  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.
