redundant signal in case of localized interference.

text: Unlike the C/A code, L2C contains two distinct PRN code sequences to provide ranging information; the civil-moderate code (called CM), and the civil-long length code (called CL). The CM code is 10,230 bits long, repeating every 20 ms. The CL code is 767,250 bits long, repeating every 1,500 ms. Each signal is transmitted at 511,500 bits per second (bit/s); however, they are multiplexed together to form a 1,023,000 bit/s signal.

text: CM is modulated with the CNAV Navigation Message (see below), whereas CL does not contain any modulated data and is called a dataless sequence. The long, dataless sequence provides for approximately 24 dB greater correlation (~250 times stronger) than L1 C/A-code.

text: When compared to the C/A signal, L2C has 2.7 dB greater data recovery and 0.7 dB greater carrier-tracking, although its transmission power is 2.3 dB weaker.

text: CM and CL codes[edit]

text: The civil-moderate and civil-long ranging codes are generated by a modular LFSR which is reset periodically to a predetermined initial state. The period of the CM and CL is determined by this resetting and not by the natural period of the LFSR (as is the case with the C/A code). The initial states are designated in the interface specification and are different for different PRN numbers and for CM/CL. The feedback polynomial/mask is the same for CM and CL. The ranging codes are thus given by:

text: where:

text: The initial states are described in the GPS interface specification as numbers expressed in octal following the convention that the LFSR state is interpreted as the binary representation of a number where the output bit is the least significant bit, and the bit where new bits are shifted in is the most significant bit. Using this convention, the LFSR shifts from most significant bit to least significant bit and when seen in big endian order, it shifts to the right. The states called final state in the IS are obtained after 7004102290000000000♠10229 cycles for CM and after 7005767249000000000♠767249 cycles for LM (just before reset in both cases).

text: The feedback bit mask is 1001001010010010101001111002. Again with the convention that the least significant bit is the output bit of the LFSR and the most significant bit is the shift-in bit of the LFSR, 0 means no feedback into that position, and 1 means feedback into that position.

text: CNAV, navigation message[edit]

text:
Message structure
(common fields)[19]

Bits[20]
Information

1–8
Preamble

9–14
PRN of transmitting satellite

15–20
Message type ID

21–37
Truncated TOW count[21]

38
Alert flag

277–300
Cyclic redundancy check

text:
Message types

Type ID
Description

10–11
Ephemeris and health

12, 31, 37
Almanac parameters

13–14, 34
Differential correction

15, 36
Text messages

30
Ionospheric and group delay correction

32
Earth orientation parameters

33
UTC parameters

35
GPS/GNSS time offset

text: The CNAV data is an upgraded version of the original NAV navigation message. It contains higher precision representation and nominally more accurate data than the NAV data. The same type of information (time, status, ephemeris, and almanac) is still transmitted using the new CNAV format; however, instead of using a frame / subframe architecture, it uses a new pseudo-packetized format made of 12-second 300-bit messages analogous to LNAV frames. While LNAV frames have a fixed information content, CNAV messages may be of one of several defined types. The type of a frame determines its information content. Messages do not follow a fixed schedule regarding which message types will be used, allowing the Control Segment some versatility. However, for some message types there are lower bounds on how often they will be transmitted.

text: In CNAV, at least 1 out of every 4 packets are ephemeris data and the same lower bound applies for clock data packets.[22] The design allows for a wide variety of packet types to be transmitted. With a 32-satellite constellation, and the current requirements of what needs to be sent, less than 75% of the bandwidth is used. Only a small fraction of the available packet types have been defined; this enables the system to grow and incorporate advances without breaking compatibility.

