Pseudorange

The pseudorange (from and range) is a first-approximation measurement for the distance between a satellite and a navigation satellite receiver—for instance Global Positioning System (GPS) receivers.

To determine its position, a satellite navigation receiver will determine the ranges to (at least) three satellites as well as their positions at time of transmitting. Knowing the satellites' orbital parameters, these positions can be calculated for any point in time. The pseudoranges are then the time the signal has taken from there to the receiver, multiplied by the speed of light.

Typically a quartz oscillator is used to do the timing. Quartz clocks in general are less accurate than 1 in a million, if the clock hasn't been corrected for a week, the distance will put you not on the earth but behind the moons orbit. Even if the clock is corrected, a second later the clock is not usable anymore for positional calculation, because after a second the error will be hundreds of meters for a typical quartz clock. But the clocks time is used to measure the ranges to the different satellites at almost the same time, this makes that all the measured ranges have the same error. Ranges with the (same) error are called pseudoranges. With four pseudoranges (and the location of the satellites) solutions for the receiver's position along the "x"-, "y"-, "z"- and $Delta\; t$- axes can be computed.

The reason we speak of "pseudo"-ranges rather than ranges, is precisely this "contamination" with unknown receiver clock offset. GPS positioning is sometimes referred to as trilateration, but would be more accurately referred to as "pseudo-trilateration".

Following the laws of error propagation, neither the receiver position nor the clock offset are computed exactly, but rather "estimated" through a least squares adjustment procedure known from geodesy.To describe this imprecision, so-called GDOP quantities have been defined: Geometric Dilution of Precision (x,y,z,t).

A clock with an accuracy of 1 in a million, will introduce an error of one millionth of a second each second. This error multiplied by the speed of light will give an error of 300 meters. For a typical satellite constellation this error will be increase by about the square root of 2 (Less if satellites are close together, more if satellites are all near the horizon).If positional calculation was done using this clock and three satellites, standing still the GPS would indicate you are traveling at a speed in excess of 300 meters a second, this is over 1000 km/hour or over 600 miles an hour. With only signals of three satellites the GPS receiver will not be able to determine the difference between the clock error and actual movement.Pseudorange calculations uses the signals of four satellites to compute the location and the clock error.

If the satellites are scattered then Value of geometric Dilution of Precision is low and if satellites are near each other the GDOP values are higher. Lower the value of GDOP the better the ratio of the position error to range error computing will be, so GDOP plays an important role once calculating the position on the surface of the earth using pseudorange and the larger the number of satellites , the better the value of GDOP will be. Pseudoranges only give the time the wave has taken to travel from the satellite to the receiver, and as we already know the speed of light the distance is found out immediately. Since range from all the satellites are calculated simultaneously, this is why this is called pseudorange. With four satellites the clock error is removed, and position x,y,z is calculated precisely.