Accuracy Evaluation of Marginalized Unscented Kalman Filter

Compared with a conventional unscented Kalman filter (UKF), the recently proposed marginalized unscented Kalman filter (MUKF) uses a partially sampling strategy to achieve similar filter accuracy with fewer sigma points, demonstrating its powerful ability to deal with state estimation with mixed linearity and nonlinearity. However, the hypothesis that the accuracy of MUKF is equivalent to that of UKF is not true for all systems. In this paper, it is proved that when the state equation is expressed as a differential equation, the accuracy of MUKF is equivalent to that of UKF only when the propagations of the states to be sampled and the states not to be sampled in MUKF are independent of each other. The above condition corresponds to a common problem in engineering, which is a system with measurement biases. Through theoretical proof and numerical simulation, it is verified in this paper that for the systems with measurement biases, the differences of the computed means and covariances in filtering recursions between MUKF and UKF are restricted to the same order infinitesimal as the square of the scaling parameter. To sum up, this paper evaluates the accuracy of MUKF, providing references for engineers to choose MUKF or UKF in different systems.