Combining excessive data for spatial environmental monitoring
Ю. В. Кулявец, Олег Богатов, Олена Анатоліївна Єрмакова · Eastern-European Journal of Enterprise Technologies · 2013
Availability of information redundancy allows obtaining a total estimate by various relatively simple measuring instruments using a minimal sufficient set of primary measurements. The analysis of the known methods for solving this problem shows that the highest emphasis is placed on identifying the influence of measurement redundancy on the accuracy of estimates, and the problem of finding optimal algorithms of combining the estimates, in general correlated, is not considered. The algorithm of indirect estimation of the state vector based on the estimates of the observation vector is well studied. Along with this, the estimated parameters are, as a rule, associated with the nonlinear functional relations measured to initial estimates. Therefore, the direct use of the maximum likelihood method leads to the necessity of solving systems of nonlinear equations. It is possible to use two different approaches: linearization of nonlinear functional relations and iterative method (method of successive approximations). Herewith, the main advantage of the linearization method is that it allows obtaining the optimal (in this case the maximum likelihood) estimates of total parameter and correlation matrix of estimation errors in an explicit form. On this account, it is shown that the solution of the problem of the optimal use of estimates of the same state vector, obtained by various methods at the same time, is reduced to the consecutive application of the algorithm of estimates filtering. Thus, the optimal rule of finding of the total estimate and its accuracy is obtained. This rule, characterizing the measurement of the current parameter, is structurally similar to formulas for obtaining estimates with an account of the pre-experimental data, but significantly differs by the methodology of their obtaining.