text: There are many important changes in the new CNAV message:

text:
It uses forward error correction (FEC) provided by a rate 1/2 convolutional code, so while the navigation message is 25 bit/s, a 50 bit/s signal is transmitted.
Messages carry a 24 bit CRC, against which integrity can be checked.
The GPS week number is now represented as 13 bits, or 8192 weeks, and only repeats every 157.0 years, meaning the next return to zero won't occur until the year 2137. This is longer compared to the L1 NAV message's use of a 10-bit week number, which returns to zero every 19.6 years.
There is a packet that contains a GPS-to-GNSS time offset. This allows better interoperability with other global time-transfer systems, such as Galileo and GLONASS, both of which are supported.
The extra bandwidth enables the inclusion of a packet for differential correction, to be used in a similar manner to satellite based augmentation systems and which can be used to correct the L1 NAV clock data.
Every packet contains an alert flag, to be set if the satellite data can not be trusted. This means users will know within 12 seconds if a satellite is no longer usable. Such rapid notification is important for safety-of-life applications, such as aviation.
Finally, the system is designed to support 63 satellites, compared with 32 in the L1 NAV message.

text: CNAV messages begin and end at start/end of GPS week plus an integer multiple of 12 seconds.[23] Specifically, the beginning of the first bit (with convolution encoding already applied) to contain information about a message matches the aforesaid synchronization. CNAV messages begin with a 8 bit preamble which is a fixed bit pattern and whose purpose is to enables the receiver to detect the beginning of a message.

text: Forward error correction code[edit]

text: The convolutional code used to encode CNAV is described by:

text: where:

text:
Since the FEC encoded bit stream runs at 2 times the rate than the non FEC encoded bit as already described, then

t
=

⌊

t
′

2

⌋

{\displaystyle t=\left\lfloor {\tfrac {t'}{2}}\right\rfloor }

. FEC encoding is performed independently of navigation message boundaries;[24] this follows from the above equations.

text: L2C frequency information[edit]

text: An immediate effect of having two civilian frequencies being transmitted is the civilian receivers can now directly measure the ionospheric error in the same way as dual frequency P(Y)-code receivers. However, users utilizing the L2C signal alone, can expect 65% more position uncertainty due to ionospheric error than with the L1 signal alone.[25]

text: Military (M-code)[edit]

text: A major component of the modernization process is a new military signal. Called the Military code, or M-code, it was designed to further improve the anti-jamming and secure access of the military GPS signals.

text: Very little has been published about this new, restricted code. It contains a PRN code of unknown length transmitted at 5.115 MHz. Unlike the P(Y)-code, the M-code is designed to be autonomous, meaning that a user can calculate their position using only the M-code signal. From the P(Y)-code's original design, users had to first lock onto the C/A code and then transfer the lock to the P(Y)-code. Later, direct-acquisition techniques were developed that allowed some users to operate autonomously with the P(Y)-code.

text: MNAV, navigation message[edit]

text: A little more is known about the new navigation message, which is called MNAV. Similar to the new CNAV, this new MNAV is packeted instead of framed, allowing for very flexible data payloads. Also like CNAV it can utilize Forward Error Correction (FEC) and advanced error detection (such as a CRC).

text: M-code frequency information[edit]

text: The M-code is transmitted in the same L1 and L2 frequencies already in use by the previous military code, the P(Y)-code. The new signal is shaped to place most of its energy at the edges (away from the existing P(Y) and C/A carriers).

text: In a major departure from previous GPS designs, the M-code is intended to be broadcast from a high-gain directional antenna, in addition to a full-Earth antenna. This directional antenna's signal, called a spot beam, is intended to be aimed at a specific region (several hundred kilometers in diameter) and increase the local signal strength by 20 dB, or approximately 100 times stronger. A side effect of having two antennas is that the GPS satellite will appear to be two GPS satellites occupying the same position to those inside the spot beam. While the whole Earth M-code signal is available on the Block IIR-M satellites, the spot beam antennas will not be deployed until the Block III satellites are deployed, tentatively in 2018.

text: An interesting side effect of having each satellite transmit four separate signals is that the MNAV can potentially transmit four different data channels, offering increased data bandwidth.

text: The modulation method is binary offset carrier, using a 10.23 MHz subcarrier against the 5.115 MHz code. This signal will have an overall bandwidth of approximately 24 MHz, with significantly separated sideband lobes. The sidebands can be used to improve signal reception.

