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66 Subspace Tracking

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Most high resolution direction-of-arrival (DOA) estimation methods rely on subspace or eigenbased information which can be obtained fromthe eigenvalue decomposition (EVD) of an estimated correlation matrix, or from the singular value decomposition (SVD) of the corresponding data matrix. | R. D. De Groat et. Al. Subspace Tracking. 2000 CRC Press LLC. http www.engnetbase.com . Subspace Tracking R.D. DeGroat The University of Texas at Dallas E.M. Dowling The University of Texas at Dallas D.A. Linebarger The University of Texas at Dallas 66.1 Introduction 66.2 Background EVD vs. SVD Short Memory Windows for Time Varying Estimation Classification of Subspace Methods Historical Overview of MEP Methods Historical Overview of Adaptive Non-MEP Methods 66.3 Issues Relevant to Subspace and Eigen Tracking Methods Bias Due to Time Varying Nature of Data Model Controlling Roundoff Error Accumulation and Orthogonality Errors Forward-Backward Averaging Frequency vs. Subspace Estimation Performance The Difficulty of Testing and Comparing Subspace Tracking Methods Spherical Subspace SS Updating A General Framework for Simplified Updating Initialization of Subspace and Eigen Tracking Algorithms Detection Schemes for Subspace Tracking 66.4 Summary of Subspace Tracking Methods Developed Since 1990 Modified Eigen Problems Gradient-Based Eigen Tracking The URV and Rank Revealing QR RRQR Updates Miscellaneous Methods References 66.1 Introduction Most high resolution direction-of-arrival DOA estimation methods rely on subspace or eigenbased information which can be obtained from the eigenvalue decomposition EVD of an estimated correlation matrix or from the singular value decomposition SVD of the corresponding data matrix. However the expense of directly computing these decompositions is usually prohibitive for real-time processing. Also because the DOA angles are typically time-varying repeated computation is necessary to track the angles. This has motivated researchers in recentyears to develop low cost eigen and subspace tracking methods. Four basic strategies have been pursued to reduce computation 1 computing only a few eigencomponents 2 computing a subspace basis instead of individual eigencomponents 3 approximating the eigencomponents or basis and 4 recursively .