Error Analysis of Certain Subspace Methods

Abstract Some subspace methods make use of an oblique projection to determine the observability matrix. There is experimental evidence (Chiuso and Picci, 1999; Kawauchi et al., 1999) that these methods perform poorly in certain situations. In this paper we present an error analysis of oblique projections and show that in some situations small errors in the subspace along which the projection is done may lead to large errors in the estimate. This may happen for instance in the N4SID algorithm. Sometimes an orthogonal projection should be recommended instead; in fact, it can be shown that the worst case "signal to noise" ratio on the rows of the estimated observability matrix is larger for orthogonal projections than for oblique projections. A variance analysis is presented and simulations are included which compare oblique projection based algorithms with the orthogonal projection.

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