On Parametric Model Mismatch in Nonlinear EKF Approximations

Standard state estimation techniques, either for linear or non-linear systems, typically assume a perfect knowledge of the system, i.e., known process and measurement functions, and the corresponding noise statistics. The filter performance strongly depends on such knowledge and a possible model mismatch may lead to a significant performance degradation, but closed-form expressions for the resulting bias and co-variance are not available. In this contribution we explore the impact in extended Kalman filter approximations of a parametric model mismatch on both system functions, and provide expressions for the estimator bias and covariance error induced by the mismatch. An illustrative example is shown to support the discussion.