Improved state estimator for linear-Gaussian systems subject to initialization errors

This paper proposes an improved state estimator for linear-Gaussian systems subject to initialization errors. A one-step prediction function depicted by the Student-t is reconstructed artificially by inserting an auxiliary variable into the original Gaussian distribution. The variational Bayesian (VB) technique is then employed to obtain the approximated posterior joint distribution of the additional variable and the state. A fixed-point iteration is used for recursions to calculate the necessary moments of state with the updated distribution of the auxiliary variable. Simulation and experiment verify the performance of the proposed algorithm. It shows that the proposed method yields significant improvements over the existing initialization approaches, such as the practical Kalman filter (KF) and the recently-developed Bayesian initialization algorithm.