Reduced-Order System Identification Using The Karhunen-Loeve Transform

Abstract

This paper presents a procedure for empirically generating a reduced- order model of a system given a plethora of sensor data. Data reduction is performed at the onset by projection onto an orthogonal subspace to yield a reduced-order state. The reduced-order state is estimated at each point in time using spatial filtering. Spatial filtering is a suboptimal state estimation technique which has the advantage of decoupling the state estimation and system identification problems. State space system identification is then performed given the estimates of the reduced-order suite. The truncated Karhunen-Loeve (KL) transform is used to define the reduced-order state. The KL transform is optimal for the initial data reduction and yields a number of simplifications in the state estimation and system identification algorithms. A recursive formulation of the entire procedure is presented. The algorithm is illustrated by application to an example.