text: L5, safety of life[edit]

text: The L5 signal provides a means of radionavigation secure and robust enough for life critical applications, such as aircraft precision approach guidance. The signal is broadcast in a frequency band protected by the ITU for aeronautical radionavigation services. It was first demonstrated from satellite USA-203 (Block IIR-M), and is available on all satellites from GPS IIF. The L5 band provides additional robustness in the form of interference mitigation, the band being internationally protected, redundancy with existing bands, geostationary satellite augmentation, and ground based augmentation. The added robustness of this band also benefits terrestrial applications.[26]

text: Two PRN ranging codes are transmitted on L5 in quadrature: the in-phase code (called I5-code) and the quadrature-phase code (called Q5-code). Both codes are 10,230 bits long, transmitted at 10.23 MHz (1 ms repetition period), and are generated identically (differing only in initial states). Then, I5 is modulated (by exclusive-or) with navigation data (called L5 CNAV) and a 10-bit Neuman-Hoffman code clocked at 1 kHz. Similarly, the Q5-code is then modulated but with only a 20-bit Neuman-Hoffman code that is also clocked at 1 kHz.

text: Compared to L1 C/A and L2, these are some of the changes in L5:

text:
Improved signal structure for enhanced performance
Higher transmitted power than L1/L2 signal (~3 dB, or 2× as powerful)
Wider bandwidth provides a 10× processing gain, provides sharper autocorrelation (in absolute terms, not relative to chip time duration) and requires a higher sampling rate at the receiver.
Longer spreading codes (10× longer than C/A)
Uses the Aeronautical Radionavigation Services band

text: I5 and Q5 codes[edit]

text: The I5-code and Q5-code are generated using the same structure but with different parameters. These codes are the combination (by exclusive-or) of the output of 2 differing linear-feedback shift registers (LFSRs) which are selectively reset.

text: where:

text:
A

{\displaystyle A}

 and

B

{\displaystyle B}

 are maximal length LFSRs. The modulo operations correspond to resets. Note that both are reset each millisecond (synchronized with C/A code epochs). In addition, the extra modulo operation in the description of

A

{\displaystyle A}

 is due to the fact it is reset 1 cycle before its natural period (which is 8,191) so that the next repetition becomes offset by 1 cycle with respect to

B

{\displaystyle B}

[28] (otherwise, since both sequences would repeat, I5 and Q5 would repeat within any 1 ms period as well, degrading correlation characteristics).

text: L5 navigation message[edit]

text: The L5 CNAV data includes SV ephemerides, system time, SV clock behavior data, status messages and time information, etc. The 50 bit/s data is coded in a rate 1/2 convolution coder. The resulting 100 symbols per second (sps) symbol stream is modulo-2 added to the I5-code only; the resultant bit-train is used to modulate the L5 in-phase (I5) carrier. This combined signal is called the L5 Data signal. The L5 quadrature-phase (Q5) carrier has no data and is called the L5 Pilot signal. The format used for L5 CNAV is very similar to that of L2 CNAV. One difference is that it uses 2 times the data rate. The bit fields within each message,[29] message types, and forward error correction code algorithm are the same as those of L2 CNAV. L5 CNAV messages begin and end at start/end of GPS week plus an integer multiple of 6 seconds (this applies to the beginning of the first bit to contain information about a message, as is the case for L2 CNAV).[30]

text: L5 frequency information[edit]

text: Broadcast on the L5 frequency (1176.45 MHz, 10.23 MHz × 115), which is an aeronautical navigation band. The frequency was chosen so that the aviation community can manage interference to L5 more effectively than L2.[31]

text: L1C is a civilian-use signal, to be broadcast on the L1 frequency (1575.42 MHz), which contains the C/A signal used by all current GPS users. The L1C will be available with the first Block III launch, tentatively scheduled for the first half of fiscal year 2017.[32]

text: L1C consists of a pilot (called L1CP) and a data (called L1CD) component.[33] These components use carriers with the same phase (within a margin of error of 100 milliradians), instead of carriers in quadrature as with L5.[34] The PRN codes are 10,230 bits long and transmitted at 1.023 Mbit/s. The pilot component is also modulated by an overlay code called L1CO (a secondary code that has a lower rate than the ranging code and is also predefined, like the ranging code).[33] Of the total L1C signal power, 25% is allocated to the data and 75% to the pilot. The modulation technique used is BOC(1,1) for the data signal and TMBOC for the pilot. The time multiplexed binary offset carrier (TMBOC) is BOC(1,1) for all except 4 of 33 cycles, when it switches to BOC(6,1).

