A Method to Compute the Probability of Positioning Failure for Vehicles in the Context of Dependence Between Parameter Estimation and Statistical Hypothesis Testing

Positioning technologies are widely used in automotive, aviation, rail, and maritime safety-critical applications. Therefore, the computation of the probability of positioning failure for vehicles, which is the probability that the position estimator is outside a safety region, is of interest for positioning safety analyses. Since parameter estimation and statistical hypothesis testing for model misspecifications are commonly employed in positioning algorithms, the resulting position estimator is conditioned on the statistical hypothesis testing outcome. Hence, the probability density function (PDF) of the vehicle position estimator that accounts for the dependence between the two inference concepts should be used in the computations. In this contribution, we propose a method to compute the probability of positioning failure using the PDF of the vehicle position estimator, which accounts for the aforementioned dependence and is based on rare event simulation techniques, specifically Importance Sampling and the Cross-Entropy method. We apply the proposed method to a satellite-based positioning scenario, in decimeter precision, of an automated vehicle. The results show that the proposed method enables extensive positioning safety-analyses giving insights that can be used in the development of positioning algorithms and deciding whether safety targets and/or requirements are met. Finally, we discuss some limitations of the method and propose several further improvements.