Combining generalized likelihood ratio and M-estimation for the detection/compensation of GPS measurement biases

In this paper, we propose a novel algorithm for the detection of faulty measurements in Global Positioning System (GPS) navigation. In this context, satellite failures result in measurement biases which greatly impair positioning accuracy. Among the different algorithms developed to solve the navigation problem while detecting the biased measurements, the generalized likelihood ratio (GLR) offers a good compromise between accuracy and computational complexity. This algorithm not only estimates the times of occurrence of the failures but also computes a least square (LS) estimate of their amplitudes. However, due to interference or multipath, the GPS noise may not be exactly Gaussian distributed. Therefore, LS estimation may have poor accuracy. To overcome this difficulty, we propose to replace the LS estimator by an M-estimator in the GLR implementation. Such algorithms are well-known to be more robust to outliers.