A modified Kalman filter for non-gaussian measurement noise

Abstract

A novel modification is proposed to the Kalman filter for the case of non-Gaussian measurement noise. We model the non-Gaussian data as outliers. Measurement data is robustly discriminated between Gaussian (valid data) and outliers by Robust Sequential Estimator (RSE). The measurement update is carried out for the valid data only. The modified algorithm proceeds as follows. Initially, the robust parameter and scale estimates of the measurement data are obtained for a sample of data using maximum likelihood estimates for a t-distribution error model through Iteratively Reweighted Least Squares (IRLS). The sample is dynamically updated with each new observation. Sequential classification of each new measurement is decided through a weighting scheme determined by RSE. State updates are carried out for the valid data only. Simulations provide satisfactory results and a significant improvement in mean square error with the proposed scheme. © 2011 Springer-Verlag Berlin Heidelberg.