Lecture-7

2.10 Principles and Methods of GPS Position Fixing

Basic principle of position fixing in surveying is resection. The position fixing with the help of GPS can be done using: Code phase or Pseudo range measurements (Ranging with PRN codes) Carrier phase

Positioning Methods Point positioning Relative positioning

Code phase or Pseudo range measurements ( anging with PRN codes)

It is defined as a measure of length of path between satellite and receiver antenna. Since this distance can’t be measured using physical methods, it is done with the help of epoch (time) of transmission and reception of codes. Each GPS satellite generates a specific PRN (pseudo random noise) code transmitted along with its signal. The same PRN code (for each satellite) is generated internally by the receiver. The transmission travel time is measured by correlating the identical PRN codes. Figure2.12 shows one-way ranging using the PRN codes.

Various errors (multipath, satellite and receiver clock offset etc.) corrupt the true rangemeasurements and it is called pseudo range. Difference between the clock offset of sender and receiver is T, the distance D can be computed by the help of: D = c*T, where c is the velocity of light/EMR (3x108 m/sec). Since the coordinates of the satellites are known at any point, the coordinates of the receiver antenna can be computed.

Figure 2.12: One-way ranging using PRN codes.

X X

2 Y Y Z

2n n n

Z 2 c.dT

Recovery of PRN Ranging codes: - The PRN codes enable receiver’s navigation to compute the transmission time of portion of satellite signal. It is achieved by modulating L1 carrier by C/A code with aided locally generated C/A code generated due to the synchronization of receiver clock to GPST or time required to travel from satellite to receiver antenna as shown in Figure 2.13.

Figure 2.13: Recovery of ranging code.

In code based positioning, 4 unknowns are identified (three position coordinates and receiver clock error dT). To solve these, 4 equations are needed for 4 unknowns, thus least square solution is carried out as:

Rn

Where,Rn is measured rangeXn, Yn, Zn is satellite position coordinates (n varies from 1 to 4)X, Y, Z is GPS receiver coordinatesc is the velocity of EMR

Carrier-Phase

It is based on the principle of EDM (electronic distance measurement) where the phase measurement is done. In GPS, the measured quantity is the difference between the phase of the internal receiveroscillator and the received satellite carrier phase (as sensed by the receiver antenna). Phasemeasurement has high accuracy of upto 3 - 10 mm.

In carrier phase based measurements, receiver measures the fraction of one wavelength when it first make fixed communication onto a satellite and compute the measurement of the carrier phase from that time consistently. However, receiver is not able to measure the complete range directly. The total phase measured at a given epoch (instant) (t0) is given by combination of a fractional phase - measured by receiver and integer number of full cycles N (which is unknown). At initial

phase, the numbers of full cycles i.e. Integer Ambiguity between the satellite & receiver and measured carr er phase indicate the range of satellite-receiver simultaneously in the range of 0° to 360°(as shown in Figure 2.14). As long as the lock on a particular GPS satellite is maintained, the ambiguity remains constant and can be solved by numerical techniques.

Figure 2.14: Carrier phase measurements.

Receiver is capable to measure only a fraction of cycle of phase at an initial instant t0 of the GPSsignal i.e. one cycle indicates one wavelength. The Integer ambiguity N(t0) i.e. remainingcounting of cycles may not be computed directly. N(t0) remains constant even if there is no loss of lock. Thus the measured phase at an epoch (ti) can be written as:

ti Frti Int ;t0 , ti N t0 Where,ti = Phase measurement at epoch ti

Frti = Fractional part of phase measured at epoch ti

Int;t0 , ti = Integer part of augmented phase at epoch ti and counted since t0

N t0 = Integer ambiguity (remains constant throughout)

Ambiguity: Determination of initial ambiguity is important for carrier phase based measurementand it is called Ambiguity Resolution. Ambiguity remains fixed after initial lock. But if thereceiver loses phase lock, it is called ‘cycle slip’ and must be identified and repaired before taking further observations. The effect of resolving the ambiguity can be seen in the figure 2.15, and once the ambiguity is resolved, the accuracy of the measurement doesn’t improve with time.

Figure 2.15: Effects of ambiguity resolution on accuracy of different surveying method (www.gpsworld.com)

Integrated Carrier Beat Phase: - It cannot be preferred for range observation because of continuously changes ambiguity which is defined as a function of receiver channel used for tracking the position and time of satellite.

Extraction of Carrier Beat Phase (Reconstruction of Carrier Wave):- Signal power is less than backgroundnoise when the sprea spectrum signal is received at GPS antenna. So, satellite signal combines withoriginal carrier frequency after removal of modulations to boost up signal power.

Point Positioning

It consists of only one GPS receiver w ich is able to track four or more satellite to compute itsown coordinates on the basis of center of the earth as shown in Figure 2.16. It is also known as stand-alone positioning. It provides different parameter for receiver coordinates and clock error in WGS 84 system and transformation parameter into local datum.

Figure 2.16: Determining position of unknown point

A single GPS unit on an unknown point is preferred for the determination of 3D coordinates ofthat unknown point referenced. Accuracy of such method depends on the duration ofobservations, ephemeris.

3-D geometry of observed satellites in space and the accuracy of satellite

Relative or Differential Positioning

It consists of two GPS receivers (reference or base and rover or remote) which are able to track four or more satellite to compute their relative coordinates on the basis of center of the earth as shown in Figure 2.17. It is also known as differential positioning. It provides different parameter for receiver coordinates and clock error in WGS 84 system and transformation parameter into local datum. Reference receiver having known coordinates remain stationary while rover receiver having unknown coordinates may vary.

Known : X,Y,Z (satellites): R1, R2, R3, R4

: X,Y,Z (base)

Unknown : X,Y,Z (rover or remote location)

ag

m

y

G

Figure 2.17: Principle of GPS relative positioning

Minimum two GPS receivers receive signals at the same time from same set of satellites. One GPS unit, known as the reference or base station, is always positioned on a known point. The observations are processed with respect to the base station to obtain the position of other station known as the rover station. Figure 2.17 shows a typical arrangement for differential positioning. Accuracy achieved by this method is much higher than that in point positioning because errors common to both receivers get cancelled. The DGPS method is classified as :

Static Positioning: All receivers remain stationary and collect carrier phase over a period oftime. Most accurate positioning technique defines Static Positioning due to some changes insatellite geometry. The estimated accuracy is in root means square i.e. 5 geodetic receiver depends on baseline

mm + 1ppm from

Fast (rapid) static:- It is somewhat similar to static Positioning. The difference is that in this case only base receiver kept stationary for whole observation.

Kinematic Positioning: Reference receiver remains fixed while rovers vary from point to point. Stop-and-go GPS surveying:- It is si ilar to other Kinematic Ps surveying. It is used where

l rge number of unknown point is to be compute within 10- 15 km of known point. Positionalaccuracy is hi

her in comparison to Kinematic surve

ing.