Detection of Bias in GPS Satellites' Measurements: A Probability Ratio Test Formulation

A sequential and multihypothesis probability ratio test is proposed for detecting and identifying a bias fault in GPS pseudorange measurements. Initially, a measurement residual variable that is only a function of the measurement noise and the possible bias fault is constructed. The probability of this residual given a certain bias hypothesis is then obtained. Subsequently, an error variable is constructed for each hypothesis based on the ratio of the probability of that hypothesis to the probability of a base hypothesis. The propagation of the error variables with time is monitored for all hypotheses. If a hypothesis is associated with the true bias on the satellite measurement, then the corresponding error variable will remain around zero in mean. Otherwise, in case of a wrong hypothesis, the associated error variable will diverge away from zero. Error bounds for declaring false hypotheses are formulated in this brief. The advantage of the proposed method is that false hypotheses are continuously removed from the hypothesis set when their error variables exceed the error bound. Therefore, the size of the hypothesis set will reduce with time, ending up with only the correct bias hypothesis. This will result in a monotonic reduction in the computational time of the method. Finally, an ultratightly coupled filter structure is used to test the performance of the proposed method and the obtained results will be presented.