Cumulant filters: Nonlinear filters for recursive state estimation of systems with non-Gaussian noise.

摘要

An innovative recursive filter algorithm for state estimation of linear systems where the Gaussian assumption is not required for the plant (process) driving noise, the initial conditions, or the measurement noise is developed and presented. The approach requires the noise to be defined by their higher-order statistics, moments or cumulants. The performance of this cumulant filter is compared to an exact Bayesian filter where the non-Gaussian noise is generated from distributions created using Gaussian sums, and for which optimal Bayesian filters have been developed. The comparison will support quantifying closeness to optimal performance and demonstrate the improvement in state estimation over the standard Kalman filter approximations.; The new non-Gaussian recursive filter will be exercised in a target tracking problem where linearized and extended Kalman filters are used extensively but are known to be susceptible to divergence and poor performance when the underlying statistics tend away from Gaussian. The cumulant filter is implemented on a problem involving a passive target-tracking application, and its performance compared to that of the traditional Kalman filter application, as well as the commonly used M-estimators, so as to demonstrate the benefits of these filters on a typical and popular application.