Nonlinearity-based adaptive sparse-grid quadrature filter

Abstract

The recently emerging sparse-grid quadrature filter (SGQF) has been shown to outperform the unscented Kalman filter owing to its higher levels of estimation accuracy It can achieve the close performance to the Gauss Hermite quadrature filter without suffering the curse-of-dimensionality problem. However, the computation efficiency of the SGQF can be further improved by exploring the inherent system structure. In this paper, a new adaptive sparse-grid quadrature filter (ASGQF) is proposed. The accuracy levels of the sparse-grid quadrature (SGQ) are adaptively selected based on the nonlinearity of the stochastic system such that a higher level of SGQ is used only when the nonlinearity measure is high, which reduces the unnecessary computation complexity. A global measure and a local measure of nonlinearity are used and compared. In a target tracking example, the ASGQF with the adaptive mixture of low level SGQ and high level SGQ is shown to achieve close performance to the sole higher level SGQF and demands much less computation load.