异常值和未知观测噪声鲁棒的卡尔曼滤波器

Outlier and unknown observation noise robust Kalman filter

给出了对异常值和未知分布的观测噪声鲁棒的卡尔曼滤波器。分析表明当以Huber损失函数替代推导卡尔曼滤波器最大后验准则中观测误差的l2范数时,就构造了一个新的准则。由于Huber损失函数可同时描述l1和l2范数,因此由这个新准则推导的卡尔曼滤波器,在具有传统卡尔曼滤波器性质的同时,也有了l1范数对异常值鲁棒的特性。而当含异常值的观测噪声统计分布未知时,利用含未知参数的高斯混合模型描述其分布以及变分贝叶斯推理,提出了对异常值和未知统计分布观测噪声鲁棒的卡尔曼滤波器。仿真和实验在验证了分析结果正确的同时,也表明提出算法的性能优于现有文献报道鲁棒类的卡尔曼滤波器。

In this paper,the Kalman filter robust to outliers and observation noise with unknown distribution is proposed.It is shown that a new criterion for deriving a Kalman filter can be constructed when the l2 norm of the observation errors in its maximum posterior criterion is replaced by the Huber loss function.Since the Huber loss function can simultaneously describe both l1 and l2 norms of an observation error,it is illustrated that the Kalman filter derived from the new criterion is robust to outliers as l1 norm and its performance is the same as the traditional one when the outliers are free.When the statistical distribution of the observation noise with outliers is unknown,a Gaussian mixture model with unknown parameters is used to describe such a distribution and the variational Bayesian is employed to infer these unknown parameters.In this way,a Kalman filter robust to outliers and unknown statistical distribution of observation noises is given.Both the correctness of the analytical results and the performance of the proposed algorithms superior to the robust Kalman filters reported in literatures are verified by simulations and experiments.