THE TRUE LOCAL MAXIMUM A-POSTERIORI PROBABILITY IN THE IDENTIFICATION AND ESTIMATION PROBLEM WITH NONDISCRETE DISTRIBUTION OF THE UNDETERMINED PARAMETERS

The combined problem of identifying the vector Y of parameters and estimation of the state X of a linear dynamic system is studied when the a priori probability density of the vector Y is defined on a nondiscrete set GAMMA, and the measurements of Z are essentially nonlinear in Y. The corresponding nonlinear programming problem for the optimal parameters (with respect to the criterion of maximum a posteriori probability density for estimates of the parameters and the state) is, in the general case, multimodal, and this gives rise to the problem of estimating the "true" extremum, that is, an extremum whose neighborhood includes the vector of the parameters that is being realized. In the region of the true local maximum a posteriori probability, specific properties of the objective function of the nonlinear programming problem are revealed. As a result, the a priori probability of existence of a true maximum a posteriori probability and the a priori probabilistic boundaries of the true local maximum a posteriori probability can be calculated. Analysis of the behavior of these probabilistic characteristics makes it possible, in practical applications, to optimize the program of measurements and to construct rational procedures for nonlinear identification.