Optimal discrete filtration of intricate phase-keyed signals

An optimum discrete filter for arbitrarily intricate phase-keyed signals is synthesized assuming that such signals arrive at the receiver in an additive mixture with Gaussian white noise. While both phase angle theta(t) and time delay (t) are described by stochastic equations, d theta/dt = omega - omega sub 0 and d tau/dt = v - sub 0 (t-time, omega sub 0-a constant frequency, v sub -a constant rate of change of time delay), the state vector X(t) is estimated from the a-priori probabilistic equation X(t)=FX(t) + GW(t) (F-state matrix, G-perturbation matrix, W sup T (t)-noise vector). The equations of optimal continuously discrete filtration are derived on the basis of the Markov nonliner filtration theory, whereupon the covariational error matrix is calculated. The accuracy and the intererence immunity of the corresponding processor structure under static and dynamic conditions depend, accordingly, on the behavior of the error matrix elements in time. The steady-state interference immunity of such an optimum discrete receiver is somewhat lower than that of the corresponding optimum analog one, the discretization process playing the major role in lowering it.