容积法则辅助的交互式多模型滤波算法

Cubature rule aided interacting multiple model filter algorithm

交互式多模型滤波(IMM)的交互环节使得系统状态量不再服从单纯的高斯分布,用现有方法对其概率分布的估计存在较大的误差.对此,考虑到模型的混合概率是时变的,IMM的交互过程可以用非线性方程来描述,因而采用容积卡尔曼滤波(CKF)中的容积法则对高斯随机变量经非线性函数传播后的概率分布进行估计,并从理论上证明了容积法则的近似精度.仿真实验表明,由于提高了对交互后随机变量概率分布的估计精度,所提出的方法能够有效改善IMM在量测噪声较大时的滤波效果.

The mixing operation which is a key component in interacting multiple model（IMM） filter yields a non-Gaussian probability density function（PDF）, IMM approximates the PDF of mixed random variable by a single Gaussian, the estimated covariance matrix is much large than the real covariance. As the mixing probability is time-varying, the mixing operation can be described as a nonlinear function, then the cubature rule in cubature Kalman filter（CKF） can be used to compute probability density function（PDF） of the mixture, that algorithm is called cubature rule aided interacting multiple model（CR-IMM） filter. The accuracy of the resulting mean and covariance are analyzed by Taylor expansion. Simulation results show the CR-IMM performs better than IMM when the measurement becomes less accurate.