Minimum Dispersion Criterion Research Articles

ADS-B overlapping signals separation based on minimum dispersion criterion

As a new generation of air traffic management (ATM) monitoring system, the airborne automatic dependent surveillance-broadcast (ADS-B) transmitters will broadcast their position, speed, and other information to enhance the efficiency and safety of air traffic. However, due to the asynchronous nature of ADS-B transmitters broadcasting their information on the same frequency, it is inevitable for multiple ADS-B signals from different aircraft to overlap. This paper proposes an ADS-B signal separation algorithm based on the minimum dispersion criterion (MD), which takes advantage of the non-Gaussian distribution properties exhibited by ADS-B signals. Firstly, the non-Gaussian distribution properties of overlapping ADS-B signals are illustrated by analyzing their probability density distribution and kurtosis. Secondly, the separation problem is formulated as a non-convex optimization problem based on the minimum dispersion criterion. Finally, the alternating direction method of multipliers (ADMM) is employed to tackle the formulated optimization problem. Simulations will demonstrate the effectiveness of the proposed algorithm.

Adaptive sign algorithm for graph signal processing

Efficient and robust online processing techniques for irregularly structured data are crucial in the current era of data abundance. In this paper, we propose a graph/network version of the classical adaptive Sign algorithm for online graph signal estimation under impulsive noise. The recently introduced graph adaptive least mean squares algorithm is unstable under non-Gaussian impulsive noise and has high computational complexity. The Graph-Sign algorithm proposed in this work is based on the minimum dispersion criterion and therefore impulsive noise does not hinder its estimation quality. Unlike the recently proposed graph adaptive least mean pth power algorithm, our Graph-Sign algorithm can operate without prior knowledge of the noise distribution. The proposed Graph-Sign algorithm has a faster run time because of its low computational complexity compared to the existing adaptive graph signal processing algorithms. Experimenting on steady-state and time-varying graph signals estimation utilizing spectral properties of bandlimitedness and sampling, the Graph-Sign algorithm demonstrates fast, stable, and robust graph signal estimation performance under impulsive noise modeled by alpha stable, Cauchy, Student’s t, or Laplace distributions.

A Total Lp-Norm Optimization for Bearing-Only Source Localization in Impulsive Noise with SαS Distribution

This paper considers the problem of robust bearing-only source localization in impulsive noise with symmetric -stable distribution based on the Lp-norm minimization criterion. The existing Iteratively Reweighted Pseudolinear Least-Squares (IRPLS) method can be used to solve the least LP-norm optimization problem. However, the IRPLS algorithm cannot reduce the bias attributed to the correlation between system matrices and noise vectors. To reduce this kind of bias, a Total Lp-norm Optimization (TLPO) method is proposed by minimizing the errors in all elements of system matrix and data vector based on the minimum dispersion criterion. Subsequently, an equivalent form of TLPO is obtained, and two algorithms are developed to solve the TLPO problem by using Iterative Generalized Eigenvalue Decomposition (IGED) and Generalized Lagrange Multiplier (GLM), respectively. Numerical examples demonstrate the performance advantage of the IGED and GLM algorithms over the IRPLS algorithm.

Transient performance study of gradient algorithm of antenna array adaptation

The paper presents a study into transient performance of the original gradient algorithm for the criterion of minimal noise dispersion. Synthesized during previous research, original gradient algorithm for the criterion of minimal dispersion shows an advantage in that it does not require formation of a reference signal for the adaptive antenna array adjustment. It is stressed, that to fully assess the possibility of practical implementation of the designed algorithm, it is necessary to carry out its comparative analysis with classical gradient algorithm of the steepest descent for root mean square error criterion. Comparison for the two algorithms is done for four interference situations by the way of computer simulation. While analyzing simulation results, it is found that adaptation of the both algorithms to a large extent is determined by the interfering signals correlation matrix parameters of antenna array, namely its eigenvalues spread. During transient performance estimation, it is revealed a tendency that the curve of adaptation for the original gradient algorithm for minimal noise dispersion criterion consists from some distinct segments with different steepness. It is postulated that these segments are determined by the number and the magnitudes of the eigenvalues of the interfering signals correlation matrix of the antenna array. The main conclusion is the one that the original gradient algorithm for minimal noise dispersion criterion and the classical gradient algorithm of the steepest descent for root mean square error criterion demonstrated pretty equal performances in the different interference environments. From the computer simulation, it is stressed that original gradient algorithm for antenna array adaptation for the noise minimum dispersion criterion can be used instead of the gradient algorithm of the steepest descent for the root mean square error criterion, especially in those applications where formation of the reference signal is impossible or problematic.

