The Simplified Quasi-Optimal Estimates of the Time and Power Parameters of a Low-Frequency Random Pulse with Arbitrary Modulating Function

Abstract

We introduce a simpler approach for obtaining of usable processing algorithms of fast fluctuating Gaussian pulses with arbitrary modulation function in conditions of parametric prior uncertainty. We carry out the synthesis and analysis of the quasi-optimal measurer of a low-frequency random pulse signal with unknown appearance time, mathematical expectation and dispersion. We find the asymptotically exact expressions for the conditional biases and variances of the resulting estimates. By methods of statistical computer modeling the usefulness and efficiency of the considered technique is corroborated, the working capacity of offered measurer is established, and applicability borders of asymptotically exact formulas for its characteristics are also defined. Keywords-fast fluctuating random signal; maximum likelihood method; decision statistics; unknown parameters; Cramer-Rao bound; quasi-optimal estimation; local Markov approximation method; statistical modeling