The numerical stability of the levinson-durbin algorithm for solving the Yule-Walker equations with a positive-definite symmetric Toeplitz matrix is studied. Arguments based on the analytic results of an error analysi...
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The numerical stability of the levinson-durbin algorithm for solving the Yule-Walker equations with a positive-definite symmetric Toeplitz matrix is studied. Arguments based on the analytic results of an error analysis for fixed-point and floating-point arithmetics show that the algorithm is stable and in fact comparable to the Cholesky algorithm. Conflicting evidence on the accuracy performance of the algorithm is explained by demonstrating that the underlying Toeplitz matrix is typically ill-conditioned in most applications.
This paper presents a new method for estimating the parameters of quarterplane two dimensional (2-D) autoregressive model based on the levinson-durbin algorithm. To achieve this aim, one-dimensional formulations relat...
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This paper presents a new method for estimating the parameters of quarterplane two dimensional (2-D) autoregressive model based on the levinson-durbin algorithm. To achieve this aim, one-dimensional formulations related to levinson-durbin algorithm are extended to 2-D case. Online parameter estimation, capability of parameters variation detection, estimation improvement by using new data and less computational requirement are the significant advantages of the proposed method. Because of not involving complex and time consuming matrix computations, the presented method is computationally efficient. Numerical simulations are presented to show the efficiency of the proposed approach.
Different forms of levinson-durbin-type algorithms, which relate the coefficients of a continuous-time autoregressive model to the residual variances of certain regressions or their ratios, are derived. The algorithms...
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Different forms of levinson-durbin-type algorithms, which relate the coefficients of a continuous-time autoregressive model to the residual variances of certain regressions or their ratios, are derived. The algorithms provide parametrizations of the model by a finite set of positive numbers. They can be used for computing the covariance structure of the process, for testing the validity of such a structure, and for stability testing.
A basic recursive property of orthogonal projections is presented which leads easily to a variety of different prediction algorithms. Examples are the classical levinson-durbin and Burg algorithms and a subset Whittle...
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A basic recursive property of orthogonal projections is presented which leads easily to a variety of different prediction algorithms. Examples are the classical levinson-durbin and Burg algorithms and a subset Whittle algorithm of Penm and Terrell. In addition, some new algorithms are derived including easily applied algorithms for the recursive calculation of best h-step predictors and a Burg algorithm for the best subset predictor. The relation to lattice algorithms is discussed. (C) 2003 Elsevier B.V. All rights reserved.
We discuss an algorithm which allows for recursive-in-order calculation of the parameters of autoregressive-moving average processes. The proposed procedure generalizes the recursion of levinson (1946) and durbin (196...
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We discuss an algorithm which allows for recursive-in-order calculation of the parameters of autoregressive-moving average processes. The proposed procedure generalizes the recursion of levinson (1946) and durbin (1960), which applies in the pure autoregressive case. We use ideas similar to the multivariate autoregressive case. Our results suggest how estimation procedures for autoregressive-moving average parameters, which include an automatic choice of model order, for example, the one proposed by Hannan & Rissanen (1982), may be made computationally more efficient.
In this paper we propose methods for obtaining the quantized reflection coefficients in an interleaved manner, where quantization alternates with optimization. The problem is relevant for the optimization involved whe...
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ISBN:
(纸本)9781424416875
In this paper we propose methods for obtaining the quantized reflection coefficients in an interleaved manner, where quantization alternates with optimization. The problem is relevant for the optimization involved when applying minimum description length principle for inference and also as a part of lossless coding schemes. It turns out that the recursive-in-order structure used in the optimal design of the linear predictors for nonquantized parameters is well suited for a greedy optimization-quantization (OQ) process. We introduce the optimization-quantization versions of two important algorithms: levinson-durbin algorithm and Burg algorithm and also discuss a direct least squares approach. The numerical results for the linear prediction with the proposed schemes show improvements in terms of mean square errors for audio signals. Results are also shown for the use of an OQ algorithm inside the MPEG-4 ALS lossless audio coder.
In this correspondence, several algorithms to compute a lower bound of the smallest eigenvalue of a symmetric positive-definite Toeplitz matrix are described and compared in terms of accuracy and computational efficie...
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In this correspondence, several algorithms to compute a lower bound of the smallest eigenvalue of a symmetric positive-definite Toeplitz matrix are described and compared in terms of accuracy and computational efficiency. Exploiting the Toeplitz structure of the considered matrix, new theoretical insights are derived and an efficient implementation of some of the aforementioned algorithms is provided.
This paper proposes the least-squares (LS) finite impulse response (FIR) fixed-lag smoother and filter in linear discrete-time wide-sense stationary stochastic systems. The FIR fixedlag smoothing estimate is given as ...
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This paper proposes the least-squares (LS) finite impulse response (FIR) fixed-lag smoother and filter in linear discrete-time wide-sense stationary stochastic systems. The FIR fixedlag smoothing estimate is given as a linear convolution sum of the impulse response function and the observed values. It is assumed that the signal is observed with additional white noise, which is uncorrelated with the signal process. By solving the simultaneous linear equations transformed from the Wiener-Hopf equation, the optimal impulse response function is obtained. The necessary information of the LS FIR fixed-lag smoothing algorithm is the auto-covariance function of the signal process and the variance of the observation noise process. In particular, this paper proposes the levinson-durbin algorithm, which needs less amount of arithmetic operations than the Gauss-Jordan elimination method in the inverse of the Toeplitz matrix, for the optimal impulse response function. From the numerical simulation example, the proposed LS FIR fixed-lag smoother and filter are superior in estimation accuracy to the RLS Wiener FIR estimators. (C) 2018 Elsevier Inc. All rights reserved.
In this paper we derive an explicit expression for the log likelihood function of a continuous-time autoregressive model. Then, using earlier results relating the autoregressive coefficients to the set of positive par...
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In this paper we derive an explicit expression for the log likelihood function of a continuous-time autoregressive model. Then, using earlier results relating the autoregressive coefficients to the set of positive parameters called residual variances ratios, we develop an iterative algorithm for computing the maximum likelihood estimator of the model, similar to one in the discrete-time case. A simple noniterative estimation method, which can be used to produce an initial estimate for the algorithm, is also proposed.
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