A NEW REDUCED-ORDER ADAPTIVE FILTER FOR STATE ESTIMATION IN HIGH-DIMENSIONAL SYSTEMS

A simple reduced-order adaptive filter, optimal in the sense of minimu m prediction error, is proposed for estimating the state of high-dimen sional systems in which the process and observation noise statistics a re unknown. It is shown that implementation of this adaptive filter re quires the solution of only two linear difference equations, the dimen sions of which are the dimensions of the full and reduced states, resp ectively, and that no solution of either an algebraic Riccati equation or a Lyapunov equation is needed. In addition, substantial gain in co mputer memory and CPU time is obtained by parametrization of the filte r gain in the form of the product of two matrices, one of which is a p rescribed projection from the reduced space onto the full space. A twi n experiment on data assimilation with a quasi-geostrophic ocean model shows the efficiency of the proposed approach. (C) 1997 Elsevier Scie nce Ltd.