On Approximate Maximum Likelihood Methods for Blind Identification: How to Cope with the Curse of Dimensionality
We discuss approximate maximum likelihood methods for blind identification and deconvolution. These algorithms are based on particle approximation versions of the EM algorithm. We consider three different methods which differ in the way the posterior distribution of the symbols is computed. The first algorithm is a particle approximation method of the fixed-interval smoothing. The two-filter smoothing and the novel joined-two-filter smoothing involve an additional backward-information filter. Because the state-space is finite, it is furthermore possible at each step to consider all the offsprings of any given particle. It is then required to construct a novel particle swarm by selecting, among all these offsprings, particle positions and computing appropriate weights. We propose here a novel unbiased selection scheme, which minimizes the expected loss with respect to general distance functions. We compare these smoothing algorithms and selection schemes in a Monte-Carlo experiment. We show a significant performance increase compared to the EMVA algorithm, a fixed-lag smoothing algorithm and the Block-CMA.