random Gaussian impulse
estimation of time delay
maximum likelihood method
method of locally-Markov approximation
statistical computer modeling of stochastic processes
The problem of an estimation of time delay of random pulse signals has wide applications in radio- and hydrolocations, radio navigation, communication, technical diagnostics, etc. Thus, as a rule, the reception of rectangular random impulses is considered in the literature. However often enough the form of the processed pulse signal can essentially differ from the rectangular one.
In the present work the synthesis and analysis of optimum estimation algorithm of time delay of the narrow-band random Gaussian impulse of arbitrary form on the background of white noise has been executed. As adequate model of a useful signal the multiplicative combination of the video impulse, the function describing the form of a signal and narrow-band stationary centered random Gaussian process with band spectral density is used. The expression for the solving statistics (the logarithm of functional of likelihood ratio) has been written down and the structure of the maximum-likelihood measurer has been found for case of «fast» fluctuations of the impulse substructure. On the base of the locally-Markov approximation method the asymptotically exact (with increasing of the output signal-noise ratio) analytical dependences for the conditional bias (systematic error) and variance (mean squares error) of estimation of time delay taking account anomalous errors have been received. By methods of statistical computer modeling it is established that the synthesized measurer is efficient and theoretical formulas for its characteristics satisfactorily approximate corresponding experimental data, at least, at values of the output signal-noise ratio more than 2…3.