异常值和未知观测噪声鲁棒的非线性滤波器

针对含异常观测值的非线性系统滤波问题，以Huber损失函数替代推导滤波器最大后验准则中观测误差的l₂范数，构造出了一种新的优化准则函数，从而给出了一种对异常值鲁棒的非线性后验线性化滤波器。分析表明：由于Huber损失函数兼具l₁和l₂范数的性质，从而使得由这个新准则推导出的滤波器，不仅具有l₂范数的低误差拟合性，也具备l₁范数对异常值的鲁棒性。而当观测噪声的分布未知时，通过引入箱线图法检测异常值，并对噪声统计分布的参数进行估计，进一步提出了对异常值和未知观测噪声分布鲁棒的非线性后验线性化滤波器。仿真实验验证了分析结果的有效性，并表明本文算法的性能优于现有文献报道的非线性滤波算法。

Nonlinear filter robust to outlier and unknown observation noise

An outlier-robust posterior linearization filter is presented to address the filtering problem of nonlinear systems with observation outliers. Analysis shows that a new optimization criterion function can be constructed when the l₂ norm of the observation errors in a maximum posterior criterion in filter derivation is replaced by the Huber loss function. Since the Huber loss function has the properties of both l₁ and l₂ norms, the filter derived from the new criterion presented in this paper not only has a low fitting error as the l₂ norm does, but is robust to outliers as the l₁ norm. When the distribution of the observation noise is unknown, a boxplot method is introduced to detect the outliers in the observations and estimate the statistical distribution parameters of the observation noise. Thus, an outlier and unknown observation noise-robust posterior linearization filter is further proposed. Simulation verifies the analytical results and further shows that the performance of the proposed algorithms surpasses that of the nonlinear filtering algorithms reported in the literature.