Abstract:

The assumption of known white noises for the linear Gaussian state-space model might be too restrictive. Both process noise and measurement noise are considered unknown, moreover, their relationship is analytically described. A hierarchical Bayesian model is built by assuming that the non-zero mean of the mea-surement noise is Gaussian and its covariance matrix is inverse Wishart distributed. By variational inference, the mean and covariance matrix of the measurement noise are reckoned as random variables and recursively estimated together with the system state. Thereafter the statistics of the unknown process noise can be updated by using the assumed functional relationship. Thus the first two moments of the measurement noise and the process noise can be obtained dynamically with acceptable accuracy even when the noises statistics are time-variant. Experiment results prove the effectiveness of the proposed algorithm.