Maximum a posteriori sequence estimation using Monte Carlo particle filters

We develop methods for performing maximum a posteriori (MAP) sequence estimation in non-linear non-Gaussian dynamic models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. MAP sequence estimation is then performed using a classical dynamic programming technique applied to the discretised version of the state space. In contrast with standard approaches to the problem which essentially compare only the trajectories generated directly during the filtering stage, our method efficiently computes the optimal trajectory over all combinations of the filtered states. A particular strength of the method is that MAP sequence estimation is performed sequentially in one single forwards pass through the data without the requirement of an additional backward sweep (as would be the case for most smoothing methods such as the Kalman smoother). In simulation, the methods are shown to outperform standard methods for a given computational complexity. An application to estimation of a non-linear time series model and to spectral estimation for timevarying autoregressions is described.