text:
Implementation will provide C/A code to ensure backward compatibility
Assured of 1.5 dB increase in minimum C/A code power to mitigate any noise floor increase
Data-less signal component pilot carrier improves tracking compared with L1 C/A
Enables greater civil interoperability with Galileo L1

text: L1C ranging code[edit]

text: The L1C pilot and data ranging codes are based on a Legendre sequence with length 7004102230000000000♠10223 used to build an intermediate code (called a Weil code) which is expanded with a fixed 7-bit sequence to the required 10,230 bits. This 10,230 bit sequence is the ranging code and varies between PRN numbers and between the pilot and data components. The ranging codes are described by:[35]

text: where:

text:
According to the formula above and the GPS IS, the first

w

i

{\displaystyle w_{i}}

 bits (equivalently, up to the insertion point of

S

{\displaystyle S}

) of

L1C

i

′

{\displaystyle {\text{L1C}}'_{i}}

 and

L1C

{\displaystyle {\text{L1C}}}

 are the first bits the corresponding Weil code; the next 7 bits are

S

{\displaystyle S}

; the remaining bits are the remaining bits of the Weil code.

text:
The IS asserts that

0
≤

p

i

′

≤
10

222

{\displaystyle 0\leq p'_{i}\leq 10\,222}

.[37] For clarity, the formula for

L1C

i

′

{\displaystyle {\text{L1C}}'_{i}}

 does not account for the hypothetical case in which

p

i

′

>
10

222

{\displaystyle p'_{i}>10\,222}

, which would cause the instance of

S

{\displaystyle S}

 inserted into

L1C

i

′

{\displaystyle {\text{L1C}}'_{i}}

 to wrap from index 7004102290000000000♠10229 to 0.

text: L1C overlay code[edit]

text: The overlay codes are 1,800 bits long and is transmitted at 100 bit/s, synchronized with the navigation message encoded in L1CD.

text: For PRN numbers 1 to 63 they are the truncated outputs of maximal period LFSRs which vary in initial conditions and feedback polynomials.[38]

text:
For PRN numbers 64 to 210 they are truncated Gold codes generated by combining 2 LFSR outputs (

S1

i

{\displaystyle {\text{S1}}_{i}}

 and

S2

i

{\displaystyle {\text{S2}}_{i}}

, where

i

{\displaystyle i}

 is the PRN number) whose initial state varies.

S1

i

{\displaystyle {\text{S1}}_{i}}

 has one of the 4 feedback polynomials used overall (among PRN numbers 64–210).

S2

i

{\displaystyle {\text{S2}}_{i}}

 has the same feedback polynomial for all PRN numbers in the range 64–210.[39]

text: CNAV-2 navigation message[edit]

text:
Subframes

Subframe
Bit count
Description

Raw
Encoded

1
9
52
Time of interval (TOI)

2
576
1,200
Time correction and
ephemeris data

3
250
548
Variable data

text:
Subframe 3 pages

Page no.
Description

1
UTC & IONO

2
GGTO & EOP

3
Reduced almanac

4
Midi almanac

5
Differential correction

6
Text

text: The L1C navigation data (called CNAV-2) is broadcast in 1,800 bits long (including FEC) frames and is transmitted at 100 bit/s.

text: The frames of L1C are analogous to the messages of L1C and L5. While L2 CNAV and L5 CNAV use a dedicated message type for ephemeris data, all CNAV-2 frames include that information.