Robust adaptive beamforming against large steering vector mismatch based on minimum dispersion

Many efforts have been recently devoted to adaptive beamformers based on the minimum dispersion (MD) criterion for non-Gaussian signals, which results in improved signal-to-noise ratio performance. However, large steering vector mismatch and inappropriate choice of uncertainty set will cause performance degradation to the existing MD-based methods. To address these issues, we develop a robust MD-based beamformer against large steering vector mismatch, which utilizes multiple small uncertainty sets to cover the whole uncertainty region. The ℓp−norm (p≥1) minimization problem turns to be nonlinear and nonconvex because of these multi-uncertainty-set constraints. To solve the problem, a projected gradient algorithm is utilized to transform the original problem into a nonconvex quadratically constrained quadratic programming (QCQP) problem. The semidefinite programming relaxation technique is then employed in each iteration to deal with the nonconvex QCQP problem. Numerical results demonstrate that the proposed beamformer offers a significant performance improvement in case of large steering vector mismatch for non-Gaussian signals compared with the conventional schemes.

Phase-Only Robust Minimum Dispersion Beamforming

A phase-only robust minimum dispersion (PO-RMD) beamformer is devised for non-Gaussian signals. Unlike conventional beamformers that adjust the complex-valued weights, including both amplitude and phase, of each antenna to fulfill spatial filtering, the proposed PO-RMD employs a unit-modulus constraint on the weights, which is equivalent to simply phase shifting at each antenna. Instead of the widely used minimum variance criterion, the PO-RMD adopts the minimum dispersion criterion, which minimizes the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm of the array output to utilize the non-Gaussianity of the signals. To achieve robustness against model uncertainty, the magnitude response of any steering vector within an uncertainty region is forced to exceed the threshold. A gradient projection (GP) algorithmic framework is developed to solve the resulting nonconvex optimization problem. In order to find a feasible point in the intersection of the unit-modulus, and robustness constraint sets in each iteration, an alternating projection algorithm is also devised. More importantly, the closed-form expressions of the projection onto the two sets are derived, which only need a low complexity of O(M) with M being the number of antennas. Convergence of the alternating projection is analyzed, and the local linear convergence rate is established. Simulation results demonstrate the fast convergence rate, and accuracy of the GP, as well as the simplicity and robustness of the PO-RMD.

Compressive Sensing Using Symmetric Alpha-Stable Distributions for Robust Sparse Signal Reconstruction

Traditional compressive sensing (CS) primarily assumes light-tailed models for the underlying signal and/or noise statistics. Nevertheless, this assumption is not met in the case of highly impulsive environments, where non-Gaussian infinite-variance processes arise for the signal and/or noise components. This drives the traditional sparse reconstruction methods to failure, since they are incapable of suppressing the effects of heavy-tailed sampling noise. The family of symmetric alpha-stable (SαS) distributions, as a powerful tool for modeling heavy-tailed behaviors, is adopted in this paper to design a robust algorithm for sparse signal reconstruction from linear random measurements corrupted by infinite-variance additive noise. Specifically, a novel greedy reconstruction method is developed, which achieves increased robustness to impulsive sampling noise by solving a minimum dispersion (MD) optimization problem based on fractional lower-order moments. The MD criterion emerges naturally in the case of additive sampling noise modeled by SαS distributions, as an effective measure of the spread of reconstruction errors around zero, due to the lack of second-order moments. The experimental evaluation demonstrates the improved reconstruction performance of the proposed algorithm when compared against state-of-the-art CS techniques for a broad range of impulsive environments.

