Lecture-7

2.10 Priinciples and

d Methods of
o GPS Posittion Fixing

 Basic principle of position fixin

ng in surveyin
ng is resectioon. The positiion fixing witth the help off GPS
can bee done using:
 Code
C phase orr Pseudo rang
ge measuremeents (Rangingg with PRN coodes)
 Carrier
C phase

 Positiioning Methods
 Point
P position
ning
 Relative
R posittioning

Code pha
ase or Pseudo
o range meassurements (R
Ranging with
h PRN codes))

 It is defined
d as a measure
m of len
ngth of path between
b satelllite and receiiver antenna. Since this disstance
can’t be measured d using physiccal methods, it is done wiith the help oof epoch (tim me) of transm mission
and reception of codes.
c Each GPS
G satellitee generates a specific PRN N (pseudo raandom noise)) code
transmmitted along with
w its signall. The same PRNP code (forr each satellitte) is generateed internally bby the
receivver. The transmission travvel time is measured
m by ccorrelating thhe identical P PRN codes. F Figure
2.12 shows
s one-waay ranging using the PRN codes.

 Various
V errorrs (multipathh, satellite an
nd receiver clock offsett etc.) corruppt the true range
measurements
m s and it is callled pseudo range.
r Differeence betweenn the clock offfset of sendeer and
receiver
r is T, the distance D can be com mputed by thee help of: D = c*T, where c is the veloccity of
light/EMR (3x108 m/sec). Since the co oordinates off the satellitees are knownn at any poinnt, the
coordinates
c off the receiver antenna can be
b computed..

Figurre 2.12: One-w

way ranging usiing PRN codess.
  Recovery
R of PRN
P Rangingg codes: - Thee PRN codes enable receivver’s navigatiion to compuute the
trransmission time
t of portio
on of satellitee signal. It is achieved byy modulating L1 carrier byy C/A
code
c with aidded locally geenerated C/AA code generaated due to tthe synchroniization of recceiver
clock
c to GPST or time req quired to travvel from satelllite to receivver antenna aas shown in F
Figure
2.13.
2

Figure
F 2.13: Reecovery of rannging code.

 In codde based positioning, 4 un nknowns are identified (thhree position coordinates and receiver clock
uations are needed for 4 unnknowns, thuss least squaree solution is carried
error dT). To solvee these, 4 equ
out ass:

Rn   X n  X 2  Yn  Y 2  Z n  Z 2  c.dT
Where,
W
Rn is measured d range
Xn, Yn, Zn is sattellite position
n coordinatess (n varies froom 1 to 4)
X,
X Y, Z is GPS receiver coorrdinates
c is the velocitty of EMR

Phase
Carrier-P

 It is based
b on the principle
p of EDM
E (electronnic distance m
measurement)) where the pphase measureement
is donne. In GPS, the
t measured quantity is the t differencee between thee phase of thhe internal recceiver
oscillaator and thee received saatellite carrieer phase (ass sensed by the receiverr antenna). Phase
measu urement has high
h accuracyy of upto 3 - 10 mm.

 n carrier phasse based meaasurements, reeceiver measuures the fracttion of one w

In wavelength w when it
measurement oof the carrier phase
fiirst make fixeed communicaation onto a satellite and coompute the m
frrom that time consistently. However, reeceiver is not able to measuure the complete range dirrectly.
The
T total phasse measured at a a given epoch (instant) (t0) is given by combinattion of a fracctional
ph ver and integeer number of full cycles N (which is unnknown). At initial
hase - measurred by receiv
 ph
hase, the nummbers of fulll cycles i.e. Integer
I Ambiiguity betweeen the satelliite & receiveer and
measured
m carriier phase indiicate the range of satellite--receiver simuultaneously inn the range off 0° to
36
60°(as shownn in Figure 2.1 14). As long as
a the lock onn a particular GPS satellitee is maintaineed, the
am
mbiguity rem
mains constantt and can be solved by num merical techniiques.

Fiigure 2.14: Carrrier phase meaasurements.

