Subspace Methods for System Identification and Signal Processing

Doctoral thesis, 1999

The main theme of this thesis is black-box mathematical modeling of discrete-time, finite-dimensional, and linear dynamical systems, i.e. system identification. The thesis addresses both systems with and without exogenous inputs. The first part of the thesis focuses on systems that are time-invariant. Special attention is given to interpretations and statistical analysis of subspace methods for system identification. Applying a novel quality measure, based on principal angles between subspaces, a result of the statistical analysis is that a new identification algorithm is proposed. Furthermore, an instrumental variable (IV) framework is proposed, which encompasses a large class of existing methods. Based on this IV approach and on a statistical analysis, the thesis proposes improvements of existing subspace methods for closed loop and errors-in-variables identification. The thesis also addresses a specific multivariable identification problem without exogenous inputs; often termed signal separation. Attention is given to statistical analysis of an existing algorithm for signal separation. As a result of this analysis, a modified algorithm is proposed, which has lower asymptotic variance of the estimated mixing parameters. The second part of the thesis focuses on systems that are time-varying. The problem of interest is adaptive estimation. In this context, the main contribution is the development of computationally efficient algorithms for adaptive identification of multivariable systems. The proposed algorithms draw heavily on the application of so-called subspace tracking algorithms. Therefore, effort is devoted to finding computationally efficient subspace tracking algorithms applicable to the studied scenario. The obtained subspace tracking algorithms are also useful in sensor array signal processing applications. Furthermore, a direction finding algorithm using sensor array data is derived, which is applicable to the case of colored measurement noise. The main strength of this method, is that no singular value decomposition needs to be computed, which decreases the overall computational cost.