text: The common structure of all messages consists of 3 frames, as listed in the adjacent table. The content of subframe 3 varies according to its page number which is analogous to the type number of L2 CNAV and L5 CNAV messages. Pages are broadcast in an arbitrary order.[40]

text: The time of messages (not to be confused with clock correction parameters) is expressed in a different format than the format of the previous civilian signals. Instead it consists of 3 components:

text:
The week number, with the same meaning as with the other civilian signals. Each message contains the week number modulo 8,192 or equivalently, the 13 least significant bits of the week number, allowing direct specification of any date within a cycling 157-year range.
An interval time of week (ITOW): the integer number of 2 hour periods elapsed since the latest start/end of week. It has range 0 to 83 (inclusive), requiring 7 bits to encode.
A time of interval (TOI): the integer number of 18 second periods elapsed since the period represented by the current ITOW to the beginning of the next message. It has range 0 to 399 (inclusive) and requires 9 bits of data.

tag: ol

text: TOI is the only content of subframe 1. The week number and ITOW are contained in subframe 2 along with other information.

text: Subframe 1 is encoded by a modified BCH code. Specifically, the 8 least significant bits are BCH encoded to generate 51 bits, then combined using exclusive or with the most significant bit and finally the most significant bit is appended as the most significant bit of the previous result to obtain the final 52 bits.[41] Subframes 2 and 3 are individually expanded with a 24 bit CRC, then individually encoded using a low-density parity-check code, and then interleaved as a single unit using a block interleaver.[42]

text: Overview of frequencies[edit]

text:
GPS Frequencies

Band
Frequency
(MHz)
Phase
Original usage
Modernized usage

L1
1575.42
(10.23×154)
In-phase (I)
Encrypted precision P(Y) code

Quadrature-
phase (Q)
Coarse/acquisition (C/A) code
C/A, L1 Civilian (L1C), and
Military (M) code

L2
1227.60
(10.23×120)
In-phase (I)
Encrypted precision P(Y) code

Quadrature-
phase (Q)
Unmodulated carrier
L2 Civilian (L2C) code and
Military (M) code

L3
1381.05
(10.23×135)

Used by Nuclear Detonation (NUDET)
Detection System Payload (NDS);
signals nuclear detonations/
high-energy infrared events.
Used to enforce nuclear test
ban treaties.

L4
1379.913
(10.23×1214/9)

N/A
Being studied for additional
ionospheric correction[43]:607

L5
1176.45
(10.23×115)
In-phase (I)
N/A
Safety-of-Life (SoL) Data signal

Quadrature-
phase (Q)
Safety-of-Life (SoL) Pilot signal

text: All satellites broadcast at the same two frequencies, 1.57542 GHz (L1 signal) and 1.2276 GHz (L2 signal). The satellite network uses a CDMA spread-spectrum technique where the low-bitrate message data is encoded with a high-rate pseudo-random (PRN) sequence that is different for each satellite. The receiver must be aware of the PRN codes for each satellite to reconstruct the actual message data. The C/A code, for civilian use, transmits data at 1.023 million chips per second, whereas the P code, for U.S. military use, transmits at 10.23 million chips per second. The L1 carrier is modulated by both the C/A and P codes, while the L2 carrier is only modulated by the P code.[44] The P code can be encrypted as a so-called P(Y) code which is only available to military equipment with a proper decryption key. Both the C/A and P(Y) codes impart the precise time-of-day to the user.

text: Each composite signal (in-phase and quadrature phase) becomes:

text:
where

P

I

{\displaystyle \scriptstyle P_{\operatorname {I} }}

 and

P

Q

{\displaystyle \scriptstyle P_{\operatorname {Q} }}

 represent signal powers;

X

I

(
t
)

{\displaystyle \scriptstyle X_{\operatorname {I} }(t)}

 and

X

Q

(
t
)

{\displaystyle \scriptstyle X_{\operatorname {Q} }(t)}

 represent codes with/without data

(
=

±
1
)

{\displaystyle \scriptstyle (=\;\pm 1)}

. This is a formula for the ideal case (which is not attained in practice) as it does not model timing errors, noise, amplitude mismatch between components or quadrature error (when components are not exactly in quadrature).

text: Demodulation and decoding[edit]

text: A GPS receiver processes the GPS signals received on its antenna to determine position, velocity and/or timing. The signal at antenna is amplified, down converted to baseband or intermediate frequency, filtered (to remove frequencies outside the intended frequency range for the digital signal that would alias into it) and digitalized; these steps may be chained in a different order. Note that aliasing is sometimes intentional (specifically, when undersampling is used) but filtering is still required to discard frequencies not intended to be present in the digital representation.

