The Navigation System with Timing And Ranging (NAVSTAR) Global Positioning System (GPS) was conceived as a ranging system from known positions of satellites in space to unknown positions on land, sea, in air and space. The GPS constellation consists of 24 satellites in 6 orbital planes with 4 satellites in each plane. The ascending nodes of the orbital planes are separated by 60 degrees and the planes are inclined 55 degrees. Each GPS satellite is in an approximately circular, semi-synchronous (20,200 km altitude) orbit. The orbits of the GPS satellites are available by broadcast - superimposed on the GPS pseudorandom noise codes (PRN), or after post-processing to get precise ephemerides, they are available from organizations such as the Jet Propulsion Lab (JPL) or the International Geodetic Service (IGS) among others. The GPS receivers convert the satellite's signals into position, velocity, and time estimates for navigation, positioning, time dissemination, or geodesy.


Each GPS satellite transmits data on two frequencies, L1 (1575.42 Mhz) and L2 (1227.60 MHz). The atomic clocks aboard the satellite produces the fundamental L-band frequency, 10.23 Mhz. The L1and L2 carrier frequencies are generated by multiplying the fundamental frequency by 154 and 120, respectively. Two pseudorandom noise (PRN) codes, along with satellite ephemerides (Broadcast Ephemerides), ionospheric modeling coefficients, status information, system time, and satellite clock corrections, are superimposed onto the carrier frequencies, L1 and L2. The measured travel times of the signals from the satellites to the receivers are used to compute the pseudoranges.

The Course-Acquisition (C/A) code, sometimes called the Standard Positioning Service (SPS), is a pseudorandom noise code that is modulated onto the L1 carrier. Because initial point positioning tests using the C/A code resulted in better than expected positions, the DoD directed "Selective Availability" (SA) in order to deny full system accuracy to unauthorized users. SA is the intentional corruption of the GPS satellite clocks and the Broadcast Ephemerides. Errors are introduced into the fundamental frequency of the GPS clocks. This clock "dithering" affects the satellite clock corrections, as well as the pseudorange observables. Errors are introduced into the Broadcast Ephemerides by truncating the orbital information in the navigation message.

The Precision (P) code, sometimes called the Precise Positioning Service (PPS), is modulated onto the L1 and L2 carriers allowing for the removal of the first order effects of the ionosphere. The P code is referred to as the Y code if encrypted. Y code is actually the combination of the P code and a W encryption code and requires a DoD authorized receiver to use it. Originally the encryption was intended as a means to safe-guard the signal from being corrupted by interference, jamming, or falsified signals with the GPS signature. Because of the intent to protect against "spoofing," the encryption is referred to as "Anti-spoofing" (A-S). A-S is either "on" or it's "off;" there is no variable effect of A-S as there is with SA.


Code Pseudorange

The pseudorange is the "distance" between the GPS satellite at some transmit time and the receiver at some receive time. Because the transmit time and the receive time are different, it is impossible to measure the true range between the satellite and the receiver. The basic definition of the pseudorange observable is:

where rho is the observed pseudorange calculated from the light time equation, rhotrue is the difference of the position of the receiver at the true receive time minus the position of the satellite at the true transmit time; and the rest of the equation represents the biases created by the errors in the clocks.

Phase Pseudorange

Another observable, based on the carrier phase of the signal, does not require the actual information being transmitted. The basic definition of the phase observable is:


where the fractional beat phase of the signal is converted into a pseudorange by scaling with the wavelength. rhotrue and the clock corrections remain the same as for the code pseudorange definition.

The integer number of cycles, N, is typically not known and varies for every receiver-satellite combination. As long as the connection between the receiver and the satellite is not broken, N remains constant while the fractional beat phase changes over time. Because of the ambiguous nature of N, it is referred to as the ambiguity and can either be solved for by using the code pseudoranges, or estimated. The loss of signal lock between a GPS satellite and the receiver is referred to as "cycle slip." If the signal lock is re-established, a new ambiguity will exist and must be solved for separately from the original ambiguity.

Atmospheric Effects

The GPS signals passing through the atmosphere encounter refraction effects including ray bending and propagation delays. These include the atmospheric effects of the troposphere and ionosphere.


