On periodic pulse interval analysis with outliers and missing observations

Sadler, Brian M.; Casey, Stephen D.

doi:10.1109/78.726812

Cited by 31 publications

(29 citation statements)

References 18 publications

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“…This claim reappeared in Ref. 11 , but as Sidiropoulos et al pointed out in Ref. 8 , the argument therein was ''incomplete''.…”

Section: The Gs Determination Problemmentioning

confidence: 83%

“…(3), it is easy to see that the MLE can be obtained by searching the peak of SðfÞ. Usually a two-step numerical search procedure is adopted [8][9][10][11] as follows.…”

Section: The Gs Determination Problemmentioning

confidence: 99%

“…For instance, if k i are generated from the Bernoulli missing model, which is frequently assumed in Refs. [7][8][9][10][11][12][13] , then the expected value of jSðfÞj 2 is given by 7…”

Section: Lower Limit Of the Mainlobe Widthmentioning

confidence: 99%

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Fast approximate maximum likelihood period estimation from incomplete timing data

Haohuan¹,

Liu²,

Wen-li³

2013

Chinese Journal of Aeronautics

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To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate (MLE) with a computational complexity of Oðn 2 Þ. Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search. ª 2013 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

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“…This claim reappeared in Ref. 11 , but as Sidiropoulos et al pointed out in Ref. 8 , the argument therein was ''incomplete''.…”

Section: The Gs Determination Problemmentioning

confidence: 83%

“…(3), it is easy to see that the MLE can be obtained by searching the peak of SðfÞ. Usually a two-step numerical search procedure is adopted [8][9][10][11] as follows.…”

Section: The Gs Determination Problemmentioning

confidence: 99%

See 1 more Smart Citation

Fast approximate maximum likelihood period estimation from incomplete timing data

Haohuan¹,

Liu²,

Wen-li³

2013

Chinese Journal of Aeronautics

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“…It has been proved in [10] and [6] that (2) yields the MLE, which is obtained by searching the peak of the S f .…”

Section: The Grid Spacing Determination Problemmentioning

confidence: 99%

“…Most of the existing estimators [6]- [10] operate based on performing grid search over a range of possible periods, such as the periodogram estimator [6], the separable least squares line search SLS2) [7] and the lattice line search (LLS) [8]. Recently, McKilliam et al have shown that the performances of these estimators are determined by the chosen grid spacing (GS) [9].…”

Section: Introductionmentioning

confidence: 98%

Efficient maximum-likelihood period estimation from incomplete timing data

Liu²,

Jiang³

2012

International Conference on Automatic Control and Artificial Intelligence (ACAI 2012)

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The problem of estimation the period of a periodic event from a sequence of noisy, incomplete time-of-arrival (TOA) observations is studied. A novel grid spacing determination strategy is proposed for a class of numerical-search estimators, whose performances is determined by grid spacing selection. A modified algorithm based on the Fogel's Periodogram estimator is proposed by employing that strategy. It is shown that our algorithm is very likely to yield the maximum likelihood estimate (MLE), with a low complexity of 2 ( ) O n . Simulation results demonstrate the superior performance of our estimator comparing with the other existing estimators.

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Periodic point processes: Theory and application

Casey

2020

Appl Stoch Models Bus & Ind

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We address the problems of extracting information generated by one dimensional periodic point processes. These problems arise in numerous situations, from astronomy and biomedical applications to reliability and quality control and signal processing. We divide our analysis into two cases, namely single and then multiple source(s). We wish to extract the fundamental period of the generator(s), and, in the second case, to deinterleave the processes. We present two algorithms, designed to work on all one dimensional periodic processes, but in particular on sparse datasets where other procedures break down. The first algorithm works on data from single period processes, computing an estimate of the underlying period. It is extremely computationally efficient and straightforward, and works on all single period processes, but in particular on sparse datasets where others break down. Its justification, however, rests on some deep mathematics, including a probabilistic interpretation of the Riemann zeta function. We then build upon this procedure to analyze data from multiple periodic processes. This second procedure relies on the Riemann zeta function, Weyl's equidistribution theorem, and Wiener's periodogram.

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On periodic pulse interval analysis with outliers and missing observations

Cited by 31 publications

References 18 publications

Fast approximate maximum likelihood period estimation from incomplete timing data

Fast approximate maximum likelihood period estimation from incomplete timing data

Efficient maximum-likelihood period estimation from incomplete timing data

Periodic point processes: Theory and application

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