Compressed Positive Quadrature Filter

Abstract

A compressed positive quadrature filter (CPQF) is proposed in this technical note. Accuracy, efficiency, and numerical stability are the main concerns for quadrature-based nonlinear Gaussian filtering, but desirable performance in all these three aspects can hardly be simultaneously achieved in previously proposed nonlinear Gaussian filters, such as unscented Kalman filter, Gauss–Hermite quadrature filter (GHQF), and sparse grid quadrature filter. To improve the overall capacity of nonlinear Gaussian filtering techniques, the CPQF is proposed by numerically solving the constrained moment matching equations. By enforcing the positivity of the quadrature weights, the CPQF is numerically as stable as the GHQF. Through exploiting the underlying sparsity while solving the moment matching equations, the CPQF can also achieve the same level of accuracy as the GHQF using far fewer quadrature points. Simulations are conducted to evaluate the effectiveness of the CPQF, and the numerical results demonstrate its superior performance over conventional Gaussian filters.