density of distribution of probabilities
a method of the moments
a method of the maximum credibility
The decision of problems of the analysis and synthesis of algorithms of processing of signals at action of hindrances in radio engineering systems of different function is connected with necessity of representation of random variables and processes by various parametrical likelihood models. It is known that the amplitude of the signals extended on channels of a radio communication, represents at any moment in a point of reception a random variable. For its statistical representation often use likelihood model in the form of density of distribution of probabilities (DOP), being function of final number of parameters. Frequently in engineering practice there is a problem of estimation of parameters DOP when kind DOP of amplitude of a radio signal is known. Estimation is made by results of the supervision presented in a kind finite-dimensional of sample values of amplitude of a radio signal. For the decision of the given problem in practice use a method of the moments and a method of the maximum credibility. However in these methods are inherent both advantages, and lacks. For example, a serious lack of a method of the moments is limitation of its use because of absence for some laws of distribution in the form of DOP the sedate moments, and also the big error of estimation of parameters at small volume of sample. The method of a maximum of credibility also has lacks. Basic of them – absence in most cases the analytical decision. Therefore represents certain interest search of other methods of estimation of parameters DOP.
In work, in particular, it is offered for estimation of parameters DOP ampli-tudy radio signals to use gradients method. As a result during work the recurrent algorithm of estimation of parameters of laws of distribution of unilateral continuous random variables is synthesized. It is established that the error of approximation ПРВ with initial parameters distribution with the parameters estimated with use of recurrent algorithm ∆ makes an order of 3-5 %, whereas for DOP with the parameters estimated by a classical method of the moments, ∆ from an order of 10-13%.
The presented algorithm can be used at the decision of a problem of overcoming of parametrical aprioristic uncertainty at the known law of distribution of amplitude of radio signals in the course of synthesis of adaptive algorithms of processing of signals of the radio engineering systems of different function functioning in the conditions of changes of characteristics of information processes and revolting influences.