Surveying: Capter-2: Station Dependent Errors in GPS signals

Multipath: when a GPS receiver is operated in any field survey measurements, it becomes an essential requirement of any measurement that the signal propagation from the satellite to the receiver should be straight through the atmosphere, but in real world this ideal condition no longer exists due to wide range of obstacles present on ground terrain, these obstruction or obstacles assembles the multipath issues with GPS signals.

GPS signals are highly vulnerable to the path of propagation from source of emission (satellite) to the receiver, it means that GPS signals also have multipath issued and GPS measurements are highly affected by multipath. The multipath errors induced by the refraction or deflection of GPS signals from their actual path of signal propagation, due to the reflection of radio signals from surrounding terrain, buildings, hard profile of ground, canyon walls, big trees and high slops etc.

Fig: Multipath Effect due to building and terrain profile

 Delay in the signal propagation through atmosphere due to these obstacles, causes GPS measurement errors which are different for different GPS signals, because of signal dependency on the wavelength. When GPS measurements are carried out in field both direct signals and indirect signals (reflected) may be received by the receiver. The path of the received signals highly dependent on the reflecting surface and the satellite position, as the satellite moves in orbit multipath effect will also be get affected by time means it is time variable. For evaluating the position of any object GPS receivers make pseudo-range measurements using ranging codes, transmitted by satellites. A multipath error in measurements are responsible for creating a false position of any objet measured by GPS receiver, due to the distortion of resulting cross correlation function and a shift in the peak of function displayed from its correct position. The shift introduced here in the correlation function causes pseudo range error. The multipath error is also dependent of the architect of the receiver. Multipath may introduced an error of positioning approximately 150m for C/A code and 15m for P code.

How to reduce or eliminate the multipath error: A very efficient way of eliminating the multipath error in GPS measurement is to set the GPS receiver at a multipath free position, means where there are no obstacles are present. But in real world it is a very hard to found a survey sight which is obstacle free because of the varying ground profile and natural obstruction.  But in case of measurements we can keep our GPS antenna far from the obstacles whenever taking observations in the field but it is not always possible. 

Narrow correlator spacing are there to mitigate the multipath error. If long delay multipath error is associated with a signal, receiver itself can encounter with this error and discard it. But for shorter delays from ground reflection in signals, special type of antennas can be used like Choke ring antenna. The shorter delays in signals are very hard to filter out by receiver because of their resemblances to routine fluctuations in atmospheric delays, so they interfere with true signals.

Station coordinates:  The ambiguity associated with station coordinates, also introduce errors in the GPS measurements thus the resolution of ambiguity becomes very important for determination of accurate and precise station coordinates. Ambiguity resolution is essential for converting biased phase observables into the unbiased range observables with the same degree of precision. It has been suggested that an improvement of 2.5 can be achieved in baseline precision of eastern component due to an ambiguity resolution of baselines having length up to 500m. A perfect station network design plays a vital role in ambiguity resolution. When talking about the confidence limit of ambiguity resolution, the baseline distance between the two receiver stations has prime concern that form double difference.  After every ambiguity resolution in station coordinates, covariance matrix is updated with new information and after resolving few ambiguities, automatically may resolve the ambiguity of entire network and got ambiguity free. High quality and dual frequency pseudo-range is helpful in successful ambiguity resolution.

Geometry dependent (Dilution of Precision: DOP):  Dilution of precision represents the satellite geometry in the sky, which is very important parameter in result accuracy assessment in the GPS measurements. Basically DOP value is a qualitative and quantitative measure of the satellite position in the sky. It is affected by the number of satellites in the receiver range and separation between them. The visible satellites grouped together closely in the space, are said to be in weak geometry and introduces high DOP values whereas if the separation is large among the satellites then it said to be in strong geometry and DOP value associates with, is low. Thus the lower DOP value causes a better GPS positioning accuracy because of the large separation between the satellites, used for calculating the GPS unit’s position.

