A.V. Sokolov - Ph. D. (Eng.), Heading Research Scientist, Joint-Stock Company «Radio Engineering Corporation «Vega» (Moscow) E-mail: alira746@yandex.ru

The article considers a new method for false-alarm probability calculation in noncoherent weighted pulse burst processing. Shortcomings of two existing methods for probability density function (p.d.f.) for integrated pulses calculation are noted: the method of the characteristic function inversion and the method of Edgeworth series expansion. The characteristic function method provides, in principle, precise analytical expressions in case of quadratic detection and any weighting function. However, numerical calculation and tabulation of results were carried out only for uniformly weighted integration. Despite the fact that working formulas were obtained for any weighting function, its structure does not admit practical numerical calculations. The Edgeworth expansion method is based, as it is known, on the p.d.f. approximation via a finite series in the vicinity of its mean value. Thus, the p.d.f. tail approximation deteriorates significantly as the false-alarm probability decreases, in addition because this series takes negative values as the detection threshold increases. In the proposed method the false-alarm probability is described by a cumulative probability function of a new random variable, its mean value coinciding with detection threshold. Its p.d.f. is approximated by normal distribution with the same first two moments in the vicinity of the mean value. Thanks to this, the accuracy of the false-alarm probability calculation increases as the probability decreases. The method accuracy was evaluated for the case of uniform weighting by comparing calculation results with precise tabulated data. With the proposed method various weighted integration effectiveness was determined. As an efficiency criterion the threshold signal level, providing the 0.5 detection probability, was used. Among the main advantages of the method are noted the following: increased accuracy of threshold signal level cal-culation; applicability to integration with any weighting function (including recursive filtering); computational simplicity.

 

1. KHelstrom K. Statisticheskaja teorija obnaruzhenija signalov: Per. s angl. pod red. JU.B. Kobzareva. M.: IL. 1963.
2. Sovremennaja radiolokacija: Per. s angl. pod red. JU.B. Kobzareva. M.: Sov. radio. 1969.
3. Teoreticheskie osnovy radiolokacii / Pod red. JA.D. SHirmana. M.: Sov. radio. 1970.
4. Amiantov I.N. Izbrannye voprosy statisticheskojj teorii svjazi. M.: Sov. radio. 1971.
5. Likharev V.A. Cifrovye metody i ustrojjstva v radiolokacii. M.: Sov. radio. 1973.
6. Feldman JU.I. Plotnost verojatnosti sluchajjnogo processa pri vesovom kvadratichnom summirovanii // Radiotekhnika. 1979. № 4.
7. Van Tris G. Teorija obnaruzhenija, ocenok i moduljacii: Per. s angl. pod red. V.I. Tikhonova. T.1. M.: Sov. radio. 1972.
8. Bakut P.A., ZHulina JU.V., Ivanchuk N.A. Obnaruzhenie dvizhushhikhsja obektov / Pod red. P.A. Bakuta. M.: Sov. radio. 1980.
9. Cantrell B.H., Trunk G.V. Angular Accuracy of a Scanning Radar Employing 2-pole Filter // IEEE Trans. AES-10. 1974. № 10.