The non-linear estimation of time-varying parameters of singals in the presence of noise is discussed. A concept of instantaneous maximum likelihood estimation is presented and is shown to be asymptotically sufficient. A new approach of optimum estimation has been found by which the diffcult problem of non-linear estimation of time-varying parameters of signals is simplified as first finding the instantaneous maximum likelihood estimation and then its optimum processing.The apparatus used to realize the instantaneous maximum likelihood estimation is defined as optimum demodulator and its general configuration is given. The application of the above theory is described with the phase-modulated signal used as an example. Finally

the results obtained in this paper are compared with those of D. C. Youla and D. L. Snyder.