IEE Proceedings F (Radar and Signal Processing)
Volume 140, Issue 6, December 1993
Volumes & issues:
Volume 140, Issue 6
December 1993
Editorial. Applications of higher order statistics
- Author(s): Jerry M. Mendel and Asoke K. Nandi
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 341 –342
- DOI: 10.1049/ip-f-2.1993.0050
- Type: Article
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p.
341
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Two-channel tests for common non-gaussian signal detection
- Author(s): J.K. Tugnait
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 343 –349
- DOI: 10.1049/ip-f-2.1993.0051
- Type: Article
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p.
343
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The problem of detecting an unknown, random, stationary, non-Gaussian signal that is common to two spatially separated sensors, is considered. The signal is assumed to have a nonvanishing bispectrum. The measurement noise sequences at the two sensors are either mutually independent with arbitrary cumulant spectra, or dependent with vanishing bispectra. Two statistical tests are presented for signal detection when the noise statistics are unknown. The performance of the tests is illustrated by computer simulation examples.
Single sensor detection and classification of multiple sources by higher-order spectra
- Author(s): M.C. Doǧan and J.M. Mendel
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 350 –355
- DOI: 10.1049/ip-f-2.1993.0052
- Type: Article
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p.
350
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The authors consider the detection and classification of multiple non-Gaussian linear sources by superposition of their waveforms available from a single sensor whose measurements are possibly corrupted by additive Gaussian noise. It is shown that by using multiple frequency lags of the trispectrum of single sensor measurements, it is possible to form a trispectral matrix C that possesses the same structure as the array covariance matrix of narrowband multisensor measurements. Consequently, techniques that are applicable to narrowband array processing can be adapted for the analysis of single sensor data; the rank of C reveals the number of sources, and a multiple signal characterisation (MUSIC)-like method can be used for source classification using a directory of candidate source spectra. Simulations are included to illustrate the proposed methods.
Blind deconvolution of coloured signals based on higher-order cepstra and data fusion
- Author(s): A.P. Petropulu and C.L. Nikias
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 356 –361
- DOI: 10.1049/ip-f-2.1993.0053
- Type: Article
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p.
356
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A new nonparametric blind deconvolution algorithm for coloured non-Gaussian signals is presented. The goal of blind deconvolution is the reconstruction of the input of an unknown linear time-invariant (LTI) mixed-phase system based only on the system output. The existing deconvolution schemes that require the least amount of knowledge about the input signal and the LTI system were developed for white input signals, or rely on parametric modelling of both the system and the input. To develop nonparametric algorithms for the deconvolution of coloured processes of unknown statistics, we are forced to consider a two-channel approach. The proposed algorithm utilises the data collected by two different receivers, each being the output of a different system due to the same input. The two systems are then reconstructed combining higherorder statistics of the measured signals and the theory of signal reconstruction from the higherorder spectral phase only.
Blind beamforming for non-gaussian signals
- Author(s): J.F. Cardoso and A. Souloumiac
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 362 –370
- DOI: 10.1049/ip-f-2.1993.0054
- Type: Article
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p.
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The paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resort to their hypothesised value. By using estimates of the directional vectors obtained via blind identification, i.e. without knowing the array manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors etc., so that neither array calibration nor physical modelling is necessary. Rather suprisingly, ‘blind beamformers’ may outperform ‘informed beamformers’ in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption on which blind identification relies is the statistical independence of the sources, which is exploited using fourth-order cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalisation of fourth-order cumulant matrices; its implementation is described, and its performance is investigated by numerical experiments.
Analysis of floating point roundoff errors in the estimation of higher-order statistics
- Author(s): D. Hatzinakos
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 371 –379
- DOI: 10.1049/ip-f-2.1993.0055
- Type: Article
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p.
371
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A floating point roundoff error analysis in the estimation of higher-order statistics, moments or cumulants of real stationary processes from single data records is provided. Closed form expressions or upper bounds are derived for the mean and variance of the quantisation noise introduced in the estimation of the all-zero and all-T (diagonal slice) moments, power, skewness and kurtosis. Numerical and simulation results show that the roundoff noise can significantly affect the moment and cumulant estimates, especially when long data records are employed for the purpose of reducing the estimation variance. The obtained results can provide guidelines in choosing a processor with the appropriate register length (in number of bits) in applications that require the calculation of higher-order statistics.
