Analysis of accuracy in evaluating gravimetric coefficients in the algorithm of spatial monitoring under conditions of excess

Abstract

Information excess allows obtaining the resulting estimate by a variety of relatively simple measuring devices and using a minimally sufficient set of primary measurements. At the same time, the estimated parameters are typically associated with the initially measured estimates on the basis of nonlinear functional equations. Therefore, a direct use of the maximum likelihood method makes it necessary to solve a system of nonlinear equations. The use of the linearization method for nonlinear functional correlations allows obtaining explicitly optimal estimates (in this case, the most plausible ones) of the resulting parameter and the correlation matrix of assessment errors. The problem of an optimal use of assessments provided by the same state vector through different simultaneously applied methods can be solved by a consistent application of the estimates’ filtering algorithm. However, the weight coefficient matrix in the expression for determining the resulting estimate depends on the measured parameter values, and it is not always known a priori. One of the possible methods of obtaining the estimates of the weight coefficients matrix is to calculate direct estimates of error correlation matrices on the basis of independent discrete samples of estimates for the parameter state vector. Analytical expressions were obtained for mathematical expectation and variance of the assessment components of the error correlation matrix for determining the parameter state vector. The study has shown that the assessment accuracy depends both on the accuracy of the measuring devices and the length of the samples’ line taken to determine the error correlation matrix for the parameter evaluation.