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A new approach is presented for estimating stochastic signals. The approach is based on the use of Markov processes and state-variable concepts. Equations are presented for approximate minimum mean-square error estimates of a Markovian state vector observed in a signal in which it is imbedded nonlinearly. A general model for analog communication via randomly time-varying channels is given and related to the state-vector estimation problem. The model includes as special cases such linear and nonlinear modulation schemes as AM, PM, FM, and PM /PM; and such continuous channels as Rayleigh and Rician channels, fixed channels with memory, and diversity channels. The state-variable approach leads automatically to physically realizable demodulators whose outputs are approximate MMSE estimates of the stochastic message and, if desired, the channel disturbances. Special consideration is given to angle modulation schemes.