Statistical Signal Processing Research Articles

Asymptotic Mean and Variance of Gini Correlation Under Contaminated Gaussian Model

This paper establishes the asymptotic closed forms of the expectation and variance of the Gini correlation (GC) under a particular type of bivariate contaminated Gaussian model emulating a frequently encountered scenario in statistical signal processing. Monte Carlo simulation results verify the correctness of the theoretical results established in this paper. In order to gain further insight into GC, we also compare GC to Pearson’s product moment correlation coefficient, Kendall’s tau, and Spearman’s rho by means of root mean squared error. The newly explored theoretical and simulational findings not only deepen the understanding of the rather new GC, but also shed new light on the topic of correlation theory, which is widely applied in statistical signal processing.

Understanding Vrikshasana using body mounted sensors: A statistical approach.

Aim:A scheme for understanding how the human body organizes postural movements while performing Vrikshasana is developed in the format of this paper.Settings and Design:The structural characteristics of the body and the geometry of the muscular actions are incorporated into a graphical representation of the human movement mechanics in the frontal plane. A series of neural organizational hypotheses enables us to understand the mechanics behind the hip and ankle strategy: (1) Body sway in the mediolateral direction; and (2) influence of hip and ankle to correct instabilities caused in body while performing Vrikshasana.Materials and Methods:A methodological study on 10 participants was performed by mounting four inertial measurement units on the surface of the trapezius, thoracolumbar fascia, vastus lateralis, and gastrocnemius muscles. The kinematic accelerations of three mutually exclusive trials were recorded for a period of 30 s.Results:The results of every trial were processed using two different approaches namely statistical signal processing (variance and cross-correlation). Conclusions obtained from both these studies were in favor of the initial hypothesis.Conclusions:This study enabled us to understand the role of hip abductors and adductors, and ankle extensions and flexions in correcting the posture while performing Vrikshasana.

Denoising in Wavelet Domain Using Probabilistic Graphical Models

Denoising of real world images that are degraded by Gaussian noise is a long established problem in statistical signal processing. The existing models in time-frequency domain typically model the wavelet coefficients as either independent or jointly Gaussian. However, in the compression arena, techniques like denoising and detection, states the need for models to be non-Gaussian in nature. Probabilistic Graphical Models designed in time-frequency domain, serves the purpose for achieving denoising and compression with an improved performance. In this work, Hidden Markov Model (HMM) designed with 2D Discrete Wavelet Transform (DWT) is proposed. A comparative analysis of proposed method with different existing techniques: Wavelet based and curvelet based methods in Bayesian Network domain and Empirical Bayesian Approach using Hidden Markov Tree model for denoising has been presented. Results are compared in terms of PSNR and visual quality.

Comparative Analyses of Stock Returns Properties and Predictability

This study investigates the stock returns of the Dow Jones Industrial Average (DJIA), Standard and Poor's (S&P) 500, and the National Association of Securities Dealers Automated Quotations (NASDAQ) to analyze and compare their properties and to determine their relative predictability. While it is commonly accepted that price per earnings ratio and corporate earnings are the main determinants of stock market returns, this assertion may not hold equally for monthly and daily stock returns. In addition, does this assertion hold equally for stock returns regardless of the stock market index? This work uses nonparametric spectral estimation to study the underlying properties of stock returns and uses monthly corporate earnings (corporate profits after tax) and 3-month Treasury bill interest rate (proxy for price per earnings ratio) to forecast the monthly stock returns of S&P 500, DJIA, and NASDAQ indices. Since corporate earnings are issued quarterly, this data set had to be interpolated to produce the monthly corporate earnings. Overall, the analyses and forecasting were facilitated with both statistical and digital signal processing techniques. Some examples of the techniques used include Hurst exponent to determine predictability, nonparametric spectral estimation to determine the underlying properties of the stock returns, and correlation and root mean square error to determine the forecasting accuracy. The results of this study provide evidence to support that economic and financial time series such as interest rates, corporate earnings, and stock market returns are time varying and nonGaussian with smooth compactly supported and essentially bandlimited power spectral density estimates. It further shows that the forecasts of the different stock market returns align well with the desired values and the S&P 500 forecasted stock returns were the best.

