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Elements of the Theory of Inverse Correlational Problems

Keywords:

D. V. Vasilyev, A. V. Gapon


Direct correlational problems, which arise during pattern recognition and signal detection, are usually solved using in-phase correlational characteristics (CC) as a measure of signal’s similarity to an etalon. Inverse correlational problems occur when it is necessary to measure a shift between signals in the processes of navigation and automatic orientation. Thus, in addition to even CCs, a class of odd “orthocorrelation” functions, suitable to be a linear measure of shifted signals’ distinction, is considered. Odd CCs make unnecessary the use of time-consuming extremum search operations. The mathematical apparatus of orthocorrelation may be applied as a generalized description of searchless algorithms for obtaining shift information from signals being compared, accounting for the input channels’ properties of a measuring unit. The algorithms developed in the article are based on the solution by the generalized least squares method of the variational problem of approximation of functions that differ in some vector of parameters. Orthocorrelation coefficient of a finite signal describes in general case the procedure of obtaining the normalized linear shift estimation between its current and etalon realizations. Orthocorrelational measuring units provide a “strict zero” of the discriminatory characteristics and a subpixel accuracy of partial shift estimation. Due to the complexity of simultaneous accounting for a large set of factors in multidimensional optoelectronic tracking systems with machine vision their optimization in practical cases is achieved step-by-step by the use of statistic modeling and simplifying approximations on each stage.
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