Based On Delta Operator Parameter Estimation And Filtering

Delta operator is a new discretization method. In processing high sampling data system, discrete time model using delta operator approaches corresponding continuous time model, and the results also tends to the corresponding ones of its continuous counterpart. As the sampling rates increase, the numerical instability problems caused by the conventional shift operator can be well conquered by the delta operator.In this thesis, the problems of parameter estimation and filtering for delta operator systems are studied. The main contributions are as follows:1) Both the state-space model and the transfer function model using delta operator are studied. Based on vectors and matrices, the transformation between Delta and Z domain transfer function is obtained. The simulation results show the validity of the proposed algorithm.2) Parameter estimation of autoregression moving average model (ARMA) is developed. By the delta matrix inverse lemma and common form of delta operator recursive least squares algorithm, the delta operator extend least squares and forgetting factor algorithm for ARMA model are derived.3) Delta least squares lattice filter is studied. Based on the least squares lattice filter by shift operator and the conception of least squares orthogonal projection in Hilbert linear vector space, the order and time update formulae are presented. In addition, the lattice algorithms of the coefficients for the delta operator AR model are also given.