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This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations. [ABSTRACT FROM AUTHOR]

In wireless sensor networks (WSNs), senor nodes are usually battery-powered with limited energy budget. The network lifetime is directly related to the energy consumption of each node. Online censoring is an effective approach to reduce the overall energy consumption by only transmitting statistical informative data. However, the network lifetime is not proportionally extended with online censoring, since individual sensor may still suffer from energy shortage due to frequent transmission of informative data or transmission over long distance. In this paper, a parameters estimation problem is considered in WSNs, where the goal is to minimize the estimation error under the network lifetime constraint. Two censoring algorithms are developed, which allow sensor nodes to make decisions locally on whether to transmit the sampled data. The proposed algorithms can extend the network lifetime with little performance loss. Simulation results validate their effectivenesses. [ABSTRACT FROM AUTHOR]

The lack of particle diversity is a vital problem in particle filtering for nonlinear dynamic systems with unknown noise statistics. In this paper, cost reference particle filter with multi-probability distribution (CRPF_MPD) is introduced to minimize the effects of the lack of particle diversity and to obtain more realistic state estimations. The core of multi-probability distribution is that two subsets are parallelly initialized and resampled by the processes of cost reference particle filter (CRPF) and are respectively updated with different distributions. Information interaction and particle selection form a set of particles with multi-probability distribution to estimate the more realistic states of systems. CRPF_MPD relies on multi-probability distribution, information interaction and particle selection to have excellent performance. As can be seen from the results of simulations, CRPF_MPDs can enhance the accuracy of state estimation and are more robust to different systems. Thus, CRPF_MPDs are available for dynamic systems with unknown noise statistics. • An estimation framework with multi-probability distribution based on the CRPF algorithm is proposed. • A resampling mechanism based on information interaction and particle selection is introduced. • The states of a 1D model and a 2D positioning model are estimated by the proposed method under complex conditions. • The proposed method has excellent accuracy and robustness for non-linear dynamic systems with unknown noise. [ABSTRACT FROM AUTHOR]

To deal with randomly delayed measurements and unknown noise statistics in multi-sensor networked systems, a distributed variational Bayesian adaptive cubature Kalman filtering algorithm (DVB_ACKF) is presented in this paper. To compensate for the effects induced by randomly delayed measurements, a refined measurement reorganization method is designed via a two-stage estimation strategy. Specifically, we first estimate the time delay step. The measurements are then rearranged based on the estimated results from the first stage. Then, a novel noise estimator with the sliding-window and variational Bayesian method is developed to estimate the mean and covariance of the unknown noise. The network topology attribute and measurement accuracy have been combined to eliminate the distributed fusion error. The tuning parameter and forgetting factor as well as their bounds are analyzed. Furthermore, numerical simulations are carried out to verify the superior performance of the developed algorithm. [ABSTRACT FROM AUTHOR]

This paper analyzes the statistical behavior of the bias-compensated sign subband adaptive filtering algorithm with individual-weighting-factors (BC-IWF-SSAF) under errors-in-variables (EIV) model. The theoretical expressions for transient and steady-state behaviors of BC-IWF-SSAF in the mean and mean-square senses are derived through utilizing some reasonable assumptions and Price's theorem. Furthermore, the stability ranges of algorithm are provided. To accomplish performance enhancement, the variable step-size version (VSS) of BC-IWF-SSAF, called VSS-BC-IWF-SSAF algorithm, is developed based on the transient model via minimizing the mean-square deviation (MSD) at every iteration to tackle the contradictory requirements of quick convergence rate and high filtering accuracy caused by fixed step-size (FSS). Finally, Monte-Carlo simulations under system identification and acoustic echo cancellation applications certificate the effectiveness of statistical analysis and variable step-size strategy. [ABSTRACT FROM AUTHOR]

Complex-valued data in statistical signal processing applications have many advantages over their real-valued counterparts. It allows us to use the complete statistical information of the signal thanks to its statistical property of non-circularity. This paper presents a general framework for developing asymptotic theoretical results on the distribution-free sample sign covariance matrix (SSCM) under circular complex-valued elliptically symmetric (C-CES) and non-circular CES (NC-CES) multidimensional distributed data. It extends some partial asymptotic results on SSCM derived for real elliptically symmetric (RES) distributed data. In particular closed-form expressions of the first and second-order of the SSCM are derived for arbitrary spectra of eigenvalues for C-CES and NC-CES distributed data which facilitates the derivation of numerous statistical properties. Then, the asymptotic distributions of associated projectors are deduced, which are applied in the study of asymptotic performance analysis of SSCM-based subspace algorithms, followed by a comparison to the asymptotic results derived using Tyler's M estimate. However, a more in-depth analytical analysis of the efficiency of the SSCM relative to Tyler's M estimate is performed, yielding that the performances of the SSCM and Tyler's M estimate are close for a high-dimensional data and not too small dimension of the principal component space. We conclude therefore that, although the SSCM is inefficient relative to Tyler's M estimate, it is of great interest from the point of view of its lower computational complexity for high-dimensional data. Finally, numerical results illustrating the theoretical analysis are presented through the direction-of-arrival (DOA) estimation CES data models. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with the problem of adaptive array beamforming using a uniform circular array (UCA) in the presence of coherent interference. The well-known scheme of spatial smoothing (SS) widely used to tackle the coherent problem in the cases of 1-D uniform linear array (ULA) and uniform rectangular array (URA) cannot work for the UCA case. This is mainly due to the fact that the direction vector of each signal received by a UCA does not possess a Vandermonde structure. In this paper, we present a method based on subarray beamforming in conjunction with an averaging scheme to effectively mitigate the effect due to coherent interference in the UCA case. Theoretical analysis regarding the validity of the proposed method is also presented. Several simulation examples are provided for showing the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper compares the nonlinear sum statistic with the standard linear statistic and with the nonlinear mean statistic that a detector can compute from multiple noisy data in a binary decision problem based on a maximum a posteriori probability (MAP) criterion. Like the nonlinear mean detector, the detection performance of the nonlinear sum detector comes close to that of the standard linear detector for Gaussian noise. For generalized Gaussian noise, it can also obtain a better detection performance compared to that of the standard linear detector, especially for those noises which concentrate their values heavily around the zero mean. This paper also gives a tentative explanation why the nonlinear detectors can improve signal detection better as the exponent parameter in the probability density function of generalized Gaussian noise becomes smaller. [Copyright &y& Elsevier]

