A.V. Sokolov - Ph.D. (Eng.), Heading Research Scientist, Joint-Stock Company «Radio Engineering Corporation «Vega» (Moscow)
The article considers the topic of determining the number of air targets in the tactical group, tracking as a single object. The initial statistics is the primary radar information – set of the number of detected radar spots obtained during a certain number of radar contact with this group.
The following basic observation conditions are assumed:
the numerical structure of the group and the detection probability of each target remain constant during the taking the decision time;
the group consists of similar objects with the same ESR and ESR fluctuations of each object are independent.
On this basis, mathematical model of statistics as a sequence of Bernoulli trials with unknown values of detection probability and the number of objects is accepted.
A number of methods for estimating the parameters of the distribution based on different principles are considered. A comparative analysis of their effectiveness is carried out. The criterion is the probability of erroneous determination of the objects number. The results are obtained analytically and by statistical mathematical simulation.
1. The method of fixing the maximum number of radar spots detected in the sample. The targets number estimate is the maximum number of spots.
2. The method of moments, according to which the value of the estimated parameter is a known function of the moments of the binomial distribution. The sample estimates are taken as its values.
3. The method of maximum likelihood of the sample.
4. The method of minimum chi-square test, according to which the estimate of the parameter is a value that minimizes this criterion.
5. The method of Kolmogorov-Smirnov test with a similar estimation rule.
6. The method of minimum Hellinger distance with a similar estimation rule.
The most effective method was found to be one of fixing the maximum number of detected spots. The method of moments gives unacceptable results in the range of source data. Other methods are similar in effectiveness, the best of them is the method of minimum Hellinger distance.