A Modified Prony Algorithm for Exponential Function Fitting

Osborne, M. R.; Smyth, Gordon K.

doi:10.1137/0916008

Cited by 203 publications

(118 citation statements)

References 36 publications

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“…We chose K as ffiffiffiffiffiffiffiffi ffi k max p , where k max represents the number of points of the empirical autocovariance. This is accomplished through a modified Prony algorithm [41]. The Prony algorithm returns two vectors,…”

Section: Autocovariance Approximation and Time Scales Identificationmentioning

confidence: 99%

Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

2004

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This paper proposes a traffic model and a parameter fitting procedure that are capable of achieving accurate prediction of the queuing behavior for IP traffic exhibiting long-range dependence. The modeling process is a discrete-time batch Markovian arrival process (dBMAP) that jointly characterizes the packet arrival process and the packet size distribution. In the proposed dBMAP, packet arrivals occur according to a discrete-time Markov modulated Poisson process (dMMPP) and each arrival is characterized by a packet size with a general distribution that may depend on the phase of the dMMPP. The fitting procedure is designed to provide a close match of both the autocovariance and the marginal distribution of the packet arrival process, using a dMMPP; a packet size distribution is fitted individually to each state of the dMMPP. A major feature of the procedure is that the number of states of the fitted dBMAP is not fixed a priori; it is determined as part of the procedure itself. In this way, the procedure allows establishing a compromise between the accuracy of the fitting and the number of parameters, while maintaining a low computational complexity.We apply the inference procedure to several traffic traces exhibiting long-range dependence. Very good results were obtained since the fitted dBMAPs match closely the autocovariance, the marginal distribution and the queuing behavior of the measured traces. Our results also show that ignoring the packet size distribution and its correlation with the packet arrival process can lead to large errors in terms of queuing behavior.

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Section: Autocovariance Approximation and Time Scales Identificationmentioning

confidence: 99%

Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

2004

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“…Solutions to (1) include complex exponentials, damped and undamped sinusoids and real exponentials, depending on the roots of the polynomial with the ξ k as coefficients (Brockwell and Davis, 1991;Osborne and Smyth, 1995). Let the roots be β j , j = 1, .…”

Section: Constant Coefficient Differential Equationsmentioning

confidence: 99%

Robust Frequency Estimation Using Elemental Sets

Smyth

Hawkins

2000

Journal of Computational and Graphical Statistics

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The extraction of sinusoidal signals from time-series data is a classic problem of ongoing interest in the statistics and signal processing literatures. Obtaining least squares estimates is difficult because the sum of squares has local minima O(1/n) apart in the frequencies. In practice the frequencies are often estimated using ad hoc and inefficient methods. Problems of data quality have received little attention. An elemental set is a subset of the data containing the minimum number of points such that the unknown parameters in the model can be identified. This paper shows that, using a variant of the classical method of Prony, parameter estimates for a sum of sinusoids can be obtained algebraically from an elemental set. Elemental set methods are used to construct finite algorithm estimators which approximately minimize the least squares, least trimmed sum of squares or least median of squares criteria. The elemental set estimators prove able in simulations to resolve the frequencies to the correct local minima of the objective functions. When used as the first stage of an MM estimator, the constructed estimators based on the trimmed sum of squares and least median of squares criteria produce final estimators which have high breakdown properties and which are simultaneously efficient when no outliers are present. The approach can also be applied to sums of exponentials, and sums of damped sinusoids. The paper includes simulations with one and two sinusoids and two data examples.Keywords: frequency estimation, sums of exponential functions, elemental sets, least trimmed sum of squares, least median of squares, MM estimators, high breakdown, high efficiency.

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“…In his 1795 seminal paper, Riche de Prony studies the parameter estimation of a finite sum of sinusoidal functions (see Riche de Prony [1795], Kahn et al [1992], Osborne et al [1995]). In this paper, we are interested in Prony's problem for a two-terms sum of complex sinusoidal functions, meaning that our aim is to estimate the parameters of the signal (see also Neves et al [2007] for a quite related study)…”

Section: Introductionmentioning

confidence: 99%

Algebraic parameter estimation of a biased sinusoidal waveform signal from noisy data

Ushirobira

Perruquetti²,

Mboup³

et al. 2012

IFAC Proceedings Volumes

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To cite this version:Rosane Ushirobira, Wilfrid Perruquetti, Mamadou Mboup, Michel Fliess. Algebraic parameter estimation of a biased sinusoidal waveform signal from noisy data. Abstract: The amplitude, frequency and phase of a biased and noisy sum of two complex exponential sinusoidal signals are estimated via new algebraic techniques providing a robust estimation within a fraction of the signal period. The methods that are popular today do not seem able to achieve such performances. The efficiency of our approach is illustrated by several computer simulations.

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A Modified Prony Algorithm for Exponential Function Fitting

Cited by 203 publications

References 36 publications

Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

Robust Frequency Estimation Using Elemental Sets

Algebraic parameter estimation of a biased sinusoidal waveform signal from noisy data

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