Motion estimation using higher order statistics

The objective of this paper is to introduce a fourth-order cost function of the displaced frame difference (DFD) capable of estimating motion even for small regions or blocks. Using higher than second-order statistics is appropriate in case the image sequence is severely corrupted by additive Gaussian noise. Some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the DFD.     

Low-rank estimation of higher order statistics

Low-rank estimators for higher order statistics are considered in this paper. The bias-variance tradeoff is analyzed for low-rank estimators of higher order statistics using a tensor product formulation for the moments and cumulants. In general, the low-rank estimators have a larger bias and smaller variance than the corresponding full-rank estimator, and the mean-squared error can be significantly smaller. This makes the low-rank estimators extremely useful for signal processing algorithms based on sample estimates of the higher order statistics. The low-rank estimators also offer considerable reductions in the computational complexity of such algorithms. The design of subspaces to optimize the tradeoffs between bias, variance, and computation is discussed, and a noisy input, noisy output system identification problem is used to illustrate the results     

Joint estimation of time delay and frequency delay in impulsivenoise using fractional lower order statistics

New methods for time delay estimation and joint estimation of time delay and frequency delay in the presence of impulsive noise are introduced. First, degradation of the conventional approaches based on second-order statistics is shown both theoretically and experimentally. Then, a new class of robust algorithms are developed using the theory of alpha-stable distributions, including the fractional lower order covariance (FLOC) method, which is formulated for the time delay estimation problem and the fractional lower order ambiguity function (FLOAF), which is defined for the joint estimation of time delay and frequency delay. It is shown that these new methods are robust for both Gaussian and non-Gaussian impulsive noise environments. The improved performance is clearly demonstrated through detailed analysis and comprehensive simulations with computer-generated data as well as actual radar and sonar clutter data     

Time delay estimation using the cross bispectrum

The cross bispectrum phase can be effectively used to estimate the time required for a nonGaussian signal to propagate between a pair of spatially separated sensors in the presence of highly correlated Gaussian noise. The authors present a consistent estimator of the phase of the cross bispectrum, derive the exact distribution of the phase of a complex Gaussian sample bispectrum, and show that in most cases the exact distribution can be approximated by a Gaussian distribution. Using this Gaussian approximation, the authors derive the variance of the time delay estimate computed from the sample cross bispectrum of a signal in additive correlated noise. These results allow the performance of time delay estimators based on the cross bispectrum phase to be quantified as a function of the sample size, the skewness of the signal, the signal-to-noise ratio (SNR), and the noise correlation     

Harmonic retrieval using higher order statistics: a deterministicformulation

Given a single record, the authors consider the problem of estimating the parameters of a harmonic signal buried in noise. The observed data are modeled as a sinusoidal signal plus additive Gaussian noise of unknown covariance. The authors define novel higher order statistics-referred to as “mixed” cumulants-that can be consistently estimated using a single record and are insensitive to colored Gaussian noise. Employing fourth-order mixed cumulants, they estimate the sinusoid parameters using a consistent, nonlinear matching approach. The algorithm requires an initial estimate that is obtained from a consistent, linear estimator. Finally, the authors examine the performance of the proposed method via simulations     

General formula for conditional mean using higher order statistics

A general formula is given for conditional mean, which is the well-known minimum variance estimator, in terms of cross-cumulants and locally optimum nonlinearities. This formula will greatly facilitate the solution of various problems emerging in nonlinear system identification, non-Gaussian estimation theory, and nonlinear signal processing     

基于零阶统计量的韧性归一化自适应时间延迟估计

依据零阶统计量理论,给出对数矩过程、对数宽平稳及对数各态遍历的定义,提出一种韧性的归一化自适应时间延迟估计方法(简称NZOSTDE).该算法用FIR滤波器对两个含有脉冲噪声的观测信号建模,利用不存在有限方差的脉冲信号经过对数变换后其各阶矩的存在性和几何功率的概念,在对数域基于最小均方误差(LMS)准则归一化自适应得到FIR滤波器的系数,该系数最大值对应的序号就是时间延迟的估计值.本文提出的新算法克服了基于分数低阶统计量(FLOS)算法的局限性.计算机仿真实验表明,NZOSTDE算法在强脉冲噪声环境下比归一化最小平均P范数时间延迟估计方法(简称NLMPTDE)算法更具有韧性.     

