Performance of integer parameter estimation algorithm for GPS signals in noisy environment

Precise positioning utilizing GPS signals relies on a precise tracking of the carrier phase of these signals. The phase generally consists of two parts: an integer part and a fractional part. With the current receiver technology, it is possible to track the fractional part of the phase of the carrier wave at accuracy of 0.001 m using phase locked loops (PLLs). The tracking of the integer part is, however, a more difficult problem because of the inevitable ambiguities associated with the determination of the integer multiple of the carrier wavelength. In an environment where noise is Gaussian with relatively small variance, a standard integer least-squares algorithm can be used, yielding millimeter range accuracy. However, in the presence of interference intentional or non-intentional, this noise can be large and not necessarily Gaussian. In this paper we evaluate the performance of Integer Least-Squares based algorithm for two different situations (i) Phase measurement noise has larger variance and (ii) noise is not Gaussian. To study the effect of larger noise variance on the performance of integer least-squares algorithm, we performed the following simulation. For a synthetic GPS setup, Pc is calculated using Monte-Carlo simulations. Values of Pc for various noise variances are plotted versus time. We observed that as noise level increases, the time it takes to achieve a certain value of Pc also increases. This time was observed to vary linearly with the noise amplitude. The significance of this result is that the performance of the integer least-squares algorithm can be predicted for a given noise level. For a desirable performance requirement, our procedure enables the maximum allowable noise power (noise tolerance limit) to be calculated. We also investigated the performance of the integer leastsquares algorithm when the distribution of the measurement noise is not Gaussian. As a particular example uniform noise was considered. To ensure fair comparison between uniform and Gaussian noise, their variances are set to be equal. Simulation results show that the nature of noise has little effect on the performance of the algorithm.