 Receiver
R is cap
pable to meassure only a frraction of cyccle of phase aat an initial innstant t0 of thee GPS
siignal i.e. onee cycle indiccates one wavelength. T The Integer aambiguity N((t0) i.e. remaaining
coounting of cyycles may nott be computed d directly. N((t0) remains cconstant evenn if there is no loss
off lock. Thus the
t measured phase at an epoch
e (ti) can be written as:

 ti   Fr ti   Int ; t0 , ti   N t 0 

Wheree,
 ti  = Phase meassurement at eppoch ti
Fr ti  = Fractioonal part of phhase measuredd at epoch ti
Int ; t0 , ti  = Integger part of auugmented phaase at epoch ti and counted since t0
N t0  = Integer am mbiguity (rem mains constantt throughout)

 Ambiguity:
A Determination
D of initial ambbiguity is impportant for caarrier phase bbased measureement
annd it is calleed Ambiguity y Resolution. Ambiguity remains fixeed after initiaal lock. But if the
reeceiver loses phase
p lock, itt is called ‘cyccle slip’ and m
must be identtified and repaired before ttaking
fu
urther observations. The effect
e of resolving the am mbiguity can bbe seen in thhe figure 2.155, and
onnce the ambig guity is resolvved, the accurracy of the meeasurement ddoesn’t improvve with time.
 Figure 2.15: Effects of
o ambiguity reesolution on accuracy of diffeerent surveyingg method (www
w.gpsworld.com)

Integratedd Carrier Beaat Phase: - Itt cannot be preferred

p for range observvation becausse of continuuously
changes ambiguity
a whhich is definedd as a functio
on of receiverr channel useed for trackinng the positioon and
time of saatellite.

Extractionn of Carrier Beat

B Phase (R Reconstruction Wave):- Signaal power is lesss than background
n of Carrier W
noise wheen the spread d spectrum siignal is receiived at GPS antenna. So, satellite signnal combiness with
original carrier frequen
ncy after remo
oval of modulations to booost up signal ppower.

 Pointt Positioning

 Itt consists of only

o one GPS S receiver wh hich is able too track four oor more satelllite to compuute its
ow wn coordinattes on the bassis of center of
o the earth aas shown in F Figure 2.16. IIt is also know
wn as
sttand-alone poositioning. It provides
p diffeerent parametter for receiveer coordinatess and clock errror in
WGS
W 84 systemm and transfo ormation paraameter into loocal datum.
 Fig
gure 2.16: Deteermining positiion of unknow
wn point

 A single GPS unit on an unnknown poin

nt is preferredd for the deteermination of 3D coordinaates of
th
hat unknown uracy of suuch method depends onn the duratioon of
n point referrenced. Accu
ob
bservations, 3-D geomettry of observved satellitess in space and the acccuracy of saatellite
ep
phemeris.

 Relattive or Differrential Positio

oning

 Itt consists of two

t GPS receeivers (referennce or base aand rover or rremote) whicch are able to track
fo
our or more satellite
s to compute their relative
r coorddinates on thee basis of cennter of the eaarth as
shhown in Figu ure 2.17. It is also known as
a differentiall positioning. It provides ddifferent paraameter
fo
or receiver co oordinates an nd clock errorr in WGS 844 system andd transformatiion parameteer into
lo
ocal datum. Reference
R receeiver having known
k coordiinates remainn stationary wwhile rover recceiver
haaving unknow wn coordinatees may vary.

 Known : X,Y
Y,Z (satellitess)
: R1, R2, R3, R4
: X,Y
Y,Z (base)

 Unknown : X,Y
Y,Z (rover or remote locatiion)
 Figuree 2.17: Princip
ple of GPS relat
ative positioninng

 Minim mum two GPS receivers receive signalls at the samee time from ssame set of satellites. Onee GPS
unit, known
k as the reference or base station, is always po sitioned on a known pointt. The observaations
are prrocessed withh respect to the base stationn to obtain thee position of oother station kknown as the rover
stationn. Figure 2.17 shows a ty ypical arrangeement for diffferential posiitioning. Acccuracy achievved by
this method
m is mucch higher thann that in pointt positioning bbecause errorrs common too both receiveers get
canceelled. The DG GPS method iss classified ass :

 Static Positioning: All recceivers remaiin stationary and collect carrier phasee over a periiod of
timme. Most acccurate positioning technique defines Static Positiooning due too some changges in
saatellite geometry. The esttimated accu uracy is in rooot means sqquare i.e. 5 m mm + 1ppm from
geeodetic receiv
ver depends ono baseline
 Fast
F (rapid) static:-
s It is somewhat sim milar to stati c Positioningg. The differeence is that iin this
caase only base receiver keptt stationary fo
or whole obseervation.
 Kinematic
K Positioning: Reeference receiiver remains ffixed while roovers vary froom point to pooint.
 Stop-and-go GPSG surveying:- It is simmilar to other Kinematic G GPs surveyingg. It is used w where
laarge number of unknown point is to bee compute w within 10- 15 km of know wn point. Posiitional
acccuracy is hig
gher in compaarison to Kineematic surveyying.