Topic
Recursive least squares filter
About: Recursive least squares filter is a research topic. Over the lifetime, 8907 publications have been published within this topic receiving 191933 citations.
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28,888 citations
Book•
01 Jan 1986
TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.
Abstract: Background and Overview. 1. Stochastic Processes and Models. 2. Wiener Filters. 3. Linear Prediction. 4. Method of Steepest Descent. 5. Least-Mean-Square Adaptive Filters. 6. Normalized Least-Mean-Square Adaptive Filters. 7. Transform-Domain and Sub-Band Adaptive Filters. 8. Method of Least Squares. 9. Recursive Least-Square Adaptive Filters. 10. Kalman Filters as the Unifying Bases for RLS Filters. 11. Square-Root Adaptive Filters. 12. Order-Recursive Adaptive Filters. 13. Finite-Precision Effects. 14. Tracking of Time-Varying Systems. 15. Adaptive Filters Using Infinite-Duration Impulse Response Structures. 16. Blind Deconvolution. 17. Back-Propagation Learning. Epilogue. Appendix A. Complex Variables. Appendix B. Differentiation with Respect to a Vector. Appendix C. Method of Lagrange Multipliers. Appendix D. Estimation Theory. Appendix E. Eigenanalysis. Appendix F. Rotations and Reflections. Appendix G. Complex Wishart Distribution. Glossary. Abbreviations. Principal Symbols. Bibliography. Index.
16,062 citations
Book•
01 Apr 1996
TL;DR: Theorems and statistical properties of least squares solutions are explained and basic numerical methods for solving least squares problems are described.
Abstract: Preface 1. Mathematical and statistical properties of least squares solutions 2. Basic numerical methods 3. Modified least squares problems 4. Generalized least squares problems 5. Constrained least squares problems 6. Direct methods for sparse problems 7. Iterative methods for least squares problems 8. Least squares problems with special bases 9. Nonlinear least squares problems Bibliography Index.
3,405 citations
1,339 citations
TL;DR: A novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem is presented, and it is shown that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation.
Abstract: Subspace estimation plays an important role in a variety of modern signal processing applications. We present a new approach for tracking the signal subspace recursively. It is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem. We show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation. The resulting algorithms have a computational complexity of O(nr) where n is the input vector dimension and r is the number of desired eigencomponents. Simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition. Relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed. >
1,325 citations