Robust estimation of third-order cumulants in applications of higher-order statistics
- Author(s): A.K. Nandi
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 380 –389
- DOI: 10.1049/ip-f-2.1993.0056
- Type: Article
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p.
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A number Of robust estimation of location algorithms are employed to estimate the third order cumulants of various lags from simulated signals representing the zero mean triangular, uniform and Gaussian distributions (as examples of symmetric distributions). Similar simulations have been performed on the output of AR, MA and ARMA systems that are being driven with random Gaussian input. Results appear to suggest that the (median), (weighted) biweight, and (weighted) wave estimators provide cumulant estimates consistent with expectations and of less variance than the mean estimator. This solves the problem with regard to symmetric distributions as these robust estimators have been designed for symmetric distributions. When these are applied to contaminated and asymmetric distributions (weighted) biweight and (weighted) wave estimators appear to give encouraging results. For asymmetric probability distributions, the various location parameters like the mean, median etc. are different, and further work with the particular emphasis on the estimation from asymmetric distributions is needed.
Distributions of particle displacements via higher-order moment functions
- Author(s): D.R. Brillinger
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 390 –394
- DOI: 10.1049/ip-f-2.1993.0057
- Type: Article
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p.
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Concern is with phenomena that are moving and developing in time. Indistinguishable particles are displaced independently, with successive displacements possibly correlated. One wishes to estimate the joint probability distribution of those displacements. It is shown how this may be done via estimates of higher-order cumulant densities and spectra. The results simplify in the case that the original placements of the particles are homogeneous Poisson. Surprisingly then the cumulant density is essentially the probability density.
ICA-based technique for radiating sources estimation: application to airport surveillance
- Author(s): E. Chaumette ; P. Comon ; D. Muller
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 395 –401
- DOI: 10.1049/ip-f-2.1993.0058
- Type: Article
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p.
395
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As aerial traffic becomes greater, it is more difficult to locate and recognise aircraft in the neighbourhood of civil airports. The technique proposed here resorts to a particular device, monopulse radar, and to a recent tool called the independent component analysis (ICA) to separate messages falling in the same radar beam. The algorithms used to compute the ICA use fourthorder cumulants of the observed signals.
Orthogonalised frequency domain volterra model for non-gaussian inputs
- Author(s): S.B. Kim and E.J. Powers
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 402 –409
- DOI: 10.1049/ip-f-2.1993.0059
- Type: Article
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p.
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An orthogonalised Volterra system model, valid for both non-Gaussian and Gaussian inputs, is presented. The approach is based on ordered sets of conditioned orthogonal higherorder input vectors in the frequency domain, and utilises co-ordinate transformation to relate the orthogonal and nonorthogonal system models. The orthogonal model exhibits no interference effects, thus facilitating physical interpretation of the nonlinear system model. The importance of non-Gaussian excitation in the nonlinear system identification procedure is discussed. The performance of the orthogonalised Volterra model is measured in terms of a generalised nonlinear system coherence function, and compared with the results of the Wiener (for Gaussian input) and Volterra models. The advantages of the orthogonalised Volterra model are illustrated by using it to model the linear and quadratic responses of a tension leg platform subject to random seas, given experimental input-output time series data.
Differential delay-doppler estimation using second and higher-order ambiguity functions
- Author(s): A.V. Dandawaté and G.B. Giannakis
- Source: IEE Proceedings F (Radar and Signal Processing), Volume 140, Issue 6, p. 410 –418
- DOI: 10.1049/ip-f-2.1993.0060
- Type: Article
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p.
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Estimation of differential delay-Doppler parameters in passive sonar and radar applications is addressed. Without assuming Gaussianity it is shown that the conventional ambiguity function is asymptotically chi-squared and yields consistent delay-Doppler estimates for narrowband signals observed in uncorrelated sensor noises. Related asymptotic covariance expressions and their computable forms are also derived. It is further shown that the performance of the ambiguity function degrades severely when the sensor noises are correlated. To deal with such noises a novel third-order ambiguity function is proposed and is shown to be consistent and theoretically immune to Gaussian and symmetrically distributed disturbances. Further, to take into account the errors due to variances of sample statistics, alternative delay-Doppler estimators are defined to minimise a cumulant matching criterion and related issues are discussed. The case of wideband signals is also addressed and, finally, extensions to kth-order ambiguity functions are proposed. Computer simulations are performed to confirm the theory. Throughout the paper the analysis treats both deterministic and stochastic signals on a common framework. Connections with active sonar and radar problems are also shown as a special case.
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