Gps

 

Three Segments of the GPS Segmen egmentt Space S

User Segmen Segmentt Contr on trol ol Segme gm ent Ground  Antennas Master Station

Monitor Stations

 

Space Segment • 24+ satellites  – 6 planes with 55° inclination  – Each plane has 4-5 satellites  – Broadcasting position and time info on 2 frequencies  – Constellation has spares

 

Space Segment • Very high orbit  – 20,200 km  – 1 revolution in approximately 12 hrs  – Travel approx. 7,000mph

• Considerations  – Accuracy  – Survivability  – Coverage

 

User Segment



Military.

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Search and rescue.

 

Disaster relief. Surveying.

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Marine, aeronautical and terrestrial navigation.

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Remote controlled vehicle and robot guidance. Satellite positioning and tracking.

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Shipping.

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Geographic Information Systems (GIS). Recreation.

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GPS Signal Requirements • Meth Method od (c (cod ode) e) to id iden enti tify fy ea each ch sa sate tellllit ite e • The The lloc ocat atio ion no off tthe he sa sate tellllit ite e or or so some me information on how to determine it • Info Inform rmat atio ion n re rega gard rdin ing g tthe he a amo moun untt of time time elapsed since the signal left the satellite • Deta Detailils s on the the sa sate tellllit ite e cloc clock k st stat atus us

 

Important Issues to Consider  • Meth Method ods s tto oe enc ncod ode e iinf nfor orma mati tion on • Signal power  • Frequency allo loc cation • Security • Numb Number er an and d ttyp ype eo off co code des s nec neces essa sary ry to satisfy system requirements

 

Overview of Satellite Transmissions • All All ttra rans nsmi miss ssio ions ns de deri rive ve fr from om a fundamental frequency of 10.23 Mhz  – L1 = 154 • 10.23 = 1575.42 Mhz  – L2 = 120 • 10.23 = 1227.60 Mhz

• All All co code des s iini niti tial aliz ized ed o onc nce e pe perr G GPS PS we week ek at midnight from Saturday to Sunday  – Chipping rate for C/A is 1.023 Mhz  – Chipping rate for P(Y) is 10.23 Mhz

 

Schematic of GPS codes and carrier phase

 

GPS Signal Characteristics

 

Codes on L1 and L2 )cos(2π  f  t ) +   AcG P (t ) D P (t )sin(2π  )sin(2π  f  t ) S  p (t ) =   A p P  p (t ) D P (t )cos(2π  1

where

1

 A p , Ac   =  am  amp pli litu tude dess (po (powe wer) r) of P(Y P(Y)) - cod code aand nd C / A - code code P P (t ) =  pse  pseud udor oran ando dom m P(Y) P(Y) - code code P G ( t ) =  C / A - code (Gold code)  D P ( t ) =  navigation data stream

and

)cos(2π  f 2 t ) S 2 p (t ) =   B p P  p (t ) D P (t )cos(2π 

1

 

 p

P

Codes onP L1 and L2 (con’t.) P

P (t ) D ( t ) an and d G ( t ) D (t ) im impl ply y mod modul ulo o - 2 ad addit ditio ion n

and an d th thee P( P(Y) Y) - co code de iiss al also so a mo modu dulo lo - 2 su sum m of tw two o  pseudorandom data streams:  p

P (t ) =   X 1 (t ) X 2 (t  −   pT ) 0 ≤   p ≤ 36 1 T   = 10.23 Mhz

The GPS system defines 36 specific phase shifts to be used, resulting in 36 unique codes (called Gold Codes) that could be trans transmitted mitted by satellites. satellites. Since the satellite number is represented in the navigation message by only 5 data bits, only 32 of these 36 codes are actually used. The othe others rs are reserved for othe otherr uses, such as ground transmitters.

 

GP GPS S sign signal al str streng ength th - fre freque quenc ncy y domain  Note that C/A code code is below nois noisee level; signal is multiplied in the Receiver by the internally calculated code to allow tracking. C/A-code chip is 1.023 Mhz P-code chip is 10.23 Mhz

Power = P(t) = y2(t) 1

Bandwidth ≡   B ≈ T  where T   ≡  is chip duration

The calculated power spectrum derives from the Fourier transform of a square wave of width 2π and unit amplitude. Common function in DSP called calle d th thee ““sinc sinc”” funct function. ion.

sin c( x ) =

sin(π  x ) sin(π    π  x

π 

=

1 iω  x   e ∂ω  2π  −π 

∫

 

Schematic of C/A-code acquisition

Since C/A-code is 1023 chips long and repeats every 1/1000 s, it is inherently ambiguous by 1 msec or ~300 km. km. Must modulo-2 add add the transmitted and received codes after correlation to increase SNR and narrow bandwidth.

