Lattice Kalman Filters

Abstract

In this paper, a new filter in the nonlinear Kalman filtering framework is proposed. The new filter is referred to as the lattice Kalman filter (LKF) and is based on a class of quasi-Monte Carlo (QMC) methods known as lattice rules. The proposed LKF method uses the Korobov type lattice rule to deterministically generate sample points that are randomly shifted based on the Cranley-Patterson shift method in order to approximate multi-dimensional integrals in the Gaussian filtering context. The mathematical formulation of the proposed LKF method as well as its error bound propagation are discussed. To evaluate the efficiency of the LKF, it is applied on a nonlinear aerospace system and compared with four other well-known methods presented in the literature. Simulation results demonstrate LKF uses significantly fewer sampling points yielding a significantly lower computational burden than another variant of QMC filter while maintaining the estimation accuracy. Furthermore, it provides asymptotically similar results to the unscented Kalman filter (UKF) but with less computational complexity, which is an important consideration in real applications.