Maximum Entropy Power Spectrum Research Articles

Oblique Projection-Based Covariance Matrix Reconstruction and Steering Vector Estimation for Robust Adaptive Beamforming

Adaptive beamforming can efficiently contract interference and noise. Due to high sensitivity of the beamformer to model mismatch, the capability of interference reduction will critically degrade when the signal model mismatch occurs, particularly when the sampling sequence contains the desired signal. For the purpose of enhancing the robustness of beamformers to signal model mismatch, we propose a new robust adaptive beamforming (RAB) method. Firstly, the precise steering vector (SV) associating with the desired signal is estimated by employing the minimum norm of subspace projection (MNSP) approach. Secondly, the nominal interference SVs are estimated via the maximum entropy power spectrum. Subsequently, the corrected interference SVs and powers are obtained by oblique projection. Finally, the interference-plus-noise covariance matrix (INCM) is reconstructed, and the proposed RAB is obtained. Multiple simulations are carried out and demonstrate the robustness of the proposed RAB method.

A microscopic ancient river channel identification method based on maximum entropy principle and Wigner-Ville Distribution and its application

In view of the problem of fine characterization of narrow and thin channels, the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution. On the basis of effectively improving the time-frequency resolution of seismic signal, a new method of microscopic ancient river channel identification is established. Based on the principle of the equivalence between the maximum entropy power spectrum and the AR model power spectrum, the prediction error and the autoregression coefficient of AR model are obtained using the Burg algorithm and Levinson-Durbin recurrence rule. Under the condition of the first derivative of autocorrelation function being 0, the Wigner-Ville Distribution of seismic signal is calculated, and the Wigner-Ville Distribution time-frequency power spectrum (MEWVD) is obtained under the maximum entropy criterion of the microscopic ancient river channel. Through analysis of emulational seismic signal and forward numerical simulation signal of narrow thin model, it is found that MEWVD can effectively avoid the interference of cross term of Wigner-Ville Distribution, and obtain more accurate spectral characteristics than STFT and CWT signal analysis methods. It is also proved that the narrow and thin river channels of different scales can be identified effectively by MEWVD of different frequencies. The method is applied to the third member of Jurassic Shaximiao Formation (J2s33-2) gas reservoir of the Zhongjiang gas field in Sichuan Basin. The spatial information of width and direction of narrow and thin river channels with width less than 500 m and sandstone thickness less than 35 m is accurately identified, providing bases for well deployment and horizontal well fracturing section selection.

Maximum Entropy-Based Interference-Plus-Noise Covariance Matrix Reconstruction for Robust Adaptive Beamforming

To ensure signal receiving quality, robust adaptive beamforming (RAB) is of vital importance in modern communications. In this letter, we propose a new low-complexity RAB approach based on interference-plus-noise covariance matrix (IPNC) reconstruction and steering vector (SV) estimation. In this method, the IPNC and desired signal covariance matrices are reconstructed by estimating all interference powers as well as the desired signal power using the principle of maximum entropy power spectrum (MEPS). Numerical simulations demonstrate that the proposed method can provide superior performance to several previously proposed beamformers.

A combined Wigner-Ville and maximum entropy method for high-resolution time-frequency analysis of seismic data

The variation of frequency content of a seismic trace with time carries information about the properties of the subsurface reflectivity sequence. As a result, analysis of the data in terms of the local frequency content can provide a worthwhile addition to the standard procedures that are used in seismic processing and seismostratigraphic interpretation. The theory of quadratic time-frequency (TF) representations, such as the Wigner-Ville distribution (WVD), provides a solid foundation for local frequency analysis of seismic data and seismic attribute extraction. However, because of its quadratic nature, the WVD processes cross terms, which can limit the readability of the decomposition. To overcome this problem, we have used the key idea of the maximum entropy method of Burg, to compute a prediction error operator associated with the power spectrum of a given signal. The operator was then used to extend the kernel of Wigner-Ville of the signal, given by the elements of its covariance matrix. The Fourier transform of the extended kernel provided a high-resolution maximum entropy power spectrum of Wigner-Ville. We found, from the framework of the proposed method, how the common seismic attributes can be extracted as characteristics of the local spectrum. Furthermore, we devised a formula to estimate a robust and stable average instantaneous frequency (AIF) in the time domain. The high resolution achieved in the TF domain has been a key aspect for applying the proposed method to the Gulf of Mexico data set. Mapping of the channels and infill lithology is made possible by analyzing the spectral variation of the AIF cube, and the spectral decomposition based on the proposed method allows reliable information on the probable location and extension of a gas reservoir.

Maximum Entropy Power Spectrum Estimation for 2-D Multirate Systems

This paper presents maximum entropy power spectrum estimation of a 2-D information signal given that multirate low-resolution observations are available. Since the exact calculation of the 2-D maximum entropy power spectrum is not practical, we propose an efficient method utilizing slices in the 2-D discrete Fourier transform (DFT) domain and the duality in convex programming. We investigate the properties of our solution and provide numerical examples to demonstrate the performance of the new method.

