On performance analysis of subspace methods in system identification and sensor array processing

Sammanfattning: This thesis addresses the issue of performance analysis of subspace-based parameter estimation methods in two different applications, namely system identification and sensor array processing.  The objective is to study the quality of the estimated models as the amount of data increases, and to suggest improvements and give user guidelines. First, state-space subspace system identification (4SID) methods are formulated in a linear regression framework. This allows us to analyze the problem in a more traditional way. One advantage is that this explains more clearly the effect of the partition of the data in past and future, which is done in  4SID. Also this formulation is useful to relate and compare different proposed approaches to 4SID. The problem of estimating the poles of dynamical systems is considered. In particular, the statistical asymptotic distributions of the parameter estimates of two different 4SID pole estimation methods are studied. The first method is  common in 4SID  and  makes use of the shift invariance structure of the observability matrix, while the  second method is a recently proposed weighted least-squares method. From these results the choice of user-specified parameters is discussed, and it is shown that this choice indeed may not be obvious for the shift invariance method. A simple example is provided to illustrate the problem. However, this problem can be mitigated using more of the system structure. It is also shown that a proposed row weighting matrix in the subspace estimation step does not affect the asymptotic properties of the pole estimates. In the second part focusing on sensor array signal processing, parameter estimation from sparse linear arrays is addressed. An algorithm based on the Expectation-Maximization approach is derived. This is an iterative algorithm for solving  maximum likelihood problems. In our application a powerful method  for uniform linear arrays is used in the maximization step. The use of preprocessing of the covariance matrix before applying a direction of arrival estimation algorithm is also considered. In particular, linear preprocessing of covariance data in conjunction with weighted subspace fitting is analyzed and the asymptotic distribution of the parameter estimates is derived. Some possible applications when the preprocessing and the analysis may be useful are also given.