FEATURES OF USE OF MONTE-CARLO METHOD FOR APPROXIMATION OF STATISTICAL DISTRIBUTIONS OF RESULTS OF NONLINEAR TRANSFORMATIONS IN RADAR-TRACKING PROBLEMS

Abstract

An approach to the decision of mathematical problems with use of modelling random variables, the method which has received the name of Monte-Carlo is considered. The given method has got the greatest popularity for numerical calculation of high frequency rate integrals because it is rather easily realised on modern computers.
Possibility of use Monte-Carlo method for statistical approximation of radar-tracking data distributions at which the initial density of probability is replaced with its discrete analogue, which formed on the basis of random samples (particles) weights is illustrated. Nonlinear transformations of observable data are widely used at the decision of some problems connected with processing of random realisations of observable signals (radar-tracking, radio navigating, coherent, etc.) Noted transformations inevitably lead to transformation of distribution laws of the solving statistics which results it is rather difficult described by analytical methods. In article the basic features of application statistical approximation method for typical distributions, formed as a result of nonlinear transformations of radar-tracking observation data are considered. It is shown, that at some nonlinear transformations errors of law the distributions approximations caused by effect «scanty» of sample are observed. It is shown, that the effect «scanty» samples is overcome by a resampling of random particles in
a vicinity of the most significant samples. The resulted material allows to expand a scope of the numerical methods, based on use of modelling random variables.