Robust LCEKF for Mismatched Nonlinear Systems with Non-Additive Noise/Inputs and Its Application to Robust Vehicle Navigation

Abstract

It is well known that the standard state estimation technique performance is particularly sensitive to perfect system knowledge, where the underlying assumptions are: (i) Process and measurement functions and parameters are known, (ii) inputs are known, and (iii) noise statistics are known. These are rather strong assumptions in real-life applications; therefore, a robust filtering solution must be designed to cope with model misspecifications. A possible way to design robust filters is to exploit linear constraints (LCs) within the filter formulation. In this contribution we further explore the use of LCs, derive a linearly constrained extended Kalman filter (LCEKF) for systems affected by non-additive noise and system inputs, and discuss its use for model mismatch mitigation. Numerical results for a robust tracking and navigation problem are provided to show the performance improvement of the proposed LCEKF, with respect to state-of-the-art techniques, that is, a benchmark EKF without mismatch and a misspecified EKF not accounting for the mismatch.