WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 15, 2016
On a Simple Numerical Method for Estimation of an Unknown Matrix. Application to Adaptive Filtering Based Innovation Approach
Authors: ,
Abstract: We describe a simple algorithm for estimating the elements of a matrix as well as its product decomposition under the condition that only the matrix-vector product is accessible. This algorithm is based on application of the stochastic simultaneous perturbation (SSP) method. Such problems arise frequently in solving inverse problems, nonlinear filtering and control of dynamical systems, especially in data assimilation in high dimensional systems where the numerical model is given by a computer code and the error covariance matrix is to be estimated in order to specify the filter gain for state estimation. Theoretical results on the convergence of the proposed algorithm are proven, its efficiency is demonstrated in numerous engineering estimation problems, especially for the design of an adaptive filter for data assimilation in a high dimensional ocean model.
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Keywords: Numerical differentiation, Stochastic simultaneous perturbation, Statistical simulation, Dynamical system, Real Schur vectors, ocean numerical model, data assimilation
Pages: 290-308
WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 15, 2016, Art. #31