Robust minimum dispersion distortionless response beamforming against fast-moving interferences

The recently proposed minimum dispersion distortionless response (MDDR) beamformer is able to improve the reception of non-Gaussian signals over the minimum variance distortionless response (MVDR) beamformer. However, the performance of the MDDR beamformer degrades in the presence of fast-moving interferences. To suppress such an interference, a robust beamformer against fast-moving interferences based on the minimum dispersion (MD) criterion is proposed, which provides a continuous deep null sector over a predefined range of dynamic angle-of-arrival (AOA). The designed beamformer ensures that the output is minimized in terms of dispersion and the average power over the dynamic AOA is zero via a quadratic constraint. In order to reduce the computational load, the optimization problem with a quadratic constraint is relaxed to its counterpart with a linear constraint. This allows us to devise an efficient beamforming approach, namely, gradient projection algorithm. Numerical results are provided to demonstrate that the developed beamformer can suppress the strong fast-moving interferences effectively.

Compass radius estimation for improved image classification using Edge-SIFT

The combination of SIFT descriptors with other features usually improves image classification, like Edge-SIFT, which extracts keypoints from an edge image obtained after applying the compass operator to a colour image. We evaluate for the first time, how the use of different radii in the compass operator affects the classification performance. We demonstrate that the value proposed in the literature, radius=4.00, is not the optimum from an image classification point of view. We also put in evidence that in ideal conditions, choosing an appropriate radius for each image yields accuracy values even higher than 95%. Finally, we propose a new method to estimate the best radius for the compass operator in each dataset. Using a training subset selected on the basis of a minimum dispersion criterion of edges density, we construct a richer dictionary for each dataset in our Bag of Words pipeline. From that dictionary it is selected a radius for the whole dataset that yields higher accuracy than using the value proposed in the literature. Using this method, we obtained improvements in the accuracy up to 24.4% in Soccer, 6.77% in COIL-RWTH-2, 4.46% in Birds, 3.82% in ImageNet_Dogs, 2.75% in ImageNet_Birds, 2.02% in Flowers and 1.75% in Caltech101 datasets.

Stable graphical models

Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce α-stable graphical (α-SG) models, a class of multivariate stable densities that can also be represented as Bayesian networks whose edges encode linear dependencies between random variables. One major hurdle to the extensive use of stable distributions is the lack of a closed-form analytical expression for their densities. This makes penalized maximum-likelihood based learning computationally demanding. We establish theoretically that the Bayesian information criterion (BIC) can asymptotically be reduced to the computationally more tractable minimum dispersion criterion (MDC) and develop StabLe, a structure learning algorithm based on MDC. We use simulated datasets for five benchmark network topologies to empirically demonstrate how StabLe improves upon ordinary least squares (OLS) regression. We also apply StabLe to microarray gene expression data for lymphoblastoid cells from 727 individuals belonging to eight global population groups. We establish that StabLe improves test set performance relative to OLS via ten-fold cross-validation. Finally, we develop SGEX, a method for quantifying di_erential expression of genes between di_erent population groups.

Adaptive Polynomial Filtering using Generalized Variable Step-Size Least Mean pth Power (LMP) Algorithm

This correspondence presents the adaptive polynomial filtering using the generalized variable step-size least mean $$p$$ p th power (GVSS-LMP) algorithm for the nonlinear Volterra system identification, under the $$\alpha $$ ? -stable impulsive noise environment. Due to the lack of finite second-order statistics of the impulse noise, we espouse the minimum error dispersion criterion as an appropriate metric for the estimation error, instead of the conventional minimum mean square error criterion. For the convergence of LMP algorithm, the adaptive weights are updated by adjusting $$p\ge 1$$ p ? 1 in the presence of impulsive noise characterized by $$1<\alpha <2$$ 1 < ? < 2 . In many practical applications, the autocorrelation matrix of input signal has the larger eigenvalue spread in the case of nonlinear Volterra filter than in the case of linear finite impulse response filter. In such cases, the time-varying step-size is an appropriate option to mitigate the adverse effects of eigenvalue spread on the convergence of LMP adaptive algorithm. In this paper, the GVSS updating criterion is proposed in combination with the LMP algorithm, to identify the slowly time-varying Volterra kernels, under the non-Gaussian $$\alpha $$ ? -stable impulsive noise scenario. The simulation results are presented to demonstrate that the proposed GVSS-LMP algorithm is more robust to the impulsive noise in comparison to the conventional techniques, when the input signal is correlated or uncorrelated Gaussian sequence, while keeping $$1<p<\alpha <2$$ 1 < p < ? < 2 . It also exhibits flexible design to tackle the slowly time-varying nonlinear system identification problem.

