Target Detection and Classification by UWB Communication Signal Based on Third-Order Cumulants
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Keywords:
Statistic
Cumulant
SIGNAL (programming language)
Higher-order statistics
Identification
Detection theory
This paper focuses on nonminimum phase FIR system identification using higher-order cyclic cumulants alone, and proposes two linear normal equation algorithms for parameter estimation and SVD-based order determination methods. The system unidentifiable from second-order cyclostationary statistics are shown to be identifiable using the proposed higher-order cyclic cumulants based algorithms. Simulations are given to verify the high performance of the new methods.
Cumulant
Cyclostationary process
Higher-order statistics
Identification
Finite impulse response
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The goal of the this work is twofold, namely: 1) to discuss a method for identification of linear 2-D nonminimum phase system using higher order cumulants alone, and to derive the almost-sure convergence properties of sample estimates of higher-order spatial statistics. The measure of almost sure convergence is obtained for the sample estimates of third and fourth order moments and cumulants. 2) The experimental cumulants are used as texture features, they are later, incorporated into classification schemes. Some applications using synthetic textures and aerial images are presented to illustrate great descriptive power of higher-order cumulants.
Cumulant
Higher-order statistics
Sample (material)
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New features based on sixth-order cumulants are proposed for classification of MPSK signals. Theoretical analysis justifies that the ability of suppressing multi-path fading improves as as the order number of cumulants features increases. Performance of proposed approach is demonstrated via computer simulations. The multi-path channel is assumed to be FIR model. MPSK signals are corrupted by Gaussian noise. The simulation results of probability of correct classification show that sixth-order cumulants method work better than fourth-order cumulants under the deeply multi-path fading channel environments and the fourth-order cumulants method work better than sixth-order cumulants when the signal-to-noise ratio (SNR) is lower than or equal to 0dB.
Cumulant
Higher-order statistics
Gaussian Noise
Modulation (music)
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In this work, the features are extracted for the arrhythmia classification from the electrocardiograph (ECG) signals by using Higher order statistics. K-nearest neighborhood algorithm is used as classifier. Cumulants are calculated from the raw signals obtained from consecutive sample values of each R peak in ECG signals and used as features. In addition to these features, different features obtained from the relations of cumulants are also used. Simulation results shows that features obtained from the relations among cumulants are more discriminative than the cumulants.
Cumulant
Higher-order statistics
Discriminative model
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This paper describes a method of estimating the parameters of sinusoidal harmonic signals buried in hybrid colored noise. We define novel high-order statistics, referred to as cross-fourth-order cumulants, that is the basis of the method proposed. The method is insensitive to hybrid colored noise. Employing cross-fourth-order cumulants, we estimated the sinusoid parameters using the moment method that has been developed on the Yule-walker equation of cross-fourth-order cumulants. Simulation results show that the new method is accurate and can suppress the effect of hybrid colored noise.
Cumulant
Higher-order statistics
Colors of noise
Colored
Basis (linear algebra)
Harmonic
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Sample estimates of moments and cumulants are known to be unstable in the presence of outliers. This problem is especially severe for higher order statistics, like kurtosis, which are used in algorithms for independent components analysis and projection pursuit. In this paper we propose robust generalizations of moments and cumulants that are more insensitive to outliers but at the same time retain many of their desirable properties. We show how they can be combined into series expansions to provide estimates of probability density functions. This in turn is directly relevant for the design of new robust algorithms for ICA. We study the improved statistical properties such as B-robustness, bias and variance while in experiments we demonstrate their improved behavior.
Cumulant
Robustness
Higher-order statistics
Kurtosis
Robust Statistics
Projection pursuit
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In this paper, we investigate the use of output 4th-order cumulants to detect the number of source signals on a multiple-input single-output (MISO) communications channel and blindly identify their respective channel coefficients. More particularly, we are interested in the case of two sources. The proposed cumulant-based order detection principle allows us for recovering the longest channel order and its coefficients. A similar procedure is applied for detecting the presence of a second source as well as estimating its associated channel order and coefficients. When only estimated cumulants are available, we implement two hypothesis tests based on three proposed test-statistics. Computer simulations illustrate the performances obtained with the methods proposed for order detection and channel identification.
Cumulant
Higher-order statistics
Identification
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A new algorithm for end-point detection in noisy background conditions based on the statistical properties of higher-order cumulants of speech signal is presented in this paper. Since the higher-order cumulants are blind for Gaussian signal, the proposed method is especially effective to the problem of end-point detection of speech signals in Gaussian noise. The above conclusions are supported by the experimental results.
Cumulant
Higher-order statistics
Gaussian Noise
Detection theory
SIGNAL (programming language)
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Most real-world signals are non-Gaussian. If they were Gaussian then they could be completely characterized by their first- and second-order statistics, because the probability density function (p.d.f.) for a Gaussian signal is completely described by these statistics. Because most real-world signals are not Gaussian, we need to use more than just first- and second-order statistics, i.e., we need to use "higher-order statistics." We could use higher-order moments, e.g., triplecorrelations, quadruple-correlations, etc., or we could use cumulants. Cumulants are related to higher-order moments, but do not necessarily always equal these moments. Reasons for preferring cumulants over moments are explained below.
Higher-order statistics
Cumulant
L-moment
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A blind acoustic source separation algorithm is presented which combines second order statistics, time-delayed autocorrelation and 4th order cumulants. Because the 4th order cumulants are not sensitive to the Gaussian signal, the combined method is more applicable for lower SNR with white Gaussian noise. In order to improve the performance, the sensor signals are orthogonalized first using 4th order cumulants, then the mixing matrix can be estimated from the preprocessed data using the combined algorithm. Experiment demonstrates that the combined algorithm is more effective than using only second order statistics, especially in hard environment
Cumulant
Higher-order statistics
Autocorrelation matrix
Decorrelation
Gaussian Noise
SIGNAL (programming language)
Source Separation
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