 

Terminology of GPS

• SPS(Standar ndard d Position oniing Se Servi rvice)  – GPS positioning service based on the single frequency C/A code

• PPS(P (Pre rec cise Pos osiitioning Service)  – GPS positioning service based on the dual frequency P code

• P eudtime orashift ngerequired to align a replica of the  –sThe GPS code generated in the receiver with the received GPS code, scaled into distance by the speed of light

 

Determining Range • Rece Receiv iver er an and d sa sate tellllit ite e use use same same cod code e • Sync Synchr hron oniz ized ed co code de ge gene nera rati tion on • Comp Compar are e iinc ncom omin ing g co code de wi with th re rece ceiv iver er generated code Measure time difference between the same part of code

Series of ones and zeroes repeating every 1023 bits. So Complicated alternation of bits that pattern looks random thus called “pseudorandom code”.

From satellite From receiver

 

Positioning e   i  t  e   e e  l  l   t   S a

   t  e    i    l    l   e    t   a    S

S  a  t  e l   l  i  t  e  S    a   t    e  l     l     i     t    e  

1. position of satellites 2. Known Range measurements from satellites Calculate position time

 

GPS Time Measurement •

Code Identifies TT

Time event -- coded pulse N

• •

Rang Range e --- Ti Time me di diff ffer eren ence ce betw betwee een n two two matc matchi hing ng even events ts Pseu Pseudo do rang range e -- Ti Time me di diff ffer eren ence ce betw betwee een n eve event nt and and inaccurate reference  Actual receive time T  R

TT

t

Transmit

Receive N

N

TT

TR

ΔT  =  T  R −  T T 

Observed receive time T  = T    '+δ T   R

ΔPT  = T     R '−   T T  •

Doppler  •

 R

N

TT

Carrier phase φ  d φ  dt 

= lim Δt →0

φ (t + Δt ) − φ (t )

Δt 

t

N

ΔPT 

TR

t

sinφ   (t ) t

0 Accumulated delta range   )  −  φ 0 (T 0 ) ; No cycle ambiguity  ADR = φ 0 (T 

t

φ 0 (t )  = Oberved  Phase

= φ (t  ) ±  2π n  Ambiguity

 

Relationship Between Pseudorange and True Range • Pseudorange ~  Ri = C ⋅  ( T user  − T sat )

= C ⋅ (T T  + T  R + T  A   + Δ  T u ) − (T T  + ΔT S  ) i

• where,

T T  T  Ri T  Ai

i

i

= system time of transmission = free space propagation time = R/C = delay due to ionosphere, troposphere

T u Δ ΔT S 

i

= user clock bias = satellite clock bias

 

Differential Correction • • • •

Tech Techni niqu que e use used d to to cor corre rect ct some some of thes these e err error ors s Refe Referr rred ed to as “dif “diffe fere rent ntia iall GPS” GPS” or DGPS GPS In DGPS DGPS,, two two GPS rece receiv iver ers s are are used used One One rece receiv iver er is is loca locate ted d at an an accu accura rate tely ly sur surve veye yed d point referred to as the “base station” • A cor correc rectio tion n is is calc calcula ulated ted by compar comparing ing the known known location to the location determined by the GPS satellites • The corre correcti ction on is then then applie applied d to to the the other other recei receiver ver’s ’s (known as the “rover”) calculated position

 

DGPS Methods • Post-processing

 – Corrections performed a after fter the data is collected collec ted  – Special software req required uired

• Real-time  – Corrections are perfo performed rmed while the data is being collected  – Need special equ equipment ipment to receive the DGPS signal

 

Wide Wid e Ar Area ea Au Augme gmenta ntatio tion n Sys System tem - WAAS WAAS • New “real-time” DGPS • Satellite based • FA FAA A in init itia iati tive ve…. ….no now w fu fulllly y op oper erat atio iona nall • Se Seri ries es of ~2 ~25 5g gro roun und d rref efer eren ence ce sta stati tion ons s rrel elay ay info to master control station • Ma Maste sterr c con ontr trol ol sta statio tion ns sen ends ds co corr rrec ectio tion n inf info o tto o WAAS satellite

 

WAAS Satellites •

WAAS satel atelllit ites es are g geo eo-s -sta tati tion onar ary y

•

On e east ast coa coast, st,Garmin) WAA WAAS S sa satel tellit lite e si sits ts o off ff c coas oastt of B Braz razilil o over ver equ equato atorr at 5 53.9 3.96° 6° West (#35 on On we west st co coas ast, t, WA WAAS AS sa sate tell llit ite es sit its so ove verr P Pac acif ific ic oc ocea ean na att 17 178. 8.0° 0° Ea East st (# (#47 47 on Garmin)

•

• • • •

Abi Abilit lity y to g get et si signa gnall det deteri eriora orates tes in n nort orther hern n la latit titude udes s (s (sate atelli llite te is low lower er on tthe he horizon) If y you ou c can an g get et W WAA AAS Ss sat atel elli lite te s sig igna nal… l……. …..~ .~3 3 mete meterr ac accu cura racy cy Ho Howe weve ver, r, ca cann nnot ot al alwa ways ys ge gett s sig igna nall d due ue to ob obst stru ruct ctio ions ns Mo More re WA WAAS AS sa sate tellllit ites es be beco comi ming ng av avai aila labl ble e iin n ffut utur ure e  – Europeans (EGNOS) (EGNOS)  – Japanese (MSAS) (MSAS)