Characterization of sleep spindles using higher order statistics and spectra

This work characterizes the dynamics of sleep spindles, observed in electroencephalogram (EEG) recorded from humans during sleep, using both time and frequency domain methods which depend on higher order statistics and spectra. The time domain method combines the use of second- and third-order correlations to reveal information on the stationarity of periodic spindle rhythms to detect transitions between multiple activities. The frequency domain method, based on normalized spectrum and bispectrum, describes frequency interactions associated with nonlinearities occurring in the observed EEG.     

Adaptive interference canceler for narrowband and widebandinterferences using higher order statistics

A new higher order statistics-based adaptive interference canceler is introduced to mitigate narrowband and wideband interferences in environments where the interference is non-Gaussian and a reference signal, which is highly correlated with the interference, is available. The new scheme uses higher order statistics (HOS) of the primary and reference inputs and employs a gradient-type algorithm for updating the adaptive filter coefficients. The update equation of the HOS-based adaptive filter is independent of uncorrelated Gaussian noises and can mitigate the interference more effectively than adaptive filters based on second-order statistics. The performance of the. HOS-based adaptive filter is much less sensitive to the choice of the step size parameter than the adaptive filters based on the LMS algorithm. It is demonstrated, by means of extensive simulations, that the HOS-based filter can mitigate both narrowband and wideband interferences effectively. Comparisons with adaptive filters based on the LMS algorithm and second-order statistics are also presented in the paper     

Time delay and spatial signature estimation using knownasynchronous signals

This paper considers the problem of estimating the parameters of known signals received asynchronously by an array of antennas. The parameters of primary interest are the time delays of the signals and their spatial signatures at the array. Estimates of the signal directions of arrival are also considered but are of secondary importance in this work. Maximum likelihood algorithms and more computationally efficient approximations are developed for both the case where all received signals are identical (the channel estimation/overlapping echo problem) and where they are all distinct. Conditions are also derived under which the standard matched filter approach yields consistent and statistically efficient parameter estimates. The issue of solution uniqueness is addressed, and in particular, an upper bound on the number of signals whose parameters may be uniquely identified is derived for a number of different cases. Typically, the bound is far greater than the number of sensors and is limited only by the number of data samples collected. Some representative simulation examples are also included to illustrate the algorithms' performance relative to the Cramer-Rao bound     

A nonparametric phase estimation method for SIMO systems based onsecond-order and higher order statistics

We present a nonparametric phase estimation algorithm for linear single-input multiple-output (SIMO) channels. Given an unknown stationary input signal with known statistics, our approach is to obtain the joint minimum mean square phase estimation based on the polyspectra and the cross-spectra of the SIMO channel outputs. By utilizing both higher order and second-order statistics of the channel outputs, our approach is shown to be more accurate and reliable than methods based on higher order statistics alone. It can be applied to SIMO channels with common zeros     

Estimation of linear parametric models using inverse filtercriteria and higher order statistics

Considers the problem of estimating the parameters of a stable, scalar ARMA (p, q) signal model (causal or noncausal, minimum phase or mixed phase) driven by an i.i.d. non-Gaussian sequence. The driving noise sequence is not observed. The Wiggins-Donoho (1978, 1991) class of inverse filter criteria for estimation of model parameters are analyzed and extended. These criteria have been considered in the past only for moving average inverse filters. These criteria are extended to general ARMA inverses. Computer simulation examples are presented to illustrate the proposed approaches     

一种基于高阶谱的广义相位数据时延估计算法

为改善高阶谱相位数据时延估计算法的性能，研究了一种基于高阶谱的广义相位数据时延估计算法。该算法采用基于双谱的相干函数在高阶谱域对相位数据进行加权和加窗处理，以提高时延估计精度。最后用实测的直升机噪声信号进行了仿真，对各种相位数据时延估计算法性能进行了比较，验证了新算法的有效性。     

On higher order statistics of the Nakagami-m distribution

This paper proposes a fading model that leads to a formal, but simple method to obtain the exact formula of the Nakagami-m published in 1960 distribution for m=n/2, with n a nonzero integer number. Based on such a model, the joint distribution of the envelope and its time derivative are accomplished, and exact formulas for the level crossing rate (closed-form formula) and for the average fade duration are derived. Simulation curves and exact formulas are checked against each other and a very good agreement between them is attained. Although derived for discrete values of m (m being an integer multiple of 1/2), there are no mathematical constraints for these expressions to be used for any real value of m⩾1/2     

