Subspace Fitting Method Research Articles

A linear regression approach to state-space subspace system identification

Recently, state-space subspace system identification (4SID) has been suggested as an alternative to the more traditional prediction error system identification. The aim of this paper is to analyze the connections between these two different approaches to system identification. The conclusion is that 4SID can be viewed as a linear regression multistep-ahead prediction error method with certain rank constraints. This allows us to describe 4SID methods within the standard framework of system identification and linear regression estimation. For example, this observation is used to compare different cost-functions which occur rather implicitly in the ordinary framework of 4SID. From the cost-functions, estimates of the extended observability matrix are derived and related to previous work. Based on the estimates of the observability matrix, the asymptotic properties of two pole estimators, namely the shift invariance method and a weighted subspace fitting method, are analyzed. Expressions for the asymptotic variances of the pole estimation error are given. From these expressions, difficulties in choosing userspecified parameters are pointed out. Furthermore, it is found that a row-weighting in the subspace estimation step does not affect the pole estimation error asymptotically.

A subspace fitting method for identification of linear state-space models

A new method is presented for the identification of systems parameterized by linear state-space models. The method relies on the concept of subspace fitting, wherein an input/output data model parameterized by the state matrices is found that best fits, in the least-squares sense, the dominant subspace of the measured data. Some empirical results are included to illustrate the performance advantage of the algorithm compared to standard techniques.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On Di's and subspace fitting approaches to direction estimation

The article relates the method for direction estimation in possibly coherent scenarios, which was proposed by Di (1985), to the class of subspace fitting (SSF) methods recently introduced in the literature. It also makes some general comments on the SSF class.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Second-order statistical analysis of totally weighted subspace fitting methods

We analyze the effects of a limited number of snapshots on a general class of multidimensional signal subspace estimation methods, termed totally weighted subspace fitting (TWSF) methods. This class is an extension of the weighted subspace fitting technique that includes row weighting and column weighting of the signal subspace matrix. We quantify the asymptotic statistical properties of the TWSF method by means of a second-order statistical analysis. The main contribution of this article is that it provides, for the first time, the estimator bias. Some simulation results are included to validate our analytical results. >

Analysis of the combined effects of finite samples and model errors on array processing performance

The principal sources of estimation error in sensor array signal processing applications are the finite sample effects of additive noise and imprecise models for the antenna array and spatial noise statistics. While the effects of these errors have been studied individually, their combined effect has not yet been rigorously analyzed. The authors undertake such an analysis for the class of so-called subspace fitting algorithms. In addition to deriving first-order asymptotic expressions for the estimation error, they show that an overall optimal weighting exists for a particular array and noise covariance error model. In a companion paper, the optimally weighted subspace fitting method is shown to be asymptotically equivalent with the more complicated maximum a posteriori estimator. Thus, for the model in question, no other method can yield more accurate estimates for large samples and small model errors. Numerical examples and computer simulations are included to illustrate the obtained results and to verify the asymptotic analysis for realistic scenarios. >

Sensor array processing based on subspace fitting

Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace-fitting-based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method. The asymptotic distribution of the estimation error is derived for a general subspace weighting, and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals. >

Subspace fitting concepts in sensor array processing

The area of sensor array processing has recently received considerable attention in the litterature. Much interest stems from the potential of applying advanced concepts from signal processing to a variety of real-world problems. In these applications, spatially distributed sensors are used to detect and locate multible emitters and/or to seperate the individual encountered in communication and radar applications, when the signal transmission is subject to undesired interference. Acoustic devices (hydrophones) are used in, e.g., underwater and seismic applications.A vast number of methods have been proposed for estimating unknown parameters of the received wavefronts. In Part II of this thesis, an attempt is made to examine the relations among many of these techniques, as well as the accuracy of the resulting estimates. Several estimation methods are posed as solutions to different versions of a basic subspace fitting problem. The asymptotic (for large data records) performance of the multidimensional subspace fitting methods is investigated in Parts II, IV, and V. A new estimator, termed the Weighted Subspace Fitting (WSF) method is introduced and analysed. The WSF method is shown to be a unification of the subspace fitting techniques and the stochastic Maximum Likelihood method, valid for large amounts of data. The analysis is carried out for the case of Gaussian noise and Gaussian/nonGaussian signal waveforms.In Part III, a numerical procedure for calculating the WSF estimates is proposed. A detection scheme based on the WSF method is also suggested, and shown to yield a consistent estimate of the number of coherent/non-coherent wavefronts.Part VI deals with the problem of separating a desired signal from unwanted disturbances. The desired signal is assumed to be absent in certain time (or frequency) intervals, and the proposed method requires no calibration of the array and involves no numerical search.