Bayesian Filtering and Smoothing with Unknown Measurement Noise Covariance

Bayesian filtering and smoothing problems with unknown measurement noise covariance are investigated for linear Gaussian systems. The measurement noise covariance is assumed to be inverse Wishart distributed. A Bayesian filter and smoother calculating the joint posteriors for the state and the measurement noise covariance are derived by using a scale Gaussian approximation of t-distribution and moment matching. The proposed filter and smoother are non-iterative unlike the existing Bayesian solutions in the literature. The performance of the proposed algorithms is illustrated on a two-dimensional target tracking scenario. The simulation results show that the proposed filter and smoother have similar performance as the state of the art solutions with lower computational load.