Stochastic stability of cubature predictive filter

Abstract

In this paper, the cubature predictive filter (CPF) is derived based on a third-degree spherical-radial cubature rule. It provides a set of cubature-points scaling linearly with the state-vector dimension, which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear predictive filter (PF). In order to facilitate the new method, the algorithm CPF is given firstly. Then, the theoretical analyses demonstrate that the estimated accuracy of the model error and system for the proposed CPF is higher than that of the traditional PF. Moreover, the authors analyze the stochastic boundedness and the error behavior of CPF for general nonlinear systems in a stochastic framework. In particular, the theoretical results present that the estimation error remains bounded and the covariance keeps stable if the system’s initial estimation error, disturbing noise terms as well as the model error are small enough, which is the core part of the CPF theory. All of the results have been demonstrated by numerical simulations for a nonlinear example system.

摘要

本文基于三阶球面径向求容积法则提出了 Cubature 预测滤波器(CPF), 该方法通过一组线性化的 Cubature 采样点近似线性化状态变量, 用以解决非线性预测滤波中所遇到的多元积分问题。 为了便于该方法理解, 首先给出 CPF 的算法流程; 通过理论分析证明所提出的 CPF 方法较传统 PF 方法具有更高的模型误差及状态估计精度。 此外, 在随机框架下分析了 CPF 滤波器的随机有界性和误差范围。 特别是在系统初始误差、 外部扰动及模型误差小于某一有界值的情况下, CPF 滤波器的估计误差及协方差将保持有界。 最后, 通过非线性系统算例进行数值仿真, 验证了本文的理论分析结果。