D. S. Dunin, V. V. Latyshev

Model of observation is an additive mixture of a signal known form with one or two unknown parameters, and noise with Gaussian probability density function. Available data has a large dimension. First, you can to implement reduction of data dimension, and then perform the parameters estimation, using a new compact representation of the data. To reduce the data dimension we obtain the orthogonal decomposition of observed data and reject the members with a small influence on the final result of solving a problem. This is similar to Kurhunen - Loeve decomposition, but we associate this with the problem of parameter estimation. As it is known, the estimation accuracy is inversely proportional to the Fisher-s information on the estimated parameter. In order to reduce the dimension without the deterioration potential accuracy of estimation we minimize the Fisher-s information losses on the estimated parameter. In the case of the Bayesian estimation procedure this approach allows to reduce significantly the amount of calculations. The article presents the results of simulation with the Doppler shift estimation. The results show that the dimension reduction of the data from 100 up to 3 does not affect the accuracy of estimation. At the same time computational complexity of the Bayesian algorithm is two order of magnitude less in this example. If the estimated parameter nonlinear associated with the observed data, a well-known method of maximum likelihood is asymptotically optimal. This means that its accuracy worse than theoretical Cramer-Rao bound for small and medium values of the signal to noise ratio. The dimension reduction gives means to increase the accuracy of estimation due to more complete extraction of the Fisher-s information of the observed data. Each component of new vector can be used to estimate the interested parameter using the method of maximum likelihood. Then separate estimates are averaged. As a result it is possible to obtain estimation error is less than for the classical realization of maximum likelihood estimate. Our method brings it closer to the theoretical Cramer-Rao bound. The reduction of dimension allows you to get additional advantage. It is possible to obtain invariant statistics for estimation of some parameters regardless of other changes. To obtain the invariant statistics we use the solution of generalized linear eigenvalues problem of matrix pairs. Each of the matrices of the pair is the Fisher-s information matrix with respect to the estimated parameter. As an illustration we use signal with phase changes in accordance to the 7-bits M-sequences.