Mitigating the effect of multipath using cross-correlation: application to underwater network cardinality estimation

Number of node cardinality is an important parameter for a networks proper operation and this parameter can be determined using conventional protocol-based techniques, but these techniques have several limitations in underwater environment due to large propagation latency, high error rate, node mobility, non-negligible capture effect and high path loss. To develop a suitable cardinality estimation technique in presence of unique characteristics of underwater network, a statistical signal processing approach based on cross-correlation of Gaussian signals received at multiple sensors has been proposed in our previous works. In the initial formulation of this approach, a simplified model has been investigated without considering the multipath propagation effect. One of the common challenges for underwater wireless communication is multipath propagation of signals which result in inter-symbol interference ISI. An important feature of cross-correlation is its ability to mitigate the multipath effect which is demonstrated in this paper and applied to our previously proposed estimation scheme for multipath compensation. It is shown that, due to high dispersion coefficient of the medium, multipath effects on estimation results are negligible and a generalised process of multipath compensation for any dispersion factor is obtained to improve the robustness of this scheme.

An Efficient SVD Shrinkage for Rank Estimation

Matrix rank estimation is a classical problem with many applications in statistical signal processing. In this letter, a logistic function based thresholding of the singular values is proposed for the rank estimation purpose. Parameters of the proposed shrinkage function are tuned using Stein’s unbiased risk estimator. The proposed method is shown to outperform the state-of-the-art methods in terms of rank estimation accuracy. Further, it is also noted to result in a better denoising performance.

Subsea Condition Monitoring: Does Effective Diagnosis Increase Availability?

Management The challenges encountered in deepwater development have led to the use of increasingly complex subsea systems. Consequently, operators have become more reliant on subsea monitoring equipment and instrumentation to provide field information for understanding production and equipment conditions. Production monitoring is typically the field operator’s main priority, and equipment condition and performance are sometimes overlooked, resulting in equipment failures and long production downtimes because of unplanned maintenance. Equipment failures often occur without warning and may sometimes, when caused by environmental factors, become inevitable. To determine the cause, field operators sift through vast amounts of distributed data from the subsea control system. The system downtime can be reduced and system availability can be increased by performing effective equipment diagnosis. With the current low-oil-price environment, subsea operators are looking to maximize returns on investment, and condition-based monitoring offers the possibility of lowering operational expenses while increasing field production. Condition Monitoring Condition monitoring is a proactive maintenance strategy combining software and people. Data are used to diagnose changes in the integrity of a system such that corrective action may be planned in a cost-effective manner to increase system availability. Condition monitoring is not a novel technology and is currently used in the aeronautical and automobile industries. The condition monitoring system takes integrity monitoring beyond traditional key performance indicators by utilizing all available data and information from the system and looking for trends of equipment degradation prior to equipment failure. A condition monitoring system is typically based on the following three-step monitoring process: Data Collection: Read-only software to acquire real-time and historical knowledge from the subsea control system. Storing historical data and supporting analysis based on historical trends. Analysis: Onshore analysis server applies statistical analysis, signal processing, mathematical modeling, and simulations to ascertain system conditions. Requires experience-based product knowledge and reliability analysis to target known failure modes and performance issues. System may be tuned and updated in order to continuously improve its online diagnostic performance. Collaboration and Discussion: Estimation of potential impact on production (availability) is built into the system based on operational and maintenance philosophy. With remote surveillance, multiple onshore and offshore users are able to operate the system on a web-based graphical user interface for monitoring and troubleshooting of the subsea field. To simplify monitoring, each component and associated potential failure mode is designed with its individual user interface.

