A theoretical analysis of exponentially decaying time series

Lawunmi, D

doi:10.1088/0957-0233/8/7/002

Cited by 4 publications

(2 citation statements)

References 4 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Among these algorithms, we propose to use the Douglas-Rachford algorithm which was observed to behave satisfactorily [45] in a number of non-convex optimization problems. For many functions the proximity operator has an explicit form [46]. For instance, the proximal operator prox ι D of ι D reduces to the projection onto D, i.e.…”

Section: Moment-based Initializationmentioning

confidence: 99%

An EM Approach for Time-Variant Poisson-Gaussian Model Parameter Estimation

Jezierska

Chaux

Pesquet

et al. 2014

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

International audienceThe problem of estimating the parameters of a Poisson-Gaussian model from experimental data has recently raised much interest in various applications, for instance in confocal fluorescence microscopy. In this context, a field of independent random variables is observed, which is varying both in time and space. Each variable is a sum of two components, one following a Poisson and the other a Gaussian distribution. In this paper, a general formulation is considered where the associated Poisson process is nonstationary in space and also exhibits an exponential decay in time, whereas the Gaussian component corresponds to a stationary white noise with arbitrary mean. To solve the considered parametric estimation problem, we follow an iterative Expectation-Maximization (EM) approach. The parameter update equations involve deriving finite approximation of infinite sums. Expressions for the maximum error incurred in the process are also given. Since the problem is non-convex, we pay attention to the EM initialization, using a moment-based method where recent optimization tools come into play. We carry out a performance analysis by computing the Cramer-Rao bounds on the estimated variables. The practical performance of the proposed estimation procedure is illustrated on both synthetic data and real fluorescence macroscopy image sequences. The algorithm is shown to provide reliable estimates of the mean/variance of the Gaussian noise and of the scale parameter of the Poisson component, as well as of its exponential decay rate. In particular, the mean estimate of the Poisson component can be interpreted as a good-quality denoised version of the data

show abstract

Section: Moment-based Initializationmentioning

confidence: 99%

An EM Approach for Time-Variant Poisson-Gaussian Model Parameter Estimation

Jezierska

Chaux

Pesquet

et al. 2014

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

“…Obviously, an on-line indication of noticeable instrumentation drift would be useful for an effective diagnostic of metrological properties of the system. Statistical analysis is an effective means for on-line analysis of time series in order to recognize drift phenomena affecting the data collected [1,2]. In particular, non-parametric tests, i.e.…”

Section: Introductionmentioning

confidence: 99%

On the robust utilization of non-parametric tests for evaluation of combined cyclical and monotonic drift

Cappa

Silvestri

Sciuto

2001

Meas. Sci. Technol.

View full text Add to dashboard Cite

Non-parametric statistical tests are usually adopted to recognize drift phenomena in data series acquired by automatic measuring systems. Sometimes different tests provide different responses with regard to the presence of drift in data sets. In particular, the application of two commonly used statistical tests (i.e. the Wald-Wolfovitz test, also known as the run test, and the Mann-Whitney test, also known as the reverse arrangement test) to data acquired during long-term trials showed that they exhibited different behaviours regarding shift detection. Thus, a deeper examination of previously indicated statistical tests in real measurements appears of interest; more precisely their effectiveness is verified (i) when cyclical and monotonous drift are concurrently present and (ii) various levels of noise are superimposed on the data gathered. Finally, on the basis of the theoretical results obtained, the statistical tests here examined are applied to the same data set in order to validate their capability in on-line drift recognition.

show abstract

A multi-function IEC 61850 packet generator based on FPGA

Wei

Cheng

2016

Meas. Sci. Technol.

View full text Add to dashboard Cite

An IEC 61850 packet generator is used to produce IEC 61850-9-2 packets by simulating the merging unit and testing the IEC 61850 digital device. While the existing IEC packet generator can produce ideal digital without any noise, it does not take into account the fact that the merging unit output signal packets will be inevitably superimposed with noise. Since the International Electrical Commission standard of the electronic current transformer specifies the minimum output signal-to-noise ratio of the merging unit to be 30 dB, and the signal superimposed with noise will influence the operation performance of the digital device, it is necessary to design a multi-function IEC 61850-9-2 packet generator for a digital device test. Therefore, in this paper, a multi-function IEC 61850 packet generator has been developed, which not only can output various IEC 61850-9-2 packets, but also can add white Gaussian noise to the signal for digital device testing. By testing three digital electricity meters from different manufacturers, we showed that the error of the digital electricity meter is significantly larger when the signal packet is superimposed with noise. Also when the signal-to-noise ration is 30 dB, the error of one of the meters exceeds the allowed range of the accuracy class. This indicates that the noise testing and the noise setting function of the system has an important role in the testing of a digital device.

show abstract

A theoretical analysis of exponentially decaying time series

Cited by 4 publications

References 4 publications

An EM Approach for Time-Variant Poisson-Gaussian Model Parameter Estimation

An EM Approach for Time-Variant Poisson-Gaussian Model Parameter Estimation

On the robust utilization of non-parametric tests for evaluation of combined cyclical and monotonic drift

A multi-function IEC 61850 packet generator based on FPGA

Contact Info

Product

Resources

About