Optimal Filtering of Pseudoranges and Phases from Single-Frequency GPS Receivers

Abstract

The filtering of observed pseudoranges with concurrent measures of phase or integrated Doppler can benefit significantly both absolute and differential positioning. The argument proceeds rather simply. If the position recovery uncertainty is predicted to be equal to the position dilution of precision (PDOP) times the range uncertainty, then reducing the range error will in turn reduce the recovered position uncertainty. With typical PDOP values of, say, 4 m/m, then for every meter improvement of the pseudorange, the recovered position uncertainty will also be reduced by 4 m. It has been argued that very significant improvements can be made when incorporating millimeter-level phases into pseudorange filtering algorithms. Here the filtering algorithm is examined, with emphasis on the ionospheric contribution. It will be argued that some degradation in the filter performance must be tolerated in order to accommodate this error source when using single-frequency receivers. During periods of peak solar activity or in geographic areas where unpredictable ionospheric activity is common, it will be seen that the optimal filter is one that averages the pseudorange and phase range measures, which then causes an improvement in the filtered pseudoranges of one-half the raw pseudorange noise. This improvement is significant. However, it is not as spectacular in its reduction as others have claimed who considered a cancellation of ionospheric contribution to the 10⁻⁶ level for relative or differential positioning.