The largest effects of the troposphere can be avoided by prescribing an elevation mask for your receiver, thereby avoiding signals from low elevation satellites. With a 15 degree elevation mask, 4-8 satellites will be simultaneously observable from a location on the Earth at any instant of time. The troposphere is composed of the "hydrostatic (dry)" portion and the "wet" portion accounting for water vapor. The dry portion constitutes 90% of the tropospheric refraction, whereas the wet portion constitutes 10%. However, the models for the dry troposphere are more accurate than the models for the wet troposphere. Therefore, the errors in the wet troposphere have a larger effect on the pseudorange bias than the errors in the dry troposphere.


Some models try to account for all effects of the ionosphere, but require much effort in modeling the highly time dependent total electron count of the atmosphere. A technique to remove the first order effects of the ionosphere linearly combines the L1 and L2 observables to form a new signal that is free of ionospheric effects. Alternatively, a correction to one of the two signals can be solved for. The first order contribution of the ionosphere to the pseudorange bias is related to the inverse of the frequency squared. Thus for the two pseudoranges:

We can form an ionosphere free pseudorange by taking a linear combination to cancel the effects
which results in an ionospheric free pseudorange observable of:

A similar development exists for the carrier phase observable. The expressions for the phase derived pseudoranges with first order ionosphere corrections are:

To actually use this new observable, it is necessary to compute the wavelength of the ionosphere free signal. Substituting values in yields a wavelength of about 48.5 cm for the ionosphere free signal or a frequency of 618.8 Mhz (60.5*f.0). Because the ratio between the L1 and L2 frequencies is not an integer value, the ambiguity term is no longer an integer. Alternatively, the ionospheric correction, a, could have been solved for.

Non-Clock Related Pseudorange Biases

There are other corrections besides the clock offsets and atmospheric effects which would appear as pseudorange biases. Receiver specific biases due to antenna phase center offset should be considered as well. The phase center of an antenna is where the signal is essentially received at and where the measurement refers to. Therefore, the distance between the antenna phase center and the point of interest needs to be known in order to correct the results to the point of interest.

When satellite signals reflect off of another surface and then arrive at the receiver simultaneously with non-reflected signals, this is known as multipath. The effect of multipath is greater on code based pseudoranges than phase based pseudoranges. Mathematical models to account for the multipath effect are impractical because the multipath effect is so highly dependent upon the specific geometry of the situation. Instead of accounting for multipath, it is recommended that multipath be avoided by placing the antenna as far from reflective objects as possible. In instances where multipath can not be avoided, the bias can be estimated from the ionospheric free combination pseudoranges; or the effects can be removed through digital filtering, wideband antennas, or radio absorbent antenna ground planes.

Because the reference frames fixed with the GPS satellite and the receiver are accelerated compared to the reference frame fixed in the Earth, special and general relativistic effects must be considered. The gravitational field of the Earth causes perturbations in the satellite orbits and space-time curvature of the satellite signal. The acceleration of the reference frames cause perturbations in the fundamental frequency of the satellite and receiver clocks.

Differential Techniques

Differential GPS

As the saying goes, necessity is the mother of invention. The DoD envisioned the civilian community using the GPS network and thus constrained them to the C/A code. The combination of the less accurate code and selective availability degraded the possible accuracy the civilian community could obtain. Civilian engineers and scientists had to find a way to improve the obtainable accuracy from GPS. The solution came in the form of differential GPS (DGPS). The basic concept of DGPS is the use of 2 receivers, one at a known location and one at an unknown position, that see GPS satellites in common. By fixing the location of one of the receivers, the other location may be found either by computing corrections to the position of the unknown receiver or by computing corrections to the pseudoranges.

By using DGPS, effects of selective availability can be removed. For short baseline distances between receivers, some of the biases from the atmosphere can be removed as well. This cancellation effect is the result of both receivers seeing the same things. If one receiver location is known, then the bias in the pseudorange to the known receiver can be calculated and used to correct the solution of the unknown receiver location. The DGPS system designed by the US Coast Guard calculates the biases at a known receiver location, and then broadcasts them on a radio frequency.

Double Difference Processing

Using double differenced observables can eliminate selective availability effects as well as other biases. Double differences are primarily used for surveying and geodetic research using phases; however, they are not limited to those applications. First, single differences are formed by subtracting observation equations from two separate receivers to a single satellite. Taking the difference between two single differences for a specific receiver pair gives the carrier phase double difference:

For coordinated receive and transmit times, all clock corrections have been removed for both of the GPS satellites and both of the receivers.

For more information about GPS, click here.

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This page created for Remote Sensing course at the University of Texas at Austin.
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