QRD-RLS Adaptive Filtering 2009 edition

Marc Notes: Includes bibliographical references and index. Review Quotes: From the reviews: Starting with a review of the history and the essential concepts in (numerical) linear algebra that are essential in the development of QR decomposition, the book continues with an overview of adaptive filtering techniques, including LMS and RLS algorithms. The chapters flow on nicely from one to the other, and the editor is to be congratulated on achieving this. The book is a useful and welcome contribution to the broad topic of numerical linear algebra. (Andrew Dale, Zentralblatt MATH, Vol. 1170, 2009) Brief Description: This book provides tools and knowledge in a simple way so that the reader is able to implement a particular QRD-RLS algorithm tailored for the application at hand. The book comprehensively compiles the research of more than a decade into a single publication. Jacket Description/Back: QRD-RLS Adaptive Filtering covers some of the most recent developments as well as the basic concepts for a complete understanding of the QRD-RLS-based adaptive filtering algorithms. It presents this research with a clear historical perspective which highlights the underpinning theory and common motivating factors that have shaped the subject. The material is divided into twelve chapters, going from fundamentals to more advanced aspects. Different algorithms are derived and presented, including basic, fast, lattice, multichannel and constrained versions. Important issues, such as numerical stability, performance in finite precision environments and VLSI oriented implementations are also addressed. All algorithms are derived using Givens rotations, although one chapter deals with implementations using Householder reflections. QRD-RLS Adaptive Filtering is a useful reference for engineers and academics in the field of adaptive filtering. Review Quotes: From the reviews: Starting with a review of the history and the essential concepts in (numerical) linear algebra that are essential in the development of QR decomposition, the book continues with an overview of adaptive filtering techniques, including LMS and RLS algorithms. The chapters flow on nicely from one to the other, and the editor is to be congratulated on achieving this. The book is a useful and welcome contribution to the broad topic of numerical linear algebra. (Andrew Dale, Zentralblatt MATH, Vol. 1170, 2009)"Table of Contents: 1. QR Decomposition: An Annotated Bibliography / Marcello L. R. de Campos, Gilbert Strang -- 1.1. Preamble -- 1.2. Eigenvalues and Eigenvectors -- 1.3. Iterative Methods for the Solution of the Eigenproblem -- 1.3.1. The LR Algorithm -- 1.3.2. The QR algorithm -- 1.4. QR Decomposition for Orthogonalization -- 1.4.1. The classical Gram-Schmidt orthogonalization method -- 1.4.2. The modified Gram-Schmidt orthogonalization method -- 1.4.3. Triangularization via Householder reflections -- 1.4.4. Triangularization via Givens plane rotations -- 1.5. QR Decomposition for Linear Least Squares Problems -- 1.5.1. QR Decomposition by systolic arrays -- 1.6. QR Decomposition for Recursive Least Squares Adaptive Filters -- 1.6.1. Fast QR Decomposition RLS adaptation algorithms -- 1.7. Conclusion -- References -- 2. Introduction to Adaptive Filters / Jose A. Apolinario Jr, Sergio L. Netto -- 2.1. Basic Concepts -- 2.2. Error