Moment-based Kalman Filter: Nonlinear Kalman Filtering with Exact Moment Propagation

Abstract: This paper develops a new nonlinear filter, called Moment-based Kalman Filter (MKF), using the exact moment propagation method. Existing state estimation methods use linearization techniques or sampling points to compute approximate values of moments. However, moment propagation of probability distributions of random variables through nonlinear process and measurement models play a key role in the development of state estimation and directly affects their performance. The proposed moment propagation procedure can compute exact moments for non-Gaussian as well as non-independent Gaussian random variables. Thus, MKF can propagate exact moments of uncertain state variables up to any desired order. MKF is derivative-free and does not require tuning parameters. Moreover, MKF has the same computation time complexity as the extended or unscented Kalman filters, i.e., EKF and UKF. The experimental evaluations show that MKF is the preferred filter in comparison to EKF and UKF and outperforms both filters in non-Gaussian noise regimes.