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Variance Estimation of Random Radioimpulse with Unknown Time Delay at Presence of the Interference with Unknown Intensity


A.P. Trifonov, O.V. Chernoyarov, D.N. Shepelev

In practical applications of the location and communication it is often necessary to measure the time and power parameters of high-frequency pulse signals observed against noise background. Gaussian random radio-impulse is wide spread as an adequate model of such signals. It is a result of the multiplicative combination of rectangular modulated function of a large duration and realization of a centered Gaussian random process. In a number of works the estimations of time delay and dispersion of Gaussian random radio-impulse synthesized under the assumption that registration errors have a nature of the additive Gaussian white noise with a priori known spectral density have been examined. However the useful signal often can be distorted by additive correlated external interference with unknown intensity in addition to own electronic system noises approximated by Gaussian white noise. In this paper the joint estimation algorithms of time delay and dispersion of random radio-impulse have been synthesized in conditions of various a priori uncertainty about the intensities of white noise and interference using the method of maximum likelihood. It has been shown that the measurers of time delay and dispersion of random radio-impulse can be realized in the form of simple single-channel devices if the spectral densities of external interference and random substructure of the useful signal accept band approximation. It has been found out that the use of adaptive approach to remove of a priori uncertainty about unknown intensity of external interference allows to receive the estimation algorithm of time and power parameters of random radio-impulse which is invariant to the intensity of white noise. On the base of the locally-Markov approximation method the asymptotically exact expressions for the biases (systematic errors) and variances (mean squares errors) of joint time delay and dispersion estimations of random radio-impulse taking account anomalous errors have been received. It has been shown that the losses in accuracy of the adaptive estimations because of ignorance of white noise and interference intensities are asymptotically absent if the observation time is much greater than duration of the useful signal or bandwidth of the external interference significantly exceeds bandwidth of the random radio-impulse substructure.

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