Dependence Between Parameter Estimation and Statistical Hypothesis Testing

Abstract

The analysis of positioning safety often employs a probability-based formulation. This approach quantifies the probability of positioning failure, which is the probability of the position estimator being outside a safety-region, and compares it against an application specific requirement. The design of positioning algorithms for safety-critical applications, such as automated/autonomous vehicles, should consider the dependence between parameter or state estimation and statistical hypothesis testing for model misspecifications in the evaluation of positioning safety. If this dependence is not considered, as this article shows, the conclusions drawn from the positioning safety analysis might be overly-optimistic. Therefore, this article focuses on the aforementioned dependence through a vehicle positioning scenario based on an Extended Kalman Filter (EKF) and the Detection, Identification, and Adaptation (DIA) method for misspecifications in the motion and measurement models. Grounded in the distributional theory for the DIA method, our positioning safety analysis utilizes the conditional probability density functions (PDFs) of the combined EKF and DIA position error, which are generally nonnormal. We compute the probability of vehicle positioning failure in two cases 1) when the dependence is considered and 2) when it is not, to quantify the over-optimism introduced by ignoring this dependence. Finally, we present our conclusions and recommendations.