Characteristic analysis and filtering algorithm design for UNGM model

针对UNGM模型的特性分析与滤波算法设计研究

¹ Shanghai Aerospace Control Technology Institute, Shanghai 201109, China
² Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai 201109, China

Received: 10 May 2022

Abstract

The univariate non-stationary growth model (UNGM) is widely used in the verification of nonlinear filters, and the unscented Kalman filter (UKF) is often used as the reference filter for comparative analysis when using this model to evaluate the filter performance. However, due to the strong nonlinearity of UNGM and the change of model properties with different parameter settings, the estimation misalignment problem due to different reasons will occur when UKF is used for filtering. To solve these problems, this paper analyzes the complex characteristics of UNGM in filtering process, and proposes an UKF with sliding sampling module(SSUKF). The algorithm is optimized on the basis of UKF, and can effectively deal with the complex characteristics of UNGM by sampling and analyzing the filtering information in the filtering process and correcting the distribution of Sigma points in real time. SSUKF is applied to UNGM under different parameters and compared with UKF and bootstrap particle filter(BPF). The simulation results show that SSUKF can effectively solve the misalignment problem when UKF is applied to UNGM, and the calculation speed is better than BPF. Compared with UKF, SSUKF is suitable as a benchmark filter for evaluating the performance of nonlinear filters using UNGM.

摘要

单变量非平稳增长模型(UNGM)与无迹卡尔曼滤波器(UKF)在非线性滤波器的比较分析中被广泛使用。但由于UNGM复杂的特性, 在使用UKF进行滤波时会出现基于不同原因的估计失准问题, 使得滤波器对比分析的严谨性不足。针对这些问题, 对UNGM的复杂特性进行了研究, 并提出一种具有滑动采样模块的UKF(SSUKF)。该算法在UKF的基础上进行了优化, 对滤波信息进行采样分析并实时修正Sigma点的分布, 能够有效应对UNGM的复杂特性。将SSUKF应用到不同参数条件下的UNGM中, 并与UKF、自举粒子滤波器(BPF)进行比较。仿真结果表明, SSUKF能够有效解决UKF应用于UNGM时的失准问题, 并且计算速度优于BPF。相较UKF, SSUKF更适合作为利用UNGM对非线性滤波器性能进行评估时的基准滤波器。