A METHOD OF DETERMINING THE TIME DELAY OF SIGNAL IN CONDITIONS OF A PRIORI UNCERTAINTY OF A COMPLEX NOISE SITUATION

P. Kostenko, V. Slobodyanuk, M. Alonkyn, M. Rovetskii, I. Rovetskii

Abstract


The conference paper presents a non-parametric method for solving the problem of estimating the time delay of a broadband impulse signal with binary phase manipulation by the Barker code taking into account the Doppler factor of the received signal using BDS (Brock, Dechert, and Scheinkman) statistics. The time delay estimation has been performed under the condition of a priori uncertainty about the probability density function of the multiplicative and additive noise in the signal observation. The method is based on minimizing the objective function that utilizes BDS statistics of the observation. The delay has been determined by minimizing the objective function concerning the unknown delay using BDS statistics Objective functions obtained for different parameters of BDS statistics have been studied.

For example, researched multiplicative and additive noise with Gaussian distribution. Special attention was paid to the case multiplicative noise was described by a random process with a Cauchy distribution, which is characterized by "heavy" tails it means large but rare values of the random process cannot be neglected. It got characteristics of delay estimation accuracy for different parameters of noise and different parameters of BDS statistics which are determined by the size of the pseudo-phase space and the radius of coverage for the image of the signal in this space. It has shown that there are parameters of the algorithm that allow implementing the proposed non-parametric method of estimating the time delay of signal and ensuring its effectiveness. A comparative analysis of the proposed method with the traditional method of maximum likelihood estimation which for Gaussian noise, reduces to the maximization of the cross-correlation function of the observation and the signal model. In the case combined action of the presented multiplicative and additive noise, the method of maximum likelihood is not effective at the same time, the proposed non-parametric method always provides sufficient evaluation efficiency in the conditions of the combined action of a priori unknown distributions of multiplicative and additive disturbances.

Key words: BPSK signal; additive noise; multiplicative noise; BDS statistics; objective function; accuracy.


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DOI: http://dx.doi.org/10.30970/eli.25.1

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