text: For each satellite used by the receiver, the receiver must first acquire the signal and then track it as long as that satellite is in use; both are performed in the digital domain in by far most (if not all) receivers.

text: Acquiring a signal is the process of determining the frequency and code phase (both relative to receiver time) when it was previously unknown. Code phase must be determined within an accuracy that depends on the receiver design (especially the tracking loop); 0.5 times the duration of code chips (approx. 0.489 µs) is a representative value.

text: Tracking is the process of continuously adjusting the estimated frequency and phase to match the received signal as close as possible and therefore is a phase locked loop. Note that acquisition is performed to start using a particular satellite, but tracking is performed as long as that satellite is in use.

text: In this section, one possible procedure is described for L1 C/A acquisition and tracking, but the process is very similar for the other signals. The described procedure is based on computing the correlation of the received signal with a locally generated replica of the ranging code and detecting the highest peak or lowest valley. The offset of the highest peak or lowest valley contains information about the code phase relative to receiver time. The duration of the local replica is set by receiver design and is typically shorter than the duration of navigation data bits, which is 20 ms.

text: Acquisition[edit]

text: Acquisition of a given PRN number can be conceptualized as searching for a signal in a bidimensional search space where the dimensions are (1) code phase, (2) frequency. In addition, a receiver may not know which PRN number to search for, and in that case a third dimension is added to the search space: (3) PRN number.

text: If the almanac information has previously been acquired, the receiver picks which satellites to listen for by their PRNs. If the almanac information is not in memory, the receiver enters a search mode and cycles through the PRN numbers until a lock is obtained on one of the satellites. To obtain a lock, it is necessary that there be an unobstructed line of sight from the receiver to the satellite. The receiver can then decode the almanac and determine the satellites it should listen for. As it detects each satellite's signal, it identifies it by its distinct C/A code pattern.

text: Simple correlation[edit]

text: The simplest way to acquire the signal (not necessarily the most effective or least computationally expensive) is to compute the dot product of a window of the digitalized signal with a set of locally generated replicas. The locally generated replicas vary in carrier frequency and code phase to cover all the already mentioned search space which is the Cartesian product of the frequency search space and the code phase search space. The carrier is a complex number where real and imaginary components are both sinusoids as described by Euler's formula. The replica that generates the highest magnitude of dot product is likely the one that best matches the code phase and frequency of the signal; therefore, if that magnitude is above a threshold, the receiver proceeds to track the signal or further refine the estimated parameters before tracking. The threshold is used to minimize false positives (apparently detecting a signal when there is in fact no signal), but some may still occur occasionally.

text: Using a complex carrier allows the replicas to match the digitalized signal regardless of the signal's carrier phase and to detect that phase (the principle is the same used by the Fourier transform). The dot product is a complex number; its magnitude represents the level of similarity between the replica and the signal, as with an ordinary correlation of real-valued time series. The argument of the dot product is an approximation of the corresponding carrier in the digitalized signal.

text: As an example, assume that the granularity for the search in code phase is 0.5 chips and in frequency is 500 Hz, then there are 1,023/0.5 = 2,046 code phases and 10,000 Hz/500 Hz = 20 frequencies to try for a total of 20×2,046 = 40,920 local replicas. Note that each frequency bin is centered on its interval and therefore covers 250 Hz in each direction; for example, the first bin has a carrier at −4.750 Hz and covers the interval −5,000 Hz to −4,500 Hz. Code phases are equivalent modulo 1,023 because the ranging code is periodic; for example, phase −0.5 is equivalent to phase 1,022.5.

text: The following table depicts the local replicas that would be compared against the digitalized signal in this example. "•" means a single local replica while "..." is used for elided local replicas:

text:
Carrier freq.
deviation
Code phase (in chips)

0.0
0.5
(more phases)
1,022.0
1,022.5

−4,750 Hz
•
•
...
•
•

−4,250 Hz
•
•
...
•
•

(more
frequencies)
...
...
...
...
...

