Prediction-error filtering and maximum-entropy spectral estimation

Haykin, S.; Kesler, S.

doi:10.1007/3-540-12386-5_9

Cited by 80 publications

(40 citation statements)

References 27 publications

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“…The idea of the method is to choose the spectrum which corresponds to the most random or unpredictable time series of which the auto-correlation function agrees with a set of known values. The attributes of MESA are that it provides greater resolution than linear methods and has the ability to analyze short data records (Haykin and Kesler, 1979). In order to compute a MESA spectrum, the so called prediction error filter (PEF) coefficients must first be computed.…”

Section: Data and Analysismentioning

confidence: 99%

The structure of low-latitude Pc3 pulsations observed by CHAMP and on the ground

Ndiitwani

Sutcliffe

2009

Ann. Geophys.

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Abstract. The structure of low-latitude continuous pulsations termed Pc3, which are naturally occurring MHD waves in the Earth's magnetosphere, were studied by comparing ground and satellite magnetic field measurements. Data from two induction magnetometers, located at Hermanus and Sutherland in South Africa were used in conjunction with Challenging Minisatellite Payload (CHAMP) satellite observations to study a Pc3 event observed on 15 February 2003, at a time when CHAMP was passing over the ground stations. We observed a number of discrete frequency oscillations for the fast mode wave, one of which drives a field line resonance (FLR) at characteristic latitude as detected by both ground and satellite measurements. Consequently, our observations confirmed the compressional wave as being the driver of the field line resonance. The toroidal mode frequency observed on CHAMP experienced a Doppler frequency shift due to the rapid motion across the resonance region. Polarization hodograms in the resonance region clearly showed the expected 90 • rotation of the field line resonant magnetic field components.

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Section: Data and Analysismentioning

confidence: 99%

The structure of low-latitude Pc3 pulsations observed by CHAMP and on the ground

Ndiitwani

Sutcliffe

2009

Ann. Geophys.

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“…Nevertheless, the use of all these criteria can be tricky because they all appear to underestimate the order of regression of a time series (Haykin and Kesler, 1983;Benoist, 1986). Moreover, such criteria can be poorly constrained (Penland et al, 1991) and do not prevent from intrinsic potential errors of the method.…”

Section: Maximum Entropy Methodsmentioning

confidence: 99%

“…More sophisticated criteria, like the auto-regressive transfer function criterion (CAT) (Parzen, 1976;Haykin and Kesler, 1983), or based on the analysis of the poles of Equation (7) can also give an estimate of a regression order M (Lacoume et al, 1983;Benoist, 1986). Nevertheless, the use of all these criteria can be tricky because they all appear to underestimate the order of regression of a time series (Haykin and Kesler, 1983;Benoist, 1986).…”

Section: Maximum Entropy Methodsmentioning

confidence: 99%

“…This means that spurious results are bound to appear for large values of the auto-regressive order 9 An upper bound for M is generally taken as N/2. Heuristic criteria have been devised to refine the choice of a reasonable M (Haykin and Kesler, 1983;Benoist, 1986), based on a minimization of the residual of a least-square fit between the autoregressive approximation and the original time series. Among those criteria, we note: -the final prediction-error (FPE) criterion (Akaike, 1969), which attempts to minimize the mean square variance of the spectral estimate:…”

Section: Maximum Entropy Methodsmentioning

confidence: 99%

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Spectral analysis of climate data

1996

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Abstract. The complexity of climate variability on all time scales requires the use of several refined tools to unravel its primary dynamics from observations. Indeed, ideas from the theory of dynamical systems have provided new ways of interpreting the information contained in climatic time series.We review the properties of several modem time series analysis methods. Those methods belong to four main classes: Fourier techniques (Blackman-Tukey and Multi-Taper), Maximum Entropy technique, Singular-specmnn techniques and wavelet analysis. Their respective advantages and limitations are illustrated by numerical experiments on synthetic time series. As climate data can be irregularly spaced in time, we also compare three interpolating methods on those time series. Those tests are aimed at showing the pitfalls of the blind use of mathematical or statistical techniques on climate data.We apply those methods to 'real' climatic data from temperature variations over the last century, and the Vostok ice core deuterium record over the last glacial cycle. Then we show how interpretations on the dynamics of climate can be derived on those time scales.

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“…Due to CHAMP's orbit, it traverses the latitudinal structure of geomagnetic field lines very rapidly and covers a latitudinal range of 1 0 -2 0 in one Pc3 wave period; consequently, traditional methods of spectral analysis such as the FFT are not suitable (Vellante et al, 2004, Ndiitwani & Sutcliffe, 2009. Maximum entropy spectral analysis (MESA) was used since it provides greater resolution than linear methods and has the ability to analyze short data records (Haykin & Kesler, 1979). We used the Ulrych and Clayton (1976) method for computing the prediction error filter (PEF) coefficients (see Ndiitwani & Sutcliffe, 2009 for details).…”

Section: Observations Of Pcpulsation Field Line Resonancesmentioning

confidence: 99%