A combined detection-estimation algorithm for the harmonic-retrieval problem

Hwang, Jeng-Kuang; Chen, Yung‐Chang

doi:10.1016/0165-1684(93)90146-2

Cited by 33 publications

(19 citation statements)

References 19 publications

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“…Moreover, as noted in the simulation study by Kundu [24], for finite observation lengths n, estimators with different penalty functions C n have quite different detection performances and over-estimation probabilities. Based on simulations, both [24] and Hwang and Chen [20] proposed C n = 2 ln n, though, as noted by Kundu, 'no theoretical justification can be given in favor of this'.…”

Section: B Previous and Related Workmentioning

confidence: 99%

“…For a fixed α ≪ 1, the proposed estimator in Eq. (20), is technically speaking not asymptotically weakly consistent, as it has a positive false alarm probability α > 0 of detecting a single sinusoid when none is present (K = 0). In order to obtain a consistent estimator it suffices to consider a monotonically decreasing sequence α n of false alarm probabilities, with α n → 0.…”

Section: B a New Model Selection Criterionmentioning

confidence: 99%

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Model Selection for Sinusoids in Noise: Statistical Analysis and a New Penalty Term

Nadler

Kontorovich

2011

IEEE Trans. Signal Process.

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Abstract-Detection of the number of sinusoids embedded in noise is a fundamental problem in statistical signal processing. Most parametric methods minimize the sum of a data fit (likelihood) term and a complexity penalty term. The latter is often derived via information theoretic criteria, such as minimum description length (MDL), or via Bayesian approaches including Bayesian information criterion (BIC) or maximum a-posteriori (MAP). While the resulting estimators are asymptotically consistent, empirically their finite sample performance is strongly dependent on the specific penalty term chosen. In this paper we elucidate the source of this behavior, by relating the detection performance to the extreme value distribution of the maximum of the periodogram and of related random fields. Based on this relation, we propose a combined detection-estimation algorithm with a new penalty term. Our proposed penalty term is sharp in the sense that the resulting estimator achieves a nearly constant false alarm rate. A series of simulations support our theoretical analysis and show the superior detection performance of the suggested estimator.Index Terms-sinusoids in noise, maxima of random fields, extreme value theory, periodogram, statistical hypothesis tests.

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Section: B Previous and Related Workmentioning

confidence: 99%

Section: B a New Model Selection Criterionmentioning

confidence: 99%

Model Selection for Sinusoids in Noise: Statistical Analysis and a New Penalty Term

Nadler

Kontorovich

2011

IEEE Trans. Signal Process.

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“…However, for a sparse channel, the original estimation problem should be formulated as a combined detection-estimation problem [12,13]. Hence, the so-called TSML channel estimator is derived in order to solve the above combined detection-estimation problem.…”

Section: Introductionmentioning

confidence: 99%

Modular Design and Implementation of FPGA-Based Tap-Selective Maximum-Likelihood Channel Estimator

Hwang

2008

2008 4th IEEE International Conference on Circuits and Systems for Communications

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-The modular design of the optimal tap-selective maximum-likelihood (TSML) channel estimator based on field-programmable gate array (FPGA) technology is studied. A novel range reduction algorithm is included in the natural logarithmic function (NLF) emulator based on the coordinate rotation digital computer (CORDIC) methodology and is integrated into the TSML channel estimator system. The low-complexity TSML algorithm, which is employed for sparse multipath channel estimation, is proposed for long-range broadband block transmission systems. Furthermore, the proposed range reduction algorithm aims to solve the limited interval problem in the CORDIC algorithm base on Xilinx's SG platforms. The modular approach facilitates the reuse of modules.

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“…Combined detection/estimation methods have also been considered; see, e.g., [3], [4], [11], [14], and [15]. The methods in [3] and [4] are based on periodogram analysis along with spectral notching and provide computationally fast but statistical suboptimal solutions.…”

mentioning

confidence: 99%

“…The methods in [3] and [4] are based on periodogram analysis along with spectral notching and provide computationally fast but statistical suboptimal solutions. Methods in [11], [14], and [15] are statistically optimal or close to optimal but require searching a large number (usually all possible) model orders.…”

mentioning

confidence: 99%

A combined order selection and parameter estimation algorithm for undamped exponentials

Ying

Sabharwal

Moses

2000

IEEE Trans. Signal Process.

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Abstract-We propose an approximate maximum likelihood parameter estimation algorithm, combined with a model order estimator, for superimposed undamped exponentials in noise. The algorithm combines the robustness of Fourier-based estimators and the high-resolution capabilities of parametric methods. We use a combination of a Wald statistic and a MAP test for order selection and initialize an iterative maximum likelihood descent algorithm recursively based on estimates at higher candidate model orders. Experiments using simulated data and synthetic radar data demonstrate improved performance over MDL, MAP, and AIC in cases of practical interest.

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A combined detection-estimation algorithm for the harmonic-retrieval problem

Cited by 33 publications

References 19 publications

Model Selection for Sinusoids in Noise: Statistical Analysis and a New Penalty Term

Model Selection for Sinusoids in Noise: Statistical Analysis and a New Penalty Term

Modular Design and Implementation of FPGA-Based Tap-Selective Maximum-Likelihood Channel Estimator

A combined order selection and parameter estimation algorithm for undamped exponentials

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