Salient point quadrature nonlinear filtering

In this paper, a new nonlinear filter named Salient Point Quadrature Filter (SPQF) using a sparse grid method is proposed. The filter is derived using the so-called salient points to approximate the integrals in the Bayesian estimation algorithm. The univariate salient points are determined by the moment match method and then the sparse-grid theory is used to extend the univariate salient point sets to multi-dimensional cases. Compared with the other point-based methods, the estimation accuracy level of the new filter can be flexibly controlled and the filter algorithm is computationally more efficient since the number of salient points for SPQF increases polynomially with the dimension, which alleviates the curse of the dimensionality for high dimensional problems. Another contribution of this paper is to show that the Unscented Kalman Filter (UKF) is a subset of the SPQF with the accuracy level 2. The performance of this new filter was demonstrated by the orbit determination problem. The simulation results show that the new filter has better performance than the Extended Kalman Filter (EKF) and UKF.