Iterative maximum entropy power spectrum estimation for multirate systems

In multirate systems, observations are generally insufficient to determine the power spectrum of the input signal. In this paper, we reformulate the problem using a novel matrix notation and the discrete entropy function. Then we present an iterative maximum entropy power spectrum estimation algorithm for the solution of this problem. Contrary to the existing solutions, the new algorithm is computationally efficient since it is based on fast Fourier transform (FFT) and simple matrix calculations. Furthermore, simulation results show that the new algorithm converges to the maximum entropy solution and can be successfully used in multirate statistical data estimation.

A high resolution time delay estimation based on the maximum entropy power spectrum estimaton

Multipath time delay estimation is constrained by the width of the signal correlation function when using correlation based methods. This paper obtains a high resolution time delay estimation by introducing Burg algorithm and Marple algorithm of the maximum entropy power spectral estimation to non-resolvable multipath time delay estimatoin. The principles, the performaces and the results of computer simulation are given.

Spatial / temporal features of antarctic climate change1

Based on January 1962–October 1993 mean value series of monthly mean temperature anomalies of 16 Antarctic stations on 10 standard isobaric surfaces from the surface to the 30 hPa, long term trends and periodic features of climate changes from the troposphere to the lower stratosphere over the Antarctic region are investigated by maximum entropy power spectrum analysis, and the relation between climate change of the stratosphere (troposphere) and total ozone (southern 500 hPa circulation) is discussed.

On the interpretation of maximum entropy power spectrum and cross-power spectrum in earth rotation investigations

On the interpretation of maximum entropy power spectrum and cross-power spectrum in earth rotation investigations

Research on geomagnetic tectonic characteristics of the crust in Haicheng seismic area

In this paper, the two metnods, rectangular spectrum (RS) and maximum entropy power spectrum (MES), have been used in calculating the geomagnetic structures of the crust in Haicheng and its adjacent areas and carrying out the geomagnetic stratification of the crust. The result of the research indicates that the crust can be devided into such three layers as nonmagnetic layer, magnetic layer and regressive magnetic layer from the top to the bottom. It is also found the distribution of the geomagnetic bottom interface (Curie surface) is consistent with the lower interface of the upper crust and the top interface of the middle crust of the velocity structure of the crust. It is very interesting that the Haicheng earthquake of Feb. 4, 1975,M 7.3 occurred at the depth gradient belt of the Curie isotherm surface. So, to research on the geomagnetic layers and the distribution characteristics of the Curie isotherm surface is meaningful in judging potential seismic foci.

A spatial power spectrum analysis of the electroencephalogram

The method of spatial power-spectrum analysis has been applied to measurements of the distribution of rms alpha-band potential on the scalp. Data was recorded using the 31-Electrode System and spatial power-spectrum estimates (PSEs) were obtained from Mercator projections of the potential interpolated using the triangular method. PSEs were calculated using the Lim and Malik algorithm for maximum-entropy power-spectrum estimation. In order to investigate the utility of spatial power-spectrum analysis, PSEs were obtained from subjects in two conditions; resting with eyes closed (EC) and resting with eyes open and fixed on a single point (EO). A stepwise discriminant analysis was performed with features from the PSEs and the resultant discriminant function was applied to data not considered in the formulation of the function. Over 92% of test data was correctly classified. The features used in the discriminant function identify spatial waves which are most useful in separating data. The results demonstrate that waves oriented along front-back and right-left lines are most important in separating data into EC and EO groups.

Further experiments with maximum entropy power spectra of sinusoids

The effect of sampling period on the quality of maximum entropy spectrum of artificial signals containing a single sinusoid with white noise added, is illustrated. Spectral line shifting lies in the range 0.2 to about 16% depending on the sampling period.

“Serpentine emission” at the high latitude antarctic station, Davis

Almost a decade has passed since Gul'elmi and Dovbnya (1974) introduced the high latitude class of ultra low frequency (ULF) pulsations known as “Serpentine Emission” (SE). The purpose of this paper is twofold; firstly, to present new morphological results of SE observed at Davis, Antarctica and secondly, to stimulate further experimental and theoretical interest by pulsation researchers. Analyses presented include the first cited amplitude-time structure of SE along with maximum entropy power spectra and digital sonagrams. SE polarizations are investigated and a limited diurnal morphological survey is presented.

A model-based approach for estimation of two-dimensional maximum entropy power spectra

A stochastic model-based approach is presented for estimation of the two-dimensional maximum entropy power spectrum (MEPS) from given finite uniform array data. The method consists of fitting an appropriate two-dimensional noncausal Gaussian-Markov random field (GMRF) model to the given data using the maximum likelihood (ML) technique for parameter estimation. The nonlinear criterion function used for ML estimation is similar in structure to the function arising in the deterministic approach of Lang and McClellan. The model-based approach provides new insights into the two-dimensional MEPS estimation problem. For example, using the asymptotic normality of ML estimates, we derive simultaneous confidence bands for the estimated MEPS. It turns out that when the true correlations are generated by a noncausal GMRF model, the two-dimensional MEPS can be obtained by solving linear equations. This approach also suggests techniques for realizing two-dimensional GMRF models from the given correlation data. Several numerical examples are given to illustrate the usefulness of the approach.

