Exact equivalence of the Steiglitz-McBride iteration and IQML

McClellan, J.H.; Lee, D.

doi:10.1109/78.80841

Cited by 45 publications

(25 citation statements)

References 6 publications

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“…The impulse-input approach to SM and IQML algorithms, such as [18], are equivalent [16], meaning that they compute the same poles at each iteration step.…”

Section: A Steiglitz-mcbride and Iqmlmentioning

confidence: 99%

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A weighted least-squares method for parameter estimation in structured models

Galrinho

Rojas

Hjalmarsson

2014

53rd IEEE Conference on Decision and Control

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Abstract-Parameter estimation in structured models is generally considered a difficult problem. For example, the prediction error method (PEM) typically gives a non-convex optimization problem, while it is difficult to incorporate structural information in subspace identification. In this contribution, we revisit the idea of iteratively using the weighted least-squares method to cope with the problem of non-convex optimization. The method is, essentially, a three-step method. First, a high order least-squares estimate is computed. Next, this model is reduced to a structured estimate using the least-squares method. Finally, the structured estimate is re-estimated, using weighted least-squares, with weights obtained from the first structured estimate. This methodology has a long history, and has been applied to a range of signal processing problems. In particular, it forms the basis of iterative quadratic maximum likelihood (IQML) and the Steiglitz-McBride method. Our contributions are as follows. Firstly, for output-error models, we provide statistically optimal weights. We conjecture that the method is asymptotically efficient under mild assumptions and support this claim by simulations. Secondly, we point to a wide range of structured estimation problems where this technique can be applied. Finally, we relate this type of technique to classical prediction error and subspace methods by showing that it can be interpreted as a link between the two, sharing favorable properties with both domains.

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“…The impulse-input approach to SM and IQML algorithms, such as [18], are equivalent [16], meaning that they compute the same poles at each iteration step.…”

Section: A Steiglitz-mcbride and Iqmlmentioning

confidence: 99%

“…Perhaps, the earliest work is the SM method, appearing in [12]. It was shown in [16] that IQML and SM are equivalent for an impulse-input case. Later work include [17], [18], and [19].…”

Section: Introductionmentioning

confidence: 99%

A weighted least-squares method for parameter estimation in structured models

Galrinho

Rojas

Hjalmarsson

2014

53rd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

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“…As (26) is not known a priori, we employ the iterative relaxation procedure [30] to solve for {ω R,f } and {α R,f }, which is summarized in Table 2. Note that this relaxation approach corresponds to the IQML technique [25] or the Steiglitz-McBride algorithm [26], which has local convergence property with linear rate of convergence [27].…”

Section: [S]mentioning

confidence: 99%

Accurate and Computationally Efficient Tensor-Based Subspace Approach for Multidimensional Harmonic Retrieval

Sun

2012

IEEE Trans. Signal Process.

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In this paper, parameter estimation for R-dimensional (R-D) sinusoids with R > 2 in additive white Gaussian noise is addressed. With the use of tensor algebra and principal-singular-vector utilization for modal analysis, the sinusoidal parameters at one dimension are first accurately estimated according to an iterative procedure which utilizes the linear prediction property and weighted least squares. The damping factors and frequencies in the remaining dimensions are then solved such that pairing of the R-D parameters is automatically achieved. Algorithm modification for a single R-D tone is made and it is proved that the frequency estimates are asymptotically unbiased while their variances approach Cramér-Rao lower bound at sufficiently high signal-to-noise ratio conditions. Computer simulations are also included to compare the proposed approach with conventional R-D harmonic retrieval schemes in terms of mean square error performance and computational complexity.

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“…This is the subspace that is orthogonal to the signal subspace spanned by the columns of a generalized Vandermonde matrix of the modes in sparse and co-prime arrays. This parameterization is of a form that is particularly suitable for utilizing approximate least squares, such as iterative quadratic maximum likelihood (IQML) (see [2], [3], and [23]), for estimating the modes. Although we present our numerical results in the context of sensor array processing, all of our results apply to the estimation of complex exponential modes from time series data.…”

Section: Introductionmentioning

confidence: 99%

“…The iterative quadratic maximum likelihood (IQML) algorithm (see [2], [3], and [23]) is another method to approximately solve (12). In the lth iteration of IQML, the parameters a l are estimated by iteratively minimizing the quadratic form…”

Section: Introductionmentioning

confidence: 99%

Modal Analysis Using Co-Prime Arrays

Pakrooh

Scharf

Pezeshki

2016

IEEE Trans. Signal Process.

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Let a measurement consist of a linear combination of damped complex exponential modes, plus noise. The problem is to estimate the parameters of these modes, as in line spectrum estimation, vibration analysis, speech processing, system identification, and direction of arrival estimation. Our results differ from standard results of modal analysis to the extent that we consider sparse and co-prime samplings in space, or equivalently sparse and co-prime samplings in time. Our main result is a characterization of the orthogonal subspace. This is the subspace that is orthogonal to the signal subspace spanned

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Exact equivalence of the Steiglitz-McBride iteration and IQML

Cited by 45 publications

References 6 publications

A weighted least-squares method for parameter estimation in structured models

A weighted least-squares method for parameter estimation in structured models

Accurate and Computationally Efficient Tensor-Based Subspace Approach for Multidimensional Harmonic Retrieval

Modal Analysis Using Co-Prime Arrays

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