Classification of Uncertainty Sources for Reliable Bayesian Estimation

Abstract

Recursive Bayesian estimation has emerged as a key tool for estimating the unknown state of a system. The wide range of applications has resulted in a correspondingly wide variety of estimation algorithms. The Kalman filter and its derivatives, like extended and unscented Kalman filters, are the most prominent examples, while non-Gaussian full-blown filters are on the rise with the increasing availability of computational power. The filtering results are naturally accompanied by an assessment of the estimate’s uncertainty. However, this assessment may mislead the user into believing that the estimate is reliable, i.e., that the uncertainty reported by the filter matches the actual uncertainty. For a filter to assess its uncertainty correctly, often strict requirements must be met. The misalignment can be attributed to different origins, for which this work proposes a classification covering different stages of a filter design. Approximations and assumptions made in each class impair the filter’s reliability. This paper provides a conceptual perspective on how reliability can be defined and how it can be assessed. An example of a reliability index is examined in a simulated scenario to illustrate how it can contribute to a better understanding of the overall performance of a filter.