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| Robust Kalman filtering algorithm with estimation of measurement biases |
| ZHU Guang-ming1,2, JIANG Rong-xin1,2, ZHOU Fan1,2, TIAN Xiang1,2, CHEN Yao-wu1,2 |
| 1. Institute of Advanced Digital Technology and Instrumentation, Zhejiang University, Hangzhou 310027, China; 2. Zhejiang Provincial Key Laboratory for Network Multimedia Technologies, Hangzhou 310027, China |
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Abstract A robust Kalman filtering algorithm with estimation of measurement biases was proposed in order to handle the problem that unknown measurement biases and random measurement noises exist in the measurement system. The nonzero-mean Gaussian distribution model was utilized to model the measurement biases and the random measurement noises of the measurement system. The Normal-Inverse-Wishart distribution was utilized to estimate the mean and covariance parameters of the Gaussian distribution. The time-variant parameters of the mixed model between the Gaussian distribution and the Normal-Inverse-Wishart distribution were inferred by the variational Bayesian approximation. The measurement biases and the time-variant covariances of the random measurement noises were estimated as the system states were recursively inferred by the cubature Kalman filter. The proposed algorithms robustness to the measurement outliers was enhanced with the estimation of the measurement biases. The simulation results demonstrate that the proposed algorithm can also precisely estimate the measurement biases and enhance its robustness with the guarantee of the high state estimation precision．
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Published: 10 September 2015
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带测量偏置估计的鲁棒卡尔曼滤波算法
针对测量系统中同时存在未知的测量偏置和随机测量噪声的问题,提出带测量偏置估计的鲁棒卡尔曼滤波算法.该算法利用非零均值高斯分布对测量系统中的测量偏置和随机测量噪声进行建模,利用正态-逆威沙特分布拟合该高斯分布的均值和协方差.该算法利用变分贝叶斯方法对该高斯分布和正态-逆威沙特分布的混合模型的时变参数进行逼近推断,在利用容积卡尔曼滤波算法进行系统状态迭代估计的同时对测量偏置进行估计以及对时变随机噪声协方差进行跟踪,在进行测量偏置估计的同时增强了滤波算法对测量野值的鲁棒性.仿真实验证明了该算法在保证系统状态估计精度的同时,能够高精度估计出测量偏置并增强了滤波算法的鲁棒性．
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