Nonlinear parameter estimation by the point-mass method taking into account correlation of partial estimates

A new solution to the problem of nonlinear parameter estimation is considered. The peculiarity of this problem is that the arguments of a nonlinear function are not only the measurement data and the required parameters, but also supplementary parameters. Supplementary parameters are a priori unknown, but they are necessary only to find optimal estimates of the required parameters. The estimate of the desired parameters is formed according to the point-mass method as a weighted sum of partial estimates obtained for the specified values of supplementary parameters. This solution allows us to eliminate a priori probabilities for supplementary parameters by taking into account additional covariance of weight coefficients and (or) specified partial estimates. The considered approach is effective in solving specified nonlinear estimation problems characterized by low accuracy of available measurement data and (or) their few number.