A fast maximum likelihood algorithm for frequency estimation of a sinusoid based on Newton's method

Abatzoglou, Theagenis J.

doi:10.1109/tassp.1985.1164541

Cited by 114 publications

(43 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Since this scheme yields an estimate of f o for which the variance is somewhat larger than the corresponding CRLB [56], we proceed to define a fast and iterative Newton's technique to solve the augmented periodogram problem starting at the estimated frequency obtained by the dichotomous search algorithm. The augmented periodogram maximisation problem is solved via Newton's method through the following iterative form [57] …”

Section: B Fine Search Stagementioning

confidence: 99%

“…It should be noted that if the initialisation value is close to the true parameter value (guaranteeing a convergence), Newton's method can achieve quadratic convergence [57], justifying its use for frequency estimation. With the so resolved MLE of frequencyf , we are now able to subsequently perform the corresponding MLEs of both the amplitudes and phases of the positive and negative phase-sequence components within the unbalanced three-phase power signals, using (26) and (22), respectively.…”

Section: B Fine Search Stagementioning

confidence: 99%

See 1 more Smart Citation

Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals

Xia

Kanna

Mandic

2018

IEEE Trans. Instrum. Meas.

View full text Add to dashboard Cite

Accurate detection of the system frequency in unbalanced three-phase power systems is a prerequisite for the operation of future smart grid. To this end, we introduce the Cramer-Rao Lower Bounds (CRLBs) for frequency estimation, based on the αβ-transformed unbalanced voltage contaminated with noise. Next, the maximum likelihood estimation (MLE) method for frequency estimation is introduced as a maximiser of an "augmented periodogram".The use of the augmented complex statistics caters for all the available second order information, including the noncircularity associated with unbalanced systems. To find the ML solution, Newton's iterative method is employed and its initialisation is implemented by a discrete Fourier transform (DFT) based dichotomous search technique.We show that the MLE of phases and amplitudes of both the positive and negative phase-sequence components within the αβ-transformed voltage can be generically derived based on the ML frequency estimates. In this way, a unified framework is provided to accurately detect voltage characteristics of the positive and negative phasesequence components within unbalanced three-phase power system when its frequency experiences off-nominal conditions. Simulations verify that the proposed MLE approaches theoretical Cramer-Rao Lower Bounds (CRLBs) for all parameters under consideration.

show abstract

Section: B Fine Search Stagementioning

confidence: 99%

Section: B Fine Search Stagementioning

confidence: 99%

Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals

Xia

Kanna

Mandic

2018

IEEE Trans. Instrum. Meas.

View full text Add to dashboard Cite

show abstract

“…Therefore, the target parameters can be obtained by estimating the frequency of the main peak position. This can be implemented by using the frequency estimation methods, such as FFT and Newton's method [28]. The estimated frequency can be expressed aŝ…”

Section: Proposed Ccae Algorithmmentioning

confidence: 99%

A Fast Motion Parameters Estimation Method Based on Cross-Correlation of Adjacent Echoes for Wideband LFM Radars

Zhang¹,

Hong²,

Yang³

et al. 2017

Preprint

View full text Add to dashboard Cite

Abstract:In wideband radar systems, the performance of motion parameters estimation can significantly affect the performance of object detection and the quality of inverse synthetic aperture radar (ISAR) imaging. Although the traditional motion parameters estimation methods can reduce the range migration (RM) and Doppler frequency migration (DFM) effects in ISAR imaging, the computational complexity is high. In this paper, we propose a new fast non-searching motion parameters estimation method based on cross-correlation of adjacent echoes (CCAE) for wideband LFM signals. A cross-correlation operation is carried out for two adjacent echo signals, then the motion parameters can be calculated by estimating the frequency of the correlation result. The proposed CCAE method can be applied directly to the stretching system, which is commonly adopted in wideband radar systems. Simulational results demonstrate that the new method can achieve better estimation performances, with much lower computational cost, compared with existing methods. The experimental results on real radar data sets are also evaluated to verify the effectiveness and superiority of the proposed method compared to the state-of-the-art existing methods.

show abstract

“…In most cases [1], [2], the maximum likelihood (ML) procedure is utilized to obtain what one expects to be a sufficiently unbiased and efficient estimator of the frequency. Due to the nonlinear nature of the frequency estimation problem, the so-called threshold effect [2], [3] takes hold whenever the SNR drops below a critical data-length dependent level SNR c (T ).…”

Section: Introductionmentioning

confidence: 99%

“…A wide variety of approaches to this problem have been proposed and evaluated [1]- [6], although most of them were operated in the halfduplex transmission mode during the startup period. In our recent publication [7], we proposed a full-duplex fast training procedure for simultaneously estimating the echo and channel responses.…”

Section: Introductionmentioning

confidence: 99%

The Barankin bound and threshold behavior in frequency estimation

Knockaert¹

1997

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-This correspondence presents the Barankin bound as a fundamental statistical tool for the understanding of the threshold effect associated with the estimation of the frequency of a sinusoid in additive white Gaussian noise. It is shown that the threshold effect takes hold whenever the Barankin bound departs significantly from the Cramer-Rao bound. In terms of the signal-to-noise ratio (SNR) and the data length T , the quantity SNR 2T=ln T is shown to be a good indicator for deciding whether the SNR is above threshold or not.

show abstract

A fast maximum likelihood algorithm for frequency estimation of a sinusoid based on Newton's method

Cited by 114 publications

References 6 publications

Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals

Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals

A Fast Motion Parameters Estimation Method Based on Cross-Correlation of Adjacent Echoes for Wideband LFM Radars

The Barankin bound and threshold behavior in frequency estimation

Contact Info

Product

Resources

About