4,250 Hz
•
•
...
•
•

4,750 Hz
•
•
...
•
•

text: Fourier transform[edit]

text: As an improvement over the simple correlation method, it is possible to implement the computation of dot products more efficiently with a Fourier transform. Instead of performing one dot product for each element in the Cartesian product of code and frequency, a single operation involving FFT and covering all frequencies is performed for each code phase; each such operation is more computationally expensive, but it may still be faster overall than the previous method due to the efficiency of FFT algorithms, and it recovers carrier frequency with a higher accuracy, because the frequency bins are much closely spaced in a DFT.

text: Specifically, for all code phases in the search space, the digitalized signal window is multiplied element by element with a local replica of the code (with no carrier), then processed with a discrete Fourier transform.

text: Given the previous example to be processed with this method, assume real-valued data (as opposed to complex data, which would have in-phase and quadrature components), a sampling rate of 5 MHz, a signal window of 10 ms, and an intermediate frequency of 2.5 MHz. There will be 5 MHz×10 ms = 50,000 samples in the digital signal, and therefore 25,001 frequency components ranging from 0 Hz to 2.5 MHz in steps of 100 Hz (note that the 0 Hz component is real because it is the average of a real-valued signal and the 2.5 MHz component is real as well because it is the critical frequency). Only the components (or bins) within 5 kHz of the central frequency are examined, which is the range from 2.495 MHz to 2.505 MHz, and it is covered by 51 frequency components. There are 2,046 code phases as in the previous case, thus in total 51×2,046 = 104,346 complex frequency components will be examined.

text: Circular correlation with Fourier transform[edit]

text: Likewise, as an improvement over the simple correlation method, it is possible to perform a single operation covering all code phases for each frequency bin. The operation performed for each code phase bin involves forward FFT, element-wise multiplication in the frequency domain. inverse FFT, and extra processing so that overall, it computes circular correlation instead of circular convolution. This yields more accurate code phase determination than the simple correlation method in contrast with the previous method, which yields more accurate carrier frequency determination than the previous method.

text: Tracking and navigation message decoding[edit]

text: Since the carrier frequency received can vary due to Doppler shift, the points where received PRN sequences begin may not differ from O by an exact integral number of milliseconds. Because of this, carrier frequency tracking along with PRN code tracking are used to determine when the received satellite's PRN code begins.[45] Unlike the earlier computation of offset in which trials of all 1,023 offsets could potentially be required, the tracking to maintain lock usually requires shifting of half a pulse width or less. To perform this tracking, the receiver observes two quantities, phase error and received frequency offset. The correlation of the received PRN code with respect to the receiver generated PRN code is computed to determine if the bits of the two signals are misaligned. Comparisons of the received PRN code with receiver generated PRN code shifted half a pulse width early and half a pulse width late are used to estimate adjustment required.[46] The amount of adjustment required for maximum correlation is used in estimating phase error. Received frequency offset from the frequency generated by the receiver provides an estimate of phase rate error. The command for the frequency generator and any further PRN code shifting required are computed as a function of the phase error and the phase rate error in accordance with the control law used. The Doppler velocity is computed as a function of the frequency offset from the carrier nominal frequency. The Doppler velocity is the velocity component along the line of sight of the receiver relative to the satellite.

text: As the receiver continues to read successive PRN sequences, it will encounter a sudden change in the phase of the 1,023 bit received PRN signal. This indicates the beginning of a data bit of the navigation message.[47] This enables the receiver to begin reading the 20 millisecond bits of the navigation message. The TLM word at the beginning of each subframe of a navigation frame enables the receiver to detect the beginning of a subframe and determine the receiver clock time at which the navigation subframe begins. The HOW word then enables the receiver to determine which specific subframe is being transmitted.[9][10] There can be a delay of up to 30 seconds before the first estimate of position because of the need to read the ephemeris data before computing the intersections of sphere surfaces.

text: Then the orbital position data, or ephemeris, from the navigation message is used to calculate precisely where the satellite was at the start of the message. A more sensitive receiver will potentially acquire the ephemeris data more quickly than a less sensitive receiver, especially in a noisy environment.[48]