Measurements -- 2.2.1. The mean-square error -- 2.2.2. The instantaneous square error -- 2.2.3. The weighted least-squares -- 2.3. Adaptation Algorithms -- 2.3.1. LMS and normalized-LMS algorithms -- 2.3.2. Data-reusing LMS algorithms -- 2.3.3. RLS-type algorithms -- 2.4. Computer Simulations -- 2.4.1. Example 1: Misadjustment of the LMS algorithm -- 2.4.2. Example 2: Convergence trajectories -- 2.4.3. Example 3: Tracking performance -- 2.4.4. Example 4: Algorithm stability -- 2.5. Conclusion -- References -- 3. Conventional and Inverse QRD-RLS Algorithms / Jose A. Apolinario Jr, Maria D. Miranda -- 3.1. The Least-Squares Problem and the QR Decomposition -- 3.2. The Givens Rotation Method -- 3.3. The Conventional QRD-RLS Algorithm -- 3.4. Initialization of the Triangularization Procedure -- 3.5. On the Q?(k) Matrix -- 3.5.1. The backward prediction problem -- 3.5.2. The forward prediction problem -- 3.5.3. Interpreting the elements of Q?(k) for a lower triangular Cholesky factor -- 3.5.4. Interpreting the elements of Q?(k) for an upper triangular Cholesky factor -- 3.6. The Inverse QRD-RLS Algorithm -- 3.7. Conclusion -- Appendix 1 Appendix 2 Appendix 3. References -- 4. Fast QRD-RLS Algorithms / Jose A. Apolinario Jr, Paulo S. R. Diniz -- 4.1. Introduction -- 4.2. Upper Triangualarization Algorithms (Updating Forward Prediction Errors) -- 4.2.1. The FQR_POS_F algorithm -- 4.2.2. The FQR_PRI_F algorithm -- 4.3. Lower Triangularization Algorithms (Updating Backward Prediction Errors) -- 4.3.1. The FQR_POS_B algorithm -- 4.3.2. The FQR_PRI_B algorithm -- 4.4. The Order Recursive Versions of the Fast QRD Algorithms -- 4.5. Conclusion -- Appendix 1 Appendix 2 Appendix 3. References -- 5. QRD Least-Squares Lattice Algorithms / Jenq-Tay Yuan -- 5.1. Fundamentals of QRD-LSL Algorithms -- 5.2. LSL Interpolator and LSL Predictor -- 5.2.1. LSL interpolator -- 5.2.2. Orthogonal bases for LSL interpolator -- 5.2.3. LSL predictor -- 5.3. SRF Givens Rotation with Feedback Mechanism -- 5.4. SRF QRD-LSL Algorithms -- 5.4.1. QRD based on interpolation -- 5.4.2. SRF QRD-LSL interpolation algorithm -- 5.4.3. SRF QRD-LSL prediction algorithm and SRF joint process estimation -- 5.5. SRF (QRD-LSL)-Based RLS Algorithm -- 5.6. Simulations -- 5.7. Conclusion -- References -- 6. Multichannel Fast QRD-RLS Algorithms / Antonio L. L. Ramos, Stefan Werner -- 6.1. Introduction -- 6.2. Problem Formulation -- 6.2.1. Redefining the input vector -- 6.2.2. Input vector for sequential-type multichannel algorithms -- 6.2.3. Input vector for block-type multichannel algorithms -- 6.3. Sequential-Type MC-FQRD-RLS Algorithms -- 6.3.1. Triangularization of the information matrix -- 6.3.2. A priori and A posteriori versions -- 6.3.3. Alternative implementations -- 6.4. Block-Type MC-FQRD-RLS Algorithms -- 6.4.1. The backward and forward prediction problems -- 6.4.2. A priori and A posteriori versions -- 6.4.3. Alternative implementations -- 6.5. Order-Recursive MC-FQRD-RLS Algorithms -- 6.6. Application Example and Computational Complexity Issues -- 6.6.1. Application example -- 6.6.2. Computational complexity issues -- 6.7. Conclusion -- References -- 7. Householder-Based RLS Algorithms / Athanasios A. Rontogiannis, Sergios Theodoridis -- 7.1. Householder Transforms -- 7.1.1. Hyperbolic Householder transforms -- 7.1.2. Row Householder transforms -- 7.2. The