均方根嵌入式容积卡尔曼滤波

Square-root imbedded cubature Kalman filtering

中文关键词  控制系统  卡尔曼滤波  嵌入式容积准则  非线性滤波  完全对称点

英文关键词  control systems  Kalman filters  imbedded cubature rule  nonlinear filtering  fully symmetric point

中文摘要

      传统容积卡尔曼滤波(CKF)的基础是三阶球面–径向容积准则, 该准则不仅要求计算n维超球体上的面积分, 还需将容积准则与扩展高斯–拉盖尔准则配合使用, 不易推导出高阶CKF滤波算法. 此外, CKF推导所采用的三阶球面容积准则也存在缺陷, 这极大地限制了CKF的滤波精度. 为避免以上问题, 本文基于嵌入式容积准则和均方根滤波技术, 提出一种加性噪声环境下, 用于非线性动态系统状态估计的全新容积卡尔曼滤波算法—–三阶均方根嵌入式容积卡尔曼滤波(SICKF). SICKF具有滤波精度高、数值稳定性强等诸多优点, 适用于动态目标跟踪、非线性系统控制等. 仿真结果表明, SICKF的滤波精度显著优于传统的非线性滤波算法.

英文摘要

      It is well known that the core of the cubature Kalman filter (CKF) is the third-degree spherical-radial cubature rule. This rule not only requires computing the integrals over an n-dimensional spherical region but also needs to combine the third-degree spherical cubature rule with the first-degree Gauss-Laguerre rule; these cause difficulties in obtaining compact forms for higher-degree filters. Moreover, the third-degree cubature rule-based filter has some drawbacks in approximation. To tackle these problems, we use the imbedded family of cubature formulae to derive an accurate but simple third-degree nonlinear filter called square-root imbedded cubature Kalman filter (SICKF). This SICKF has advantages in numerical stability and high filtering accuracy, making it the ideal algorithm for target tracking, nonlinear system control, etc. Experimental results obtained by the proposed methods demonstrate that the performances of the SICKF are superior to the conventional nonlinear filters.