Towards Bayesian Filtering on Restricted Support

Linear state-space model with uniformly distributed innovations is considered. Its state and parameters are estimated under hard physical bounds. Off-line maximum a posteriori probability estimation reduces to linear programming. No approximation is required for sole estimation of either model parameters or states. The noise bounds are estimated in both cases. The algorithm is extended to: (i) on-line mode by estimating within a sliding window, and (ii) joint state and parameter estimation. This approach may be used as a starting point for full Bayesian treatment of distributions with restricted support.