Householder RLS (HRLS) Algorithm -- 7.2.1. Applications -- 7.3. The Householder Block Exact QRD-RLS Algorithm -- 7.4. The Householder Block Exact Inverse QRD-RLS Algorithm -- 7.5. Sliding Window (SW) Householder Block Implementation -- 7.6. Conclusion -- References -- 8. Numerical Stability Properties / Phillip Regalia, Richard Le Borne -- 8.1. Introduction -- 8.2. Preliminaries -- 8.2.1. Conditioning, forward stability, and backward stability -- 8.3. The Conditioning of the Least-Squares Problem -- 8.3.1. The conditioning of the least-squares problem -- 8.3.2. Consistency, stability, and convergence -- 8.4. The Recursive QR Least-Squares Methods -- 8.4.1. Full QR decomposition adaptive algorithm -- 8.5. Fast QR Algorithms -- 8.5.1. Past input reconstruction -- 8.5.2. Reachable states in fast least-squares algorithms -- 8.5.3. QR decomposition lattice algorithm -- 8.6. Conclusion -- References -- 9. Finite and Infinite-Precision Properties of QRD-RLS Algorithms / Paulo S. R. Diniz, Marcio G. Siqueira -- 9.1. Introduction -- 9.2. Precision Analysis of the QR-Decomposition RLS Algorithm -- 9.2.1. Infinite-precision analysis -- 9.2.2. Stability analysis -- 9.2.3. Error propagation analysis in steady-state -- 9.2.4. Simulation results -- 9.3. Precision Analysis of the Fast QRD-Lattice Algorithm -- 9.3.1. Infinite-precision analysis -- 9.3.2. Finite-precision analysis -- 9.3.3. Simulation results -- 9.4. Conclusion -- References -- 10. On Pipelined Implementations of QRD-RLS Adaptive Filters / Jun Ma, Keshab K. Parhi -- 10.1. QRD-RLS Systolic Architecture -- 10.2. The Annihilation-Reording Look-Ahead Technique -- 10.2.1. Look-ahead through bloack processing -- 10.2.2. Look-ahead through iteration -- 10.2.3. Relationship with multiply-and look-ahead -- 10.2.4. Parallelism in annihilation-recording look-ahead -- 10.2.5. Pipelined and block processing implementations -- 10.2.6. Invariance of bounded input and bounded output -- 10.3. Pipelined CORDIC-Based RLS Adaptive Filters -- 10.3.1. Pipelined QRD-RLS with implicit weight extraction -- 10.3.2. Stability analysis -- 10.3.3. Pipelined QRD-RLS with explicit weight extraction -- 10.4. Conclusion -- Appendix -- References -- 11. Weight Extraction of Fast QRD-RLS Algorithms / Stefan Werner, Mohammed Mobien -- 11.1. FQRD-RLS Preliminaries -- 11.1.1. QR decomposition algorithms -- 11.1.2. FQR_POS_B algorithm -- 11.2. System Identification with FQRD-RLS -- 11.2.1. Weight extraction in the FQRD-RLS algorithm -- 11.2.2. Example -- 11.3. Burst-trained Equalizer with FQRD-RLS -- 11.3.1. Problem description -- 11.3.2. Equvalent-output filtering -- 11.3.3. Equivalent-output filtering with explicit weight extraction -- 11.3.4. Example -- 11.4. Active Noise Control and FQRD-RLS -- 11.4.1. Filtered-s RLS -- 11.4.2. Modified filtered-x FQRD-RLS -- 11.4.3. Example -- 11.5. Multichannel and Lattice Implementations -- 11.6. Conclusion -- References -- 12. On Linearly Constrained QRD-Based Algorithms / Shiunn-Jang Chern -- 12.1. Introduction -- 12.2. Optimal Linearly Constrained QRD-LS Filter -- 12.3. The Adaptive LC-IQRD-RLS Filtering Algorithm -- 12.4. The Adaptive GSC-IQRD-RLS Algorithm -- 12.5. Applications -- 12.5.1. Application 1: Adaptive LCMV filtering for spectrum estimation -- 12.5.2. Application 2: Adaptive LCMV antenna array beamformer -- 12.6. Conclusion -- References -- Index.