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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TL;DR: This letter proposes two new variable step-size algorithms for normalized least mean square and affine projection that lead to faster convergence rate and lower misadjustment error.
Abstract: This letter proposes two new variable step-size algorithms for normalized least mean square and affine projection. The proposed schemes lead to faster convergence rate and lower misadjustment error.
529 citations
01 Jan 1998
TL;DR: This paper presents a numerically stable non-iterative algorithm for fitting an ellipse to a set of data points based on a least squares minimization which leads to a simple, stable and robust fitting method which can be easily implemented.
Abstract: This paper presents a numerically stable non-iterative algorithm for fitting an ellipse to a set of data points. The approach is based on a least squares minimization and it guarantees an ellipse-specific solution even for scattered or noisy data. The optimal solution is computed directly, no iterations are required. This leads to a simple, stable and robust fitting method which can be easily implemented. The proposed algorithm has no computational ambiguity and it is able to fit more than 100,000 points in a second.
520 citations
TL;DR: In this article, an optimal two-stage identification algorithm is presented for Hammerstein-Wiener systems, where two static nonlinear elements surround a linear block, and the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise.
519 citations
30 Jul 2007
TL;DR: The message-passing approach to model-based signal processing is developed with a focus on Gaussian message passing in linear state-space models, which includes recursive least squares, linear minimum-mean-squared-error estimation, and Kalman filtering algorithms.
Abstract: The message-passing approach to model-based signal processing is developed with a focus on Gaussian message passing in linear state-space models, which includes recursive least squares, linear minimum-mean-squared-error estimation, and Kalman filtering algorithms. Tabulated message computation rules for the building blocks of linear models allow us to compose a variety of such algorithms without additional derivations or computations. Beyond the Gaussian case, it is emphasized that the message-passing approach encourages us to mix and match different algorithmic techniques, which is exemplified by two different approaches - steepest descent and expectation maximization - to message passing through a multiplier node.
517 citations
01 May 2004
TL;DR: In this paper, the authors present an overview of the literature on adaptive filtering for speech processing and its application in the context of noise control. But their focus is on the use of lowpass filters.
Abstract: List of Figures.List of Tables.Preface.Acknowledgments.Abbreviations and Acronyms.Part I: Basics.1 Introduction.1.1 Some History.1.2 Overview of the Book.2 Acoustic Echo and Noise Control Systems.2.1 Notation.2.2 Applications.3 Fundamentals.3.1 Signals.3.2 Acoustic Echoes.3.3 Standards.Part II: Algorithms.4 Error Criteria and Cost Functions.4.1 Error Criteria for Adaptive Filters.4.2 Error Criteria for Filter Design.4.3 Error Criteria for Speech Processing and Control Purposes.5 Wiener Filter.5.1 Time-Domain Solution.5.2 Frequency-Domain Solution.6 Linear Prediction.6.1 Normal Equations.6.2 Levinson{Durbin Recursion.7 Algorithms for Adaptive Filters.7.1 The Normalized Least Mean Square Algorithm.7.2 The Affine Projection Algorithm.7.3 The Recursive Least Squares Algorithm.7.4 The Kalman Algorithm.Part III: Acoustic Echo and Noise Control.8 Traditional Methods for Stabilization of Electroacoustic Loops.8.1 Adaptive Line Enhancement.8.2 Frequency Shift.8.3 Controlled Attenuation.9 Echo Cancellation.9.1 Processing Structures.9.2 Stereophonic and Multichannel Echo Cancellation.10 Residual Echo and Noise Suppression.10.1 Basics.10.2 Suppression of Residual Echoes.10.3 Suppression of Background Noise.10.4 Combining Background Noise and Residual Echo Suppression.11 Beamforming.11.1 Basics.11.2 Characteristics of Microphone Arrays.11.3 Fixed Beamforming.11.4 Adaptive Beamforming.Part IV: Control and Implementation Issues.12 System Control-Basic Aspects.12.1 Convergence versus Divergence Speed.12.2 System Levels for Control Design.13 Control of Echo Cancellation Systems.13.1 Pseudooptimal Control Parameters for the NLMS Algorithm.13.2 Pseudooptimal Control Parameters for the Affine Projection Algorithm.13.3 Summary of Pseudooptimal Control Parameters.13.4 Detection and Estimation Methods.13.5 Detector Overview and Combined Control Methods.14 Control of Noise and Echo Suppression Systems.14.1 Estimation of Spectral Power Density of Background Noise.14.2 Musical Noise.14.3 Control of Filter Characteristics.15 Control for Beamforming.15.1 Practical Problems.15.2 Stepsize Control.16 Implementation Issues.16.1 Quantization Errors.16.2 Number Representation Errors.16.3 Arithmetical Errors.16.4 Fixed Point versus Floating Point.16.5 Quantization of Filter Taps.Part V: Outlook and Appendixes.17 Outlook.Appendix A: Subband Impulse Responses.A.1 Consequences for Subband Echo Cancellation.A.2 Transformation.A.3 Concluding Remarks.Appendix B: Filterbank Design.B.1 Conditions for Approximately Perfect Reconstruction.B.2 Filter Design Using a Product Approach.B.3 Design of Prototype Lowpass Filters.B.4 Analysis of Prototype Filters and the Filterbank System.References.Index.
498 citations