V.A. Belokurov – Ph.D.(Eng.), Associate Professor, 

Department «Radio Systems», Ryazan State Radio Engineering University named after V.F. Utkin

E-mail: belokurov.v.a@rsreu.ru

V.I. Koshelev – Dr.Sc.(Eng.), Head of Department «Radio Systems», 

Ryazan State Radio Engineering University named after V.F. Utkin E-mail: koshelev.v.i@rsreu.ru

One of the promising directions of the development of radar is to increase the probability of correct detection, and as a result, the detection range of small objects is multi-frame accumulation. The main problem of existing tracking before detection algorithms based on a recursive calculation of the generalized likelihood ratio is a large number of hypothesis traces, the number of which increases exponentially. This leads to difficulties in practical implementation on a modern element base, in addition, the calculation of the detection threshold in accordance with the Neyman-Pearson criterion leads to the fact that the probability of false alarm on each hypothesis path increases significantly due to a sharp increase in the detection threshold. One of the possible solutions to this problem is the introduction of a primary detection threshold, the subsequent accumulation of samples that exceed this detection threshold and the decision on the presence of an object based on the accumulation results, taking into account the law of distribution of samples that exceed the primary detection threshold. The input of the primary detection threshold receives samples of the amplitude spectrum from the output of the correlation filter scheme for processing radar information. The amplitude fluctuations in this paper correspond to the Sverling model 1.

In this paper, we propose an algorithm for calculating the distribution density of the sum of samples that exceed the primary detection threshold obtained at the output of the drive. The probability density functions are calculated analytically for the hypotheses of the absence (hypothesis H0) and the presence (H1) of a useful signal based on the use of the apparatus of characteristic functions. Using this apparatus allows you to bypass the operation of calculating the convolution of probability density densities when finding the distribution law of the sum of samples after the primary detection threshold. In order to verify the obtained results, a simulation was carried out in the framework of which empirical and theoretical characteristic functions were constructed, as well as theoretical and empirical distribution functions of the sum of samples at the input of the secondary threshold device were constructed. 

In order to correctly calculate the distribution laws at the input of the secondary threshold device, the criterion of agreement was used. In this paper, the criterion «Chi-square» is used. Used by the significance level of the criterion α = 0.05. The paper considers cases corresponding to various values of the primary detection threshold. The number of reviews was chosen equal to 5. In all cases, the statistics of the Chi-square criterion does not exceed the critical value of the criterion for a given level of significance, which confirms the correctness of the results presented in the article.

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