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Linear Prediction Theory A Mathematical Basis for Adaptive Systems

Lnear prediction theory and the related algorithms have matured to the point where they now form an integral part of many real-world adaptive systems. When it is necessary to extract information from a random process, we are frequently faced with the problem of analyzing and solving special systems...

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Bibliographic Details
Main Author: Strobach, Peter
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1990, 1990
Edition:1st ed. 1990
Series:Springer Series in Information Sciences
Subjects:
Engineering Mathematics
Calculus Of Variations And Optimization
Control Theory
Systems Theory, Control
System Theory
Mathematical Physics
Discrete Mathematics
Engineering / Data Processing
Mathematical Optimization
Theoretical, Mathematical And Computational Physics
Mathematical And Computational Engineering Applications
Calculus Of Variations
Mathematical Methods In Physics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 4.5 Recursive QR Decomposition Using a Second-Order Window
  • 4.6 Alternative Formulations of the QRLS Problem
  • 4.7 Implicit Error Computation
  • 4.8 Chapter Summary
  • 5. Recursive Least-Squares Transversal Algorithms
  • 5.1 The Recursive Least-Squares Algorithm
  • 5.2 Potter’s Square-Root Normalized RLS Algorithm
  • 5.3 Update Properties of the RLS Algorithm
  • 5.4 Kubin’s Selective Memory RLS Algorithms
  • 5.5 Fast RLS Transversal Algorithms
  • 5.6 Descent Transversal Algorithms
  • 5.7 Chapter Summary
  • 6. The Ladder Form
  • 6.1 The Recursion Formula for Orthogonal Projections
  • 6.2 Computing Time-Varying Transversal Predictor Parameters from the Ladder Reflection Coefficients
  • 6.3 Stationary Case — The PARCOR Ladder Form
  • 6.4 Relationships Between PARCOR Ladder Form and Transversal Predictor
  • 6.5 The Feed-BackPARCOR Ladder Form
  • 6.6 Frequency Domain Description of PARCOR Ladder Forms
  • 6.7 Stability of the Feed-Back PARCOR Ladder Form
  • 6.8 Burg’s Harmonic Mean PARCOR Ladder Algorithm
  • 6.9 Determination of Model Order
  • 6.10 Chapter Summary
  • 7. Levinson-Type Ladder Algorithms
  • 7.1 The Levinson-Durbin Algorithm
  • 7.2 Computing the Autocorrelation Coefficients from the PARCOR Ladder Reflection Coefficients — The “Inverse” Levinson-Durbin Algorithm
  • 7.3 Some More Properties of Toeplitz Systems and the Levinson-Durbin Algorithm
  • 7.4 Split Levinson Algorithms
  • 7.5 A Levinson-Type Least-Squares Ladder Estimation Algorithm
  • 7.6 The Makhoul Covariance Ladder Algorithm
  • 7.7 Chapter Summary
  • 8 Covariance Ladder Algorithms
  • 8.1 The LeRoux-Gueguen Algorithm
  • 8.2 The Cumani Covariance Ladder Algorithm
  • 8.3 Recursive Covariance Ladder Algorithms
  • 8.4 Split Schur Algorithms
  • 8.5 Chapter Summary
  • 9. Fast Recursive Least-Squares Ladder Algorithms
  • 9.1 The Exact Time-Update Theorem of Projection Operators
  • 9.2 The Algorithm of Lee and Morf
  • 9.3 Other Forms of Lee’s Algorithm
  • 1. Introduction
  • 2. The Linear Prediction Model
  • 2.1 The Normal Equations of Linear Prediction
  • 2.2 Geometrical Interpretation of the Normal Equations
  • 2.3 Statistical Interpretation of the Normal Equations
  • 2.4 The Problem of Signal Observation
  • 2.5 Recursion Laws of the Normal Equations
  • 2.6 Stationarity — A Special Case of Linear Prediction
  • 2.7 Covariance Method and Autocorrelation Method
  • 2.8 Recursive Windowing Algorithms
  • 2.9 Backward Linear Prediction
  • 2.10 Chapter Summary
  • 3. Classical Algorithms for Symmetric Linear Systems
  • 3.1 The Cholesky Decomposition
  • 3.2 The QR Decomposition
  • 3.3 Some More Principles for Matrix Computations
  • 3.4 Chapter Summary
  • 4. Recursive Least-Squares Using the QR Decomposition
  • 4.1 Formulation of the Growing-Window Recursive Least-Squares Problem
  • 4.2 Recursive Least Squares Based on the Givens Reduction
  • 4.3 Systolic Array Implementation
  • 4.4 Iterative Vector Rotations — The CORDIC Algorithm
  • 9.4 Gradient Adaptive Ladder Algorithms
  • 9.5 Lee’s Normalized RLS Ladder Algorithm
  • 9.6 Chapter Summary
  • 10. Special Signal Models and Extensions
  • 10.1 Joint Process Estimation
  • 10.2 ARMA System Identification
  • 10.3 Identification of Vector Autoregressive Processes
  • 10.4 Parametric Spectral Estimation
  • 10.5 Relationships Between Parameter Estimation and Kalman Filter Theory
  • 10.6 Chapter Summary
  • 11. Concluding Remarks and Applications
  • A.1 Summary of the Most Important Forward/Backward Linear Prediction Relationships
  • A.2 New PORLA Algorithms and Their Systolic Array Implementation
  • A.3 Vector Case of New PORLA Algorithms

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