Normal-Gamma IMM Filter for Linear Systems with Non-Gaussian Measurement Noise

Abstract

In this paper, we consider state estimation of systems with non-Gaussian measurement noise. The non-Gaussian measurement noise and an auxiliary variable (to quantify the uncertainty in measurement-noise covariance) are modeled by a mixture of normal-gamma distributions. The normal-gamma distribution has been used to model heavy-tailed measurement noise in our previous work and proved effective. In the normal-gamma mixture, the auxiliary variable can quantify different levels of the uncertainty. Compared with traditional Gaussian mixture models, this normal-gamma mixture model is more flexible and powerful. We propose a filter in the interacting multiple model (IMM) framework with each filter being a normal-gamma filter. The proposed filter takes advantage of the IMM approach better than many existing methods. It also inherits properties of the normal-gamma filter in effectiveness and efficiency. Performance of the proposed filter is evaluated for estimation in several cases. Simulation results show that the proposed method outperforms the traditional Gaussian IMM filter, by much in some cases.