The Equivalency of Minimum Error Entropy Criterion and Minimum Dispersion Criterion for Symmetric Stable Signal Processing

The minimum error entropy (MEE) criterion in information theoretic learning is an efficient way to deal with non-Gaussian signal processing. And the minimum dispersion (MD) criterion has been widely applied in stable signal processing. In this letter, we show that there exists an equivalence between the MD criterion and the MEE criterion where symmetric $\alpha$ -stable $(S\alpha S)$ random variables are considered as the errors of the adaptive signal processing. As an application, we propose an algorithm with the MEE criterion for the time delay estimation (TDE) problem which was solved by the MD criterion.

New blind estimation method of evoked potentials based on minimum dispersion criterion and fractional lower order statistics

Evoked potentials (EPs) have been widely used to quantify neurological system properties. Tra-ditional EP analysis methods are developed under the condition that the background noises in EP are Gaussian distributed. Alpha stable distribution, a generalization of Gaussian, is better for modeling impulsive noises than Gaussian distribution in biomedical signal proc-essing. Conventional blind separation and es-timation method of evoked potentials is based on second order statistics or high order Statis-tics. Conventional blind separation and estima-tion method of evoked potentials is based on second order statistics (SOS). In this paper, we propose a new algorithm based on minimum dispersion criterion and fractional lower order statistics. The simulation experiments show that the proposed new algorithm is more robust than the conventional algorithm.

Nonlinear system identification in impulsive environments

Nonlinear system identification has been studied under the assumption that the noise has finite second and higher order statistics. In many practical applications, impulsive measurement noise severely weakens the effectiveness of conventional methods. In this paper, /spl alpha/-stable noise is used as a noise model. In such case, the minimum mean square error (MMSE) criterion is no longer an appropriate metric for estimation error due to the lack of finite second-order statistics of the noise. Therefore, we adopt minimum dispersion criterion, which in turn leads to the adaptive least mean pth power (LMP) algorithm. It is shown that the LMP algorithm under the /spl alpha/-stable noise model converges as long as the step size satisfies certain conditions. The effect of p on the performance is also investigated. Compared with conventional methods, the proposed method is more robust to impulsive noise and has better performance.

Blind separation of impulsive alpha-stable sources using minimum dispersion criterion

This letter introduces a novel blind source separation (BSS) approach for extracting impulsive signals from their observed mixtures. The impulsive signals are modeled as real-valued symmetric alpha-stable (S/spl alpha/S) processes characterized by infinite second- and higher-order moments. The proposed approach uses the minimum dispersion (MD) criterion as a measure of sparseness and independence of the data. A new whitening procedure by a normalized covariance matrix is introduced. We show that the proposed method is robust, so-named for the property of being insensitive to possible variations in the underlying form of sampling distribution. Algorithm derivation and simulation results are provided to illustrate the good performance of the proposed approach. The new method has been compared with three of the most popular BSS algorithms: JADE, EASI, and restricted quasi-maximum likelihood (RQML).

Detection in alpha-stable noise environments based on prediction

In this paper we consider detection of baseband signals in partial response signalling (PRS) systems in the presence of additive, coloured noise. The additive noise in the system is a mixture of Gaussian noise and impulsive noise modelled as an alpha-stable process. The dependence in observation samples results from the excess bandwidth in the matched filters of the receivers. The detectors proposed are based on a noise estimation–cancellation technique. In particular, by exploiting past decisions as well as past received samples, we estimate the noise and subsequently cancel it. We adopt two approaches for designing predictors: in the first we use a minimum mean square error (MMSE) criterion and we employ Volterra filters as predictors; in the second we use the minimum dispersion (MD) criterion and we limit our attention to linear predictors. The effects of the predictor order, the number of exploited samples and the filtering allocation on the system performance are examined through Monte Carlo simulations. It is demonstrated that the proposed detectors, while having simple structures, offer substantial performance improvements over conventional detectors. © 1997 John Wiley & Sons, Ltd.