The advent of internet has been a boon to society. It has helped in information retrieval and is a great help in communication. Nowadays, communication comprises digital information in images, videos, GIFs, and many other formats. Amongst the digital data, images are one of the most transmitted data. Therefore, the security of image data has gained the attention of researchers. This paper addresses the drawbacks of Abdelfatah's method, a block-based image encryption scheme based on a chaotic system and elliptic curve cryptography. One of the issues is caused when multiple pixels are grouped to form large integers, which turns out to be more than the modulo prime of the elliptic curve leading to incorrect decryption. Another issue is to transfer extra information for the number of pixels that are grouped. In order to overcome, an algorithm is proposed that uses the largest 512 bits elliptic curve prime modulo along with confusion and diffusion operation using a chaotic system. Security and statistical analysis are conducted to substantiate the strength of the proposed enciphering method. [ABSTRACT FROM AUTHOR]

New economic conditions have led to innovations in retail industries, such as more dynamic retail approaches based on flexible strategies. We propose and compare different approaches incorporating nonlinear methods for promotional decision-making using retail aggregated data registered at the point of the sale. Specifically, this paper describes a reliable quantification tool as an effective information system leveraged on recent and historical data that provides managers with an operative vision. Furthermore, a new set of indicators are proposed to evaluate the reliability and stability of the data model in the multidimensional feature space by using nonparametric resampling techniques. This allows the user to make a clearer comparison among linear, nonlinear, static, and dynamic data models, and to identify the uncertainty of different feature space regions, for example, corresponding to the most frequent deal features. This methodology allows retailers to use aggregated data in suitable conditions that will result in acceptable confidence intervals. To test the proposed methodology, we used a database containing the sales history of representative products registered by a Spanish retail chain. The results indicate that: (1) the deal effect curve analysis and the time series linear model do not provide enough expressive capacity, and (2) nonlinear promotional models more accurately follow the actual sales pattern obtained in response to the implemented sales promotions. The quarterly temporal analysis conducted enabled the authors to identify long-term changes in the dynamics of the model for several products, especially during the early stage of most recent economic crisis, consistent with the information provided by the reliability indices in terms of the feature space. We conclude that the proposed method provides a reliable operative tool for decision support, allowing retailers to alter their strategies to accommodate consumer behavior. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a novel stochastic method is developed for despeckling transrectal ultrasound (TRUS) images of the prostate. By incorporating the circular probe acquisition particularities and speckle noise statistics of TRUS images of the prostate into a likelihood-weighted Monte Carlo estimation scheme, the proposed method can better remove speckle noise while preserving image structures and details that are relevant for image screening, allowing for a better delineation of the lesion contour. Our in silico and in vivo experimental results are promising, which was confirmed by a clinical evaluation of the in vivo test cases by experienced clinicians, and indicate that our method potentially can perform better than other previously proposed methods. [Copyright &y& Elsevier]

Abstract: A novel signal detection approach is proposed in this paper. The approach exhibits the UMVUE of the probability density distribution function with respect to the received signal detection threshold value in wireless fading channels with unknown channel statistics characteristics. Multiscale particle filter is employed to extract the channel state information (CSI) from noisy observations available and to obtain a sufficient complete statistics of parameters. Based on the sufficient complete statistics, a conditional posterior probability density distribution for detection threshold value is derived via the Bayes statistic inference theorem in the presence of the additive white Gaussian noise (AWGN). Simulation results are given to illustrate the proposed novel scheme advantages. [Copyright &y& Elsevier]

Abstract: The importance of high precision matching in fingerprint cannot be over-emphasized. This paper presents a novel fingerprint verification algorithm which improves matching accuracy by overcoming the shortcomings of poor image quality. The proposed method involves determination of a singular point using orientation field reliability, extraction of a square-sub-image (SSI); pixels, statistical analysis of the co-occurrence matrices as well as application of dual analyses on experimental results; Pattern Recognition and Image Processing Laboratory (FVC2002) testing protocol and Program for Rate Estimation and Statistical Summaries (PRESS). The efficiency of the proposed method has been demonstrated by the experimental results which show equal error rate (EER) of 28% and a comparatively more accurate and robust means for reliable fingerprint verification. [Copyright &y& Elsevier]

Abstract: This paper employs a wavelet-based denoising technique for the recovery of signal contaminated by white additive Gaussian noise and investigates the noise free reconstruction property of universal threshold. A new thresholding procedure is proposed, called subband adaptive. The parameters of this procedure are chosen by difference in mean method. Simulations are carried out in MATLAB using various ECG signals. The results show that the proposed thresholding technique outperforms the existing thresholding techniques. [Copyright &y& Elsevier]

A statistical analysis of the least squares matching methods for single-tone frequency estimation is carried out in this paper. Based on asymptotic derivations, an accurate frequency variance expression is provided for different least squares matching methods with variable parameters. Two representative least squares matching methods are involved to show the validity of the variance expression, however, their performances have been proved suboptimal with current parameter settings. After wide discussion, we propose new strategies to choose parameters and achieve further improvements both in accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]