In this paper, new robust Gaussian approximate (GA) filter and smoother are proposed to solve the problem of nonlinear state estimation with colored heavy tailed measurement noise. Firstly, the nonlinear state estimation problem with one-step delayed state and white heavy tailed measurement noise after measurement differencing is transformed into a standard nonlinear state estimation problem with heavy tailed measurement noise based on the state augmentation approach. Secondly, new GA filter and smoother are designed for the problem of unknown scale matrix and degrees of freedom (DOF) parameter of noise of the model after measurement differencing. The state, scale matrix and DOF param-eter are estimated simultaneously by building the conjugate prior distributions for unknown parameters and estimated state and using variational Bayesian approach. Finally, the efficiency and superiority of the proposed robust GA filter and smoother with colored heavy tailed measurement noise, as compared with existing method, are shown in the simulation of target tracking.%为了解决带有色厚尾量测噪声的非线性状态估计问题,本文提出了新的鲁棒高斯近似(Gaussian approximate, GA)滤波器和平滑器。首先,基于状态扩展方法将量测差分后带一步延迟状态和白色厚尾量测噪声的非线性状态估计问题,转化成带厚尾量测噪声的标准非线性状态估计问题。其次,针对量测差分后模型中的噪声尺度矩阵和自由度(Degrees of freedom, DOF)参数未知问题,设计了新的高斯近似滤波器和平滑器,通过建立未知参数和待估计状态的共轭先验分布,并利用变分贝叶斯方法同时估计未知的状态、尺度矩阵、自由度参数。最后,利用目标跟踪仿真验证了本文提出的带有色厚尾量测噪声的鲁棒高斯近似滤波器和平滑器的有效性以及与现有方法相比的优越性。
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