Estimation for rotational processes with one degree of freedom--Part I: Introduction and continuous-time processes

A class of bilinear estimation problems involving single-degree-of-freedom rotation is formulated and resolved. Continuous-time problems are considered here, and discrete-time analogs will be studied in a second paper. Error criteria, probability densities, and optimal estimates on the circle are studied. An effective synthesis procedure for continuous-time estimation is provided, and a generalization to estimation on arbitrary Abelian Lie groups is included. Applications of these results to a number of practical problems including frequency demodulation will be considered in a third paper.