A Variational Bayesian Truncated Adaptive Filter for Uncertain Systems with Inequality Constraints

In this paper, a variational Bayesian (VB) truncated adaptive filter for uncertain systems with inequality constraints is proposed. By choosing the skew-t and inverse Wishart distributions as the prior information of the measurement noise and predicted error covariance matrix, the state vector, the predicted error covariance matrix, and noise parameters are inferred and approximated by using the VB method. To achieve the inequality-constrained estimation, the constrained state is computed by truncating the probability density function (PDF) of the estimated state after the variational update stage; the mean and covariance of the constrained state are the first and second moments of the truncated PDF. Considering the model uncertainties where the system dynamics are unpredictable, a multiple model VB truncated adaptive filter is proposed in the interacting multiple model framework. The performances of the proposed algorithms are evaluated via the target tracking simulations and the robot positioning experiments. Results show that the proposed algorithms improve estimation accuracy compared with the existing adaptive filters when the states suffer inequality constraints.