A Note on the Complexity of Proximal Iterative Hard Thresholding Algorithm

The iterative hard thresholding (IHT) algorithm is a powerful and efficient algorithm for solving \(\ell _0\)-regularized problems and inspired many applications in sparse-approximation and image-processing fields. Recently, some convergence results are established for the proximal scheme of IHT, namely proximal iterative hard thresholding (PIHT) algorithm (Blumensath and Davies, in J Fourier Anal Appl 14:629–654, 2008; Hu et al., Methods 67:294–303, 2015; Lu, Math Program 147:125–154, 2014; Trzasko et al., IEEE/SP 14th Workshop on Statistical Signal Processing, 2007) on solving the related \(\ell _0\)-optimization problems. However, the complexity analysis for the PIHT algorithm is not well explored. In this paper, we aim to provide some complexity estimations for the PIHT sequences. In particular, we show that the complexity of the sequential iterate error is at o(1 / k). Under the assumption that the objective function is composed of a quadratic convex function and \(\ell _0\) regularization, we show that the PIHT algorithm has \({\mathbb {R}}\)-linear convergence rate. Finally, we illustrate some applications of this algorithm for compressive sensing reconstruction and sparse learning and validate the estimated error bounds.

On the Intrinsic Relationship Between the Least Mean Square and Kalman Filters [Lecture Notes

The Kalman filter and the least mean square (LMS) adaptive filter are two of the most popular adaptive estimation algorithms that are often used interchangeably in a number of statistical signal processing applications. They are typically treated as separate entities, with the former as a realization of the optimal Bayesian estimator and the latter as a recursive solution to the optimal Wiener filtering problem. In this lecture note, we consider a system identification framework within which we develop a joint perspective on Kalman filtering and LMS-type algorithms, achieved through analyzing the degrees of freedom necessary for optimal stochastic gradient descent adaptation. This approach permits the introduction of Kalman filters without any notion of Bayesian statistics, which may be beneficial for many communities that do not rely on Bayesian methods [1], [2].

Recursive Hybrid Cramér–Rao Bound for Discrete-Time Markovian Dynamic Systems

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. As a contribution to the hybrid estimation framework, we introduce a recursive hybrid Cramer–Rao lower bound for discrete-time Markovian dynamic systems depending on unknown deterministic parameters. Additionally, the regularity conditions required for its existence and its use are clarified.

A Promising Technique for Blind Identification: The Generic Statistics

The generic statistics, related to lower-order derivatives of the log characteristic function (CAF) evaluating at the processing points located away from the origin, are frequently used in multivariate statistical signal processing. In comparison with the conventional statistics, e.g., cumulants, the generic statistics have the following advantages: (a) they can offer the structural simplicity and controllable statistical stability of lower-order statistics, and retain higher-order statistical information; (b) if the derivatives of the log CAF were evaluated at all (infinitely many) possible processing-points, a complete description of the joint CAF would be obtained. Furthermore, we show in this paper that even if a random process is symmetrically distributed, the odd-order generic statistics are not equal to zero, while in such a case the odd-order cumulants are equal to zero. For these reasons, a family of blind identification (BI) methods, in which the mixing matrix is obtained by decomposing the tensor constructed by the higher order derivatives of the log CAF of the observations, is proposed to achieve BI of underdetermined mixtures. Simulation results show that the BI methods based on generic statistics have superior performance to the existing cumulant-based method, such as FOOBI method, especially, when the SNR of the observations is high and/or the data block is short.

An Overview of a Class of Clock Synchronization Algorithms for Wireless Sensor Networks: A Statistical Signal Processing Perspective

Recently, wireless sensor networks (WSNs) have drawn great interest due to their outstanding monitoring and management potential in medical, environmental and industrial applications. Most of the applications that employ WSNs demand all of the sensor nodes to run on a common time scale, a requirement that highlights the importance of clock synchronization. The clock synchronization problem in WSNs is inherently related to parameter estimation. The accuracy of clock synchronization algorithms depends essentially on the statistical properties of