Fourier series and estimation on the circle with applications to synchronous communication-II: Implementation

The practical implementation of the infinite-dimensional optimal estimation results presented in Part I of this series is considered. Several techniques are described in detail. Included among these is the so-called “assumed density” approximation technique. Finite-dimensional suboptimal filtering equations based on this method are derived for several of the phase-tracking/demodulation problems studied in Part I. Finally, these techniques are applied to a phase tracking problem of importance in navigation systems such as Omega, and simulation results are reported that favorably compare a system designed using these techniques to an optimal phase-lock loop and an optimal linear system.