GNSS Positioning Safety: Probability of Positioning Failure and its Components

GNSS-based positioning plays an important role in safety-critical applications (e.g., automotive, aviation, shipping, rail) where positioning safety is paramount. Safety analyses typically include a probability-based formulation, such as calculating the probability that the position estimator falls outside a safety region (probability of positioning failure). Once this probability is being computed, it can be compared to an application specific requirement to decide whether or not this requirement is met. In this context, we carry out a component-wise analysis of the probability of positioning failure for the Detection, Identification, and Adaptation (DIA) estimator. The probability of positioning failure is formulated based on the DIA estimator’s probability density function (PDF) which accounts for the dependence between parameter estimation and statistical hypothesis testing. The probability of positioning failure can be further expressed in terms of its conditional components via the law of total probability which enables the assessment of the Most Impactful Components (MICs). Knowledge about the MICs can be useful to determine the main contributors to the probability of positioning failure. Using a dual GNSS (GPS and Galileo) positioning model for an automated vehicle, we compute the MICs based on the conditional PDFs components of the DIA estimator. Furthermore, we determine the worst-case scenario by computing the maximum total probability of positioning failure over a range of magnitudes for the outliers in the observables and over different orientations of the vehicle. These types of analyses can be useful during the design stage of DIA estimators to verify whether the safety requirements for positioning are met. Lastly, we summarize our contributions and provide an outlook on future work.