Performance evaluation of M-estimators as observation noise model in Kalman filter

A Gaussian model used for observation noise in Kalman filter (KF) does not consider at least two types of anomalies: a few large deviations in the data, often thought of as outliers, and a uniformly distributed error component arising from rounding and quantization. These rogue observations can excessively influence the state estimates computation by the KF. In this paper, we model the non-Gaussian observation errors by a class of maximum-likelihood estimators (M-estimators) and compare their performance as observation noise model. Since most M-estimators do not have a target distribution, these are reformulated as W-estimators through a simple linearization procedure. Each incoming measurement is assigned a weight by the respective w-estimate and the weights thus obtained are embedded in the KF through Robust Sequential Estimator (RSE) of our own design. The RSE acts as the sequential classifier for the measurements as valid data or an outlier. Kalman Filter state and error covariance updates are carried out for the valid data only while the outliers are suppressed and are not permitted to influence the estimates. We evaluate the performance of these estimators by computing the mean square error under different noise conditions and M-estimators' tuning constants.