Algorithm for Sequential Detection of Trajectory of Small Sized UAV by FMCW Radar According to Strongest Neighbor Criterion
DOI:
https://doi.org/10.20535/RADAP.2024.98.23-29Keywords:
trajectory detection, Wald's maximin model, likelihood ratio, false alarm, decision statistic, chi-square distribution, target pip, gateAbstract
To ensure an acceptable probability of detection of small UAVs, it is necessary to reduce the detection threshold, which leads to a significant increase of the probability of false alarm in the range-doppler bin (more than 10-3). To increase efficiency of solving the problems of secondary radar processing information with an increase of the number of false pips, the decision statistic of pips obtained during signal detection are used. The known algorithms for sequential target trajectory detection using decisive pips statistics require significant computational costs.
To solve the problem of detecting the target trajectory, a sequential Wald likelihood ratio criterion with constant thresholds is used, which are based on the given probabilities of true and false detection probabilities of the target trajectory. A mathematical expression of the partial likelihood ratio is obtained, which considers the probability density of the decision statistic of the pip, provided that it is a target or not, as well as the probabilities of: target detection and false alarm in the bin, the target pip falling into the trajectory confirmation gate, and the absence of false pips in the gate.
The analysis of the proposed algorithm and its comparison with the known one, in which the pips are identified by the criterion of the nearest neighbor, is carried out using statistical modeling using FMCW radar data (range and radial velocity of the target). The non-central and central chi-square distributions with two degrees of freedom are used to describe the probability densities of the decisive statistics of a pip, provided that it is either a target or a false pip.
For the considered example, unlike the known algorithm, which does not consider the decisive statistics of the pip, the developed algorithm provides an increase in the probability of detection the target trajectory at α =10-2, 5 x 10-3 by 14%-50% and 4%-34%, respectively. At the same time, the average number of cycles at α = 10-2, 5 x 10-3 decreases by approximately 4 and 2.5 times. The probability of false detection of the target trajectory FΣт for the developed algorithm is less than an order of magnitude. At the same time, the average number of times at α =10-2, 5 x 10-3 decreases by approximately 3.8 and 2.3 times, respectively.
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