The purpose of this monograph is to develop a general theory of the estimation (or recovery) of a random process that has been nonlinearly transformed and also corrupted by noise, the effects of which need not be simply additive. The estimation procedures are developed within the formalism of state-variable modeling techniques and continuous-time, continuous-state Markov processes.
The theory assumes that the observations from which the original random process (or message) is to be estimated are taken continuously in time and that the entire past history of the observations is available for generating an estimate at each point in time, but that future observations will not be used to update or improve previous estimates. The theory is applicable to numerous practical systems involving message transmission and estimation, such as radio communication systems, radar, sonar, radio astronomy, and automatic control.
In order to obtain new results as well as illustrate the approach, several applications of the theory are made to analog communication systems. Linear and nonlinear modulation methods, especially angle modulation methods like frequency modulation, and continuous random channels, are discussed. Corresponding to each method, an appropriate optimum demodulator is derived. New results are also obtained in a study of the performance characteristics of optimum phase and frequency demodulators.
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