Diagnosis of outlier of type multipath in GPS pseudo-range observations

The nonlinear Gauss-Jacobi algorithm which exploits the capability of algebraic tools of Groebner basis and Multipolynomial resultants to solve in a closed form polynomial system of GPS pseudo-range equations is here proposed as a possible tool for detecting the satellite, whose pseudo-range has been contaminated by the error of type Multipath. By injecting gross errors of 200m and 500m on the pseudorange observations from two satellites, it is demonstrated how the Gauss-Jacobi combinatorial algorithm detects the falsified satellite and in addition identifies poor geometrical combination of the satellites, which is normally identified via PDOP. Indeed, the Gauss-Jacobi combinatorial algorithm proposed is a straightforward tool, which adopts a deterministic approach that deviates from the statistical stochastic approaches to outlier detection. Outliers are simply detected based on the combinatorial approach first proposed by C. F. Gauss in 1828 and published posthumously but which C. G. I. Jacobi later independently published in 1841. The computing engine for the Gauss-Jacobi combinatorial algorithm, Groebner basis or Multipynomial resultant algorithms for computing pseudo-ranges hove already been prepared by J. L. Awange and E. W. Grafarend and can be accessed in the GPS toolbox via http://www.ngs.noaa.gov/gps-toolbox//awange.htm. The proposed algebraic approach proves to be a powerful tool in detecting outliers and could be applied not only to GPS pseudo-range problem but to any problem that permits the conversion of its system of equations into algebraic (polynominal form). This is demonstrated using the planor ranging problem.