Estimation for Rotational Processes with One Degree of Freedom. Part II. Discrete-Time Processes.

摘要

General error criteria and probability distributions on the circle are studied in connection with estimation by using their Fourier series representations. Conditional probability densities for certain discrete-time folded normal processes, which are analogous to the continuous-time processes associated with the bilinear problems considered in Part 1 of this series, are computed. An intrinsic physical difference between the discrete-time and continuous-time problems is discussed, and the complexity of the estimation equations in the discrete-time case is analyzed in this setting. Suboptimal sequential filtering schemes are briefly discussed. In addition, Fourier analysis of conditional probability distributions exposes the inherent rich structure in quite general classes of estimation problems on the circle. (Author)