Examples of two and three dimensional phase demodulation problems are presented. Computer realizations for the optimal nonlinear phase estimator are discussed in detail, with emphasis on parallel computer architectures. Implementation of the nonlinear filter on various computer architectures, including the CDC6600/76G9, CDC STAR-100, lliiac IV, the CRAY-I, and the Floating Point Systems AP120B is reviewed. Detailed Monte Carlo performance analysis is presented for the two-dimensional system,

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... le partial results are included for the three dimensional case. Implications concerning the role of computer architecture upon nonlinear filter realization are discussed. This article is a revision and update of the authors' technical report [ I] "New Frontiers in Nonlinear Filtering". Revisions are primarily involved with the inclusion of up-to-date results and general conclusions.