Linear filtering with timing uncertainty

Linear filtering in the presence of timing uncertainty is considered. In the model assumed here the true measurement times are intermittently available and noisy measurement times are always available. The estimation problem involves jointly estimating the state and the timing error parameters. The optimal Bayesian estimator cannot be found in closed-form so three approximations are proposed. The first estimates parameters only when the true measurement time is available, the second replaces unknown measurement times by estimates and the third is based on a sequential Monte Carlo approximation to the posterior distribution of the measurement time sequence. A performance analysis via numerical simulations shows that the best performance is achieved by the sequential Monte Carlo method, even with reasonably small sample sizes and a mismatched timing error distribution.