Fig: Satellite Geometric Dilution Precision (GDOP)

The presence of obstacles such as buildings, nearby mountains can also alter the effective DOP value. It can also be represented as HDOP, VDOP, PDOP and TDOP respectively for horizontal, vertical positional (3D) and temporal dilution of precision. GPS receiver is able to obtain the DOP value when taking measurements. 

Fig: Good GDOP with obstacles

 Thus the higher DOP values introduces error in  measured coordinates, and represents the weak satellite geometry thus the weak signals, also closely spaced satellites have low coverage of area under observation so may introduce positional error too in DGPS surveys.

The geometry of satellites introduces the positional errors, which called geometric dilution of precision and it can be denoted as

GDOP= positional error/ range error

For assessing the error introduced by satellite geometry let us take an example of 4satellite geometry which forms the tetrahedron. The larger the volume acquired by tetrahedron the better will be the GDOP value obtained. If the volume is small then the GDOP value get worse. Similarly larger the no of satellites better will be the obtained GDOP.

The description of some DOP values given below;

DOP=1; Ideal DOP value, gives highest possible confidence level

DOP=1 to 2; Excellent DOP value, used in highly sensitive position measurements

DOP=2 to 5; Good DOP,

DOP=5 to 10; Moderate DOP,

DOP=10 to 20; Fair DOP,

DOP>20; Poor DOP,

User Equivalent Range Error (UERE):  

User equivalent range error is a commutative effect of various errors associated with the receiver and satellites, which is contributing in the total error budget. It can be define as a equivalent error in the range between the satellite and receiver. It can be introduced by different sources thus independent of each other.  The UERE can be calculated by taking square root of the sum of the squares of all the errors. Their errors can be listed as their descending order of contribution to the total error budget, as follow:

1.      Satellite clock error: actually receivers are used in calculating the distance between satellite and receiver position as function of time difference in signals, when signal transmitted from satellite to receiver on ground. NAVSTAR satellite clocks (atomic clocks) are very accurate, the possibility of their stray-up from standard GPS time is negligible or of the order of milliseconds. And the amount of satellite drift is calculated in the GPS control segment, generally called monitoring station.  Satellites which are able to make clock correction, reduces the satellite clock errors significantly. 

2.      Upper atmosphere (Ionospheric error): the atmosphere has varying density by latitude all through the length of 50km to 1000km in atmosphere above the earth surface, seasonally and with time also, due to these variation in density signals propagating through atmosphere undergo various interference like delay in signal propagation from satellite to receiver and also signal may get deflected through their actual path. Satellite orbited vary close to the horizon, has tendency to transmit a signal by taking a long route through the ionosphere than the satellites overhead, so these signals greatly affected by interference.  The ionosphere's density in response to the Sun's ultraviolet radiation, solar storms and maximums, and the stratification of the ionosphere itself. The GPS Control Segment is able to model ionospheric biases, however. Monitoring stations transmit corrections to the NAVSTAR satellites, which then broadcast the corrections along with the GPS signal. Such corrections eliminate only about three-quarters of the bias, however, leaving the ionosphere the second largest contributor to the GPS error budget.

3.      Receiver clock error: Surveying receivers are equipped with the quartz crystal clock whereas, NAVSTAR satellites have atomic clock. Quartz crystal clocks are less stable than that of atomic clocks, thus due to the un-stability in time measurement by the quartz clock some error introduced in the receiver co-ordinates observed.

4.      Satellite orbit: the shape of orbit of satellite is greatly affected by the gravitational attraction of earth, sun and moon, the monitoring station calculates the deviation in the in satellite eccentricities by observing the satellite location in orbit and calculating the eccentricities of orbits. The deviations are documented as ephemerids. An ephemeris is compiled for each satellite and broadcast with the satellite signal. GPS receivers that are able to process ephemerides can compensate for some orbital errors.

5.      Lower atmosphere (Topospheric error): The atmospheric delays in GPS signals are also adding slightly to the calculated distances between satellites and receivers. Satellites close to the horizon transmit signals having mostly delayed, since they pass through more atmosphere than signals from satellites overhead.

6.      Multipath error: physical bodies obstruct the signals propagating through atmosphere, thus introduces the error of multipath.