Nonlinear fault detection threshold optimization method for RAIM algorithm using a heuristic approach

Abstract

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 falsealert 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.

Navigation Algorithm-Agnostic Integrity Monitoring based on Solution Separation with Constrained Computation Time and Sensor Noise Overbounding

“…He et al [9] highlighted that a detection statistic should account for both optimal availability and integrity, and it should be independent of underlying statistical assumptions. Taking this into consideration, they tested a nonlinear optimization algorithm for the fault detection bound, using the cumulative LLR statistic.…”

“…He et al [9] introduced a method to optimize the fault detection bound for improved integrity and availability. Their method uses the cumulative LLR to identify sensors that are likely faulty.…”

“…• We demonstrate that a SS IM algorithm, working independently of any navigation algorithm, can employ statistics on Log Likelihoods of various measurement subsets: such metrics can identify presence of measurement faults as well as improve the understanding of underestimated uncertainties provided by the navigation algorithm. We propose a simple statistic based on the rolling standard deviation of Log Likelihood (LLRSD) of each subset that can accurately detect inconsistencies in time, instead of the already studied but more complex Log Likelihood Ratio (LLR) [9] • Multi-sensor fusion must account for sensor noise models which lead to underestimated uncertainties and invalid bounds. We propose overbounding the common case of time-correlated noise.…”

Systematic exploration of signal-based indicators for failure diagnosis in the context of cyber-physical systems

“…In this method, the fault indicator is interpreted as a deviation of the observed data from a defined threshold (Johnson, 1996). Due to its simplicity, limit checking has been widely used in rule-based approaches (where experts determine the value of a threshold based on their knowledge and experience), or in distribution-based approaches (He et al, 2016). However, the use of thresholds for analyzing failures in non-linear systems is difficult for two reasons: (1) non-linear systems have an unpredictable behavior, which requires the specification of a wide range of threshold values;…”

RAIM-NET: A Deep Neural Network for Receiver Autonomous Integrity Monitoring

“…To solve the non-linear and non-Gaussian problem for integrity monitoring, Peng proposed a temporal RAIM algorithm based on particle filter [23]. Pan et al optimized the detection threshold of the particle filter by applying the genetic algorithm [24]. In [25], the particle filter-based RAIM algorithm is modularly designed and implemented on a field programmable gate array (FPGA).…”