V.N. Zhurakovsky - Ph.D. (Eng.), Associate Professor, Department SM-6, BMSTU E-mail: Zhurakovsky@sm.bmstu.ru A.S. Logvinenko - Engineer of SM2-2, NIISM GOU VPO BMSTU (Moscow) E-mail: nyusha.logvinenko@mail.ru

The use of MLE for different kinds of problems often associated with computational problems, as in most cases, the task of finding the extremes of objective functions, obtained by transformation of the likelihood function has no analytical solution, therefore, numerical methods must be solved. Despite the development in the field of digital processing, the issue of optimization of computing time remains relevant. The article describes an example of solving such problems - optimization of multimodal objective function resulting from the use of the LME to assess the frequency mixed signal. In modern literature as a multimodal function optimization techniques given in the main scanning method and the method of polygonal lines. The first - a costly, high accuracy required, the second - is not always guaranteed to give the correct result. Therefore, it was decided to identify the main features of the behavior of the objective function on the basis of the information received to synthesize optimization algorithm for a particular problem to be solved. In this regard, a study was conducted of influence of the main parameters of the input signal (SNR, amplitude, frequency of absolute values and their difference) in the form of the objective function, in which was revealed the general behavior of the objective function. The following features were identified: There is a minimum width of the segment considered unimodal objective function in which the local maximum is global. Based on this information it was synthesized by two-stage optimization algorithm, involving sequential determination area near global extremum via scan method and with a big step further clarification of its values using standard unimodal optimization functions. A comparison of simple scanning method and the proposed combined method of optimization in their application to this problem. The comparison showed the effectiveness of the synthesized algorithm optimization - when specifying the precision of finding the extremum of the computation time in the second algorithm is reduced by ten times compared with the scanning method. A similar method of synthesis optimization algorithm can be used to solve optimization problems of various multimodal objective functions arising from the application of MLE to other tasks.

 

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