Abstract: 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.

Key words: robust filtering, Huber function, boxplot, Kalman filter, nonlinear filtering