Interpretation of Subspace Methods : Consistency Analysis

Technical reports from the Automatic Control group in Linkk oping are available by anonymous ftp at the address ftp.control.isy.liu.se. This report is contained in the compressed postscript le 2103.ps.Z. Abstract: So called subspace methods for direct identiication of linear state space models form a very useful alternative to maximum-likelihood type approaches, in that they are non-iterative and ooer eecient numerical implementations. The algorithms consist of series of quite complex projections, and it is not so easy to intuitively understand how they work. The asymptotic analysis of them is also complicated. This contribution describes an interpretation of how they work in terms of k-step ahead predictors of carefully chosen orders. It speciically deals how consistent estimates of the dynamics can be achieved, even though correct predictors are not used. This analysis gives some new angles of attack to the problem of asymptotic behavior of the subspace algorithms.