Robust linearly constrained extended Kalman filter for mismatched nonlinear systems

Abstract

Standard state estimation techniques, ranging from the linear Kalman filter (KF) to nonlinear extended KF (EKF), sigma-point or particle filters, assume a perfectly known system model, that is, process and measurement functions and system noise statistics (both the distribution and its parameters). This is a strong assumption which may not hold in practice, reason why several approaches have been proposed for robust filtering, mainly because the filter performance is particularly sensitive to different model mismatches. In the context of linear filtering, a solution to cope with possible system matrices mismatch is to use linear constraints. In this contribution we further explore the extension and use of recent results on linearly constrained KF for robust nonlinear filtering under both process and measurement model mismatch. We first investigate how linear equality constraints can be incorporated within the EKF and derive a new linearly constrained extended KF (LCEKF). Then we detail its use to mitigate parametric modeling errors in the nonlinear process and measurement functions. Numerical results are provided to show the performance improvement of the new LCEKF for robust vehicle navigation.