Maximum entropy spectral estimation for regular time series of degenerate rank

This paper deals with multichannel time series of degenerate rank, and extends the maximum entropy method over the degenerate rank case. In order to define the entropy of a multichannel time series of degenerate rank, we must first clarify all the deterministic relationships in the time series. This will be done for any regular time series matching given finite data <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{R_{0}, R_{1},..., R_{n}}</tex> of the autocorrelation sequence <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{R_{k}\}\min{-\infin}{\infin}</tex> . A necessary and sufficient condition of the existence of a regular time series matching the data will be presented. Next, the entropy H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> (P) of a time series with its power spectrum P(ω) of rank less than equal to m is defined by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H_{m}(P) =\int{\min{-\pi}\max{\pi}\logS_{m}[P(\omega)] d\omega</tex> where S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> [P] denotes the sum of all the principal minors of order m of the matrix P. The main purpose of this paper is to show that the maximum entropy power spectrum (i.e., the power spectrum which maximizes the entropy) is identical with the autoregressive power spectrum (i.e., the power spectrum obtained by the autoregressive fitting) even in the degenerate rank case.

Ocean tidal perturbations on the orbit of the satellite “STARLETTE”

A continuous 300-day, world-wide laser-ranging data of the satellite STARLETTE between October 1976 and July 1977 was used to analyse the perturbation of the orbit by ocean tide. The long-period (longer than 20d) perturbations in the orbital inclination by the four main tide components K 1, P 1, K 2, S 2 were clearly identifiable in the maximum entropy power spectrum and periodogram. By comparing orbits including and excluding the tidal terms, the effect of the tide on the position of the satellite over 5 days was found to be of the order of one meter.

Observations indicating parametric instabilities in internal gravity waves at thermospheric heights

Abstract Theoretical studies predict a parametric instability of finite-amplitude internal gravity waves which hitherto has been observed only in laboratory experiments. The occurrence of this process in the atmosphere is of basic interest because finite-amplitude gravity waves, which are almost ubiquitous especially at upper atmospheric heights, would produce unstable flows even at large Richardson numbers. Maximum entropy power spectra of a strong internal gravity wave in the thermosphere, which was generated by a volcanic eruption and detected on records of the Doppler shift of high-frequency radio waves, in fact show good agreement with the spectra of synthetic Doppler records obtained from a calculated unstable gravity wave. The frequencies and wavenumbers observed in the gravity wave domain satisfy in particular the theoretically predicted resonance conditions. The observed Doppler records also show two significant lines in the acoustic domain which probably result from a nonlinear interaction with ...

Maximum entropy power spectrum estimation with uncertainty in correlation measurements

The purpose of this paper is to present a multidimensional MEM algorithm, valid for nonuniformly sampled arrays, which satisfies a "correlation-approximating" constraint. To this end, the correlation matching equality constraints of the usual MEM are replaced by a single inequality constraint whose form is based on a measure of the noise in the given autocovariance function (ACF). In this way, one can incorporate into the model knowledge of the noisy nature of the "given" ACF, since the "given" ACF is usually estimated from the samples of the wavefield. Specifically, the covariance matrix of the correlation estimates is used in a quadratic form that weights the difference between the "given" ACF and the one matched by the power spectrum. The maximization of entropy under this inequality constraint leads, ultimately, to a steepest-descent algorithm. The algorithm has been tested with 1-D synthetic data representing multiple sinusoids buried in additive white noise. The performance of this modified MEM algorithm is compared to a traditional MEM algorithm for extendible ACF's and for different SNR's. Examples of the MEM spectrum are given for the case of nonextendible ACF's.

Properties of two-dimensional maximum entropy power spectrum estimates

In this paper we present the results of a number of experiments that have been performed to study the properties of two-dimensional maximum entropy spectral estimates. The results presented include studies on the resolution differences for real and complex data, resolution properties of the spectral estimates, and the determination of the relative power of the sinusoids from the spectral estimates. The results also include the effects of signal-to-noise ratio, size and shape of the known autocorrelation region, and data length and initial phase of a sinusoid, on the spectral estimates. In most cases studied, the properties of two-dimensional maximum entropy spectral estimates can be viewed as simple extensions of their one-dimensional counterparts.

Maximum entropy power spectrum estimation of signals with missing correlation points

A computationally simple algorithm has been recently proposed by Lim and Malik [1] to solve the two-dimensional (2-D) maximum entropy (ME) power spectrum estimation (PSE) problem. In this note, we illustrate that this algorithm also solves the ME PSE problem for both 1-D and 2-D signals when the region in which the correlation function is known has any arbitrary shape that includes the origin.