分数低阶循环统计量及其在脉冲噪声环境下时延估计中的应用

本文以α稳定分布作为噪声模型,研究了非高斯噪声对传统的二阶循环统计量的影响,提出了分数低阶循环统计量的概念,研究并证明了其性质。在此基础上提出基于分数低阶循环统计量的新的时延估计方法—RCCC(Robust Corre- lated Cyclic Covariation)。计算机模拟表明,这种算法是一种在高斯和α稳定分布噪声条件下具有良好韧性的时延估计方法。     

Identification and deconvolution of multichannel linearnon-Gaussian processes using higher order statistics and inverse filtercriteria

This paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple-input multiple-output (MIMO) system given only the measurements of the vector output of the system. The system is assumed to be driven by a temporally i.i.d. and spatially independent non-Gaussian vector sequence (which is not observed). An iterative, inverse filter criteria-based approach is developed using the third-order or the fourth-order normalized cumulants of the inverse filtered data at zero lag. Stationary points of the proposed cost functions are investigated. The approach is input iterative, i.e., the input sequences are extracted and removed one by one. The matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs. Identifiability conditions are analyzed. The strong consistency of the proposed approach is also briefly discussed. Computer simulation examples are presented to illustrate the proposed approaches     

Texture decomposition by harmonics extraction from higher order statistics

In this paper, a method of harmonics extraction from Higher Order Statistics (HOS) is developed for texture decomposition. We show that the diagonal slice of the fourth-order cumulants is proportional to the autocorrelation of a related noiseless sinusoidal signal with identical frequencies. We propose to use this fourth-order cumulants slice to estimate a power spectrum from which the harmonic frequencies can be easily extracted. Hence, a texture can be decomposed into deterministic components and indeterministic components as in a unified texture model through a Wold-like decomposition procedure. The simulation and experimental results demonstrated that this method is effective for texture decomposition and it performs better than traditional lower order statistics based decomposition methods.     

Detection of quadratic phase coupling from human EEG signals using higher order statistics and spectra

Interactions among neural signals in different frequency components have become a focus of strong interest in biomedical signal processing. The bispectrum is a method to detect the presence of quadratic phase coupling (QPC) between different frequency bands in a signal. The traditional way to quantify phase coupling is by means of the bicoherence index (BCI), which is essentially a normalized bispectrum. The main disadvantage of the BCI is that the determination of significant QPC becomes compromised with noise. To mitigate this problem, a statistical approach that combines the bispectrum with an improved surrogate data method to determine the statistical significance of the phase coupling is introduced. The method was first tested on two simulation examples. It was then applied to the human EEG signal that has been recorded from the scalp using international 10–20 electrodes system. The frequency domain method, based on normalized spectrum and bispectrum, describes frequency interactions associated with nonlinearities occurring in the observed EEG.     

Detection and classification of spectrally equivalent processesusing higher order statistics

This paper addresses the problem of detecting two spectrally equivalent processes, which are modeled by a noisy AR process and an ARMA process. Higher order statistics (HOS) are shown to be efficient tools for detection. Two HOS-based detectors are derived for the binary hypothesis testing problem (i.e., known signal spectrum): The first detector exploits the asymptotic Gaussianity of the sample estimates of the cumulants. The second detector exploits the singularity of a certain matrix based on HOS. The more general composite hypothesis testing problem (i.e., with unknown signal spectrum) is then considered and a detector proposed. The performances of the different detectors are compared in terms of receiver operating characteristic (ROC) curves. Approximate closed-form expressions are derived for the threshold and the ROCs of the three detectors     

Application of higher order statistics to surface electromyogram signal classification

We propose a novel approach for surface electromyogram (sEMG) signal classification. This approach utilizes higher order statistics of sEMG signal to classify four primitive motions, i.e., elbow flexion, elbow extension, forearm supination, and forearm pronation. In documented research, the sEMG signal generated during isometric contraction is modeled by a stationary process whose probability density function (pdf) is assumed to be either Gaussian or Laplacian. In this paper, using Negentropy, we demonstrate that the level of non-Gaussianity of sEMG signal recorded in muscular forces below 25% of maximum voluntary contraction (MVC) is significant. Therefore, application of higher order statistics in sEMG signal processing is justified, due to the fact that more useful information can be extracted from the corresponding higher order statistics. An accurate classification is achieved by using the sequential forward selection (SFS) method for reducing of the dimensionality of feature space and the K-nearest neighbor (KNN) classifier. The results indicate that the proposed approach provides higher sEMG correct classification rates as compared to the existing methods.