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A Normal-Gamma Filter for Linear Systems with Heavy-Tailed Measurement Noise

This paper considers state estimation of stochastic systems with outliers in measurements. Traditional filters, which assume Gaussian-distributed measurement noise, may have degraded performance in this case. Recently, filters using heavy-tailed distributions (e.g., Student's t-distribution) to describe measurement noise are gaining momentum. This paper proposes a new model for the state and an auxiliary variable (related to measurement noise) as having a normal-gamma distribution. This modeling has three advantages: first, it can describe heavy-tailed measurement noise since the measurement noise is t-distributed; second, using a joint distribution naturally considers the interdependence between the state and the measurement noise; third, it helps to develop a simple recursive filter. We derive the normal-gamma filter for linear systems. Analysis shows its superiority in robustness to traditional filters. Performance of the proposed filters is evaluated for estimation and tracking problems in two scenarios. Simulation results show the efficiency and effectiveness of the proposed normal-gamma filter compared with traditional filters and other robust filters.