Nonlinear Fault Detection Threshold Optimization Method for RAIM Algorithm Using a Heuristic Approach

The threshold value used in receiver autonomous integrity monitoring algorithms to identify faults has a significant impact on positioning integrity and GPS/GNSS availability. The value is usually selected empirically or under certain distribution assumptions; its calculation for a non-Gaussian test statistic has not been solved. For fault detection methods using a particle filter, a new heuristic method is proposed to select an appropriate fault detection threshold value using an optimization model. In this method, a non-Gaussian cumulative log likelihood ratio (LLR) value is used as the test statistic. Its threshold is determined using an integrity risk minimization problem with an availability constraint. Since there is no closed form for this optimization model, a genetic algorithm with a local search strategy is adopted to find a near-optimal solution. Experimental results show that this method can be used to compute the non-Gaussian fault detection threshold value subject to different availability constraints. Comparisons with empirical and distribution-based methods indicate that while meeting the same probability for false-alert constraint, the probability of missed detection in the optimized approach is much lower than for other methods, especially for small numbers of errors. Since the cumulative LLR value does not exhibit obvious statistical features for any distribution, the performance of our optimized approach is stable for different test cases and satellite data sets.