Global Positioning System (GPS)

Code Phase is one processing technique that gathers data via a C/A (coarse acquisition) code receiver. Basically, the position is determined by using the information contained in the satellite signals (the pseudo-random code).

The GPS satellites transmit PRC sequence-modulated radio waves. The PRC used in this technique is called C/A code.

The C/A codes are set of binary data generated from the satellite clock that serves as the time of transmission encoding for the signals. This C/A code is a digital code unique to each satellite, designed to be complex enough to ensure that the receiver does not accidentally sync up to some other signal. It allows the GPS receiver to differentiate between the signals and guarantees the receiver would not pick up another satellite’s signal. Therefore, same frequency can be used for all the satellite without disturbing others.

The receiver will pick up the signal from each satellite, and then generate a precise replica C/A sequence, refer to its local clock. This replica code is compare to the signal from satellite which containing the actual C/A code. The receiver slides its code forward and backwards in time by a code-tracking loop until it syncs up with the satellite code that reach the maximum correlation. The magnitude of the slewing is the observed indicated transit time of the signal, known as the signal’s travel time.

The correlation between both of the satellite’s PRC and the replica PRC generate by receiver will be explained in detail.

Remark:

The upper row shows C/A code of a satellite, the middle row shows the same replica code generate by the receiver (delayed code). The green column symbolizes starting of the code.

It can be seen that in the first example the code of the receiver is a little behind time. In the cross correlation, the signals are multiplied with each other, resulting in the signal in the lowest row. The signals in the lowest row are summed up,

giving a value of 9 {(9 x 1) + (39 x 0)}.

Now the signal of the receiver is shifted step by step and after each shift a cross correlation is done. Each shift resulted in a different set of code. In the second example both signals are in same position. The sum at the end of the cross correlation is bigger than before (more ‘1′ is form in the bottom roll). Thus, when the bottom roll is sum up, the correlation 25 is achieved (different set of C/A code will have different correlation value), where this is known as maximum correlation.

If the signal is shifted further, the cross correlation again leads to smaller correlation values.

The graph below shows correlation value for shift from -7 to 13.

Maximum correlation 1 (mean 100% correlation) is achieved when signal shift of 3 in this example.

The clock in the GPS receiver is not exactly synchronized with the satellite clock. The receiver clock has a bias which is found by the data-processor of the GPS receiver set (normally is slower than the satellite clock). When the observed indicated transit time is multiplied by the signal propagation delay to find the geometric range, the receiver clock bias must be included. This total range is termed a pseudo range (PR) measurement. The measured PRs are affected by the tropospheric and ionospheric propagation delays. Thus, the calculation of indicated transit time of the signal includes both the propagation delay and the clock offset.