Robustification of Kalman Filter Models
针对卡尔曼滤波模型对异常值不稳健的问题，提出一种基于多元t分布和poly-t近似的稳健化方法，使后验分布在遇到极端异常观测时回归先验分布，并给出递归实现机制。
Abstract Kalman filter models based on the assumption of multivariate Gaussian distributions are known to be nonrobust. This means that when a large discrepancy arises between the prior distribution and the observed data, the posterior distribution becomes an unrealistic compromise between the two. In this article we discuss a rationale for how to robustify the Kalman filter. Specifically, we develop a model wherein the posterior distribution will revert to the prior when extreme outlying observations are encountered, and we point out that this can be achieved by assuming a multivariate distribution with Student-t marginals. To achieve fully robust results of the kind desired, it becomes necessary to forsake an exact distribution-theory approach and adopt an approximation method involving “poly-t” distributions. A recursive mechanism for implementing the multivariate-t—based Kalman filter is described, its properties are discussed, and the procedure is illustrated by an example.