Monte Carlo filtering and smoothing with application to time-varying spectral estimation

We develop methods for performing filtering and smoothing in non-linear non-Gaussian dynamical models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. In particular, novel techniques are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass of the Viterbi algorithm applied to a discretised version of the state space. An application to spectral estimation for time-varying autoregressions is described.

PARTIALLY COHERENT DYNAMIC PROGRAMMING ALGORITHM FOR CPM DETECTION.

A dynamic programming algorithm for joint data detection and carrier phase estimation of continuous-phase-modulated signal is presented. The intent is to combine the robustness of noncoherent detectors with the superior performance of coherent ones. The algorithm differs from the Viterbi algorithm only in the metric that it maximizes over the possible transmitted data sequences. This metric is influenced both by the correlation with the received signal and the current estimate of the carrier phase. Carrier-phase estimation is based on decision guiding, but there is no external phase-locked loop. Instead, the phase of the best complex correlation with the received signal over the last few signaling intervals is used. The algorithm is slightly more complex than the coherent Viterbi algorithm but does not require narrowband filtering of the recovered carrier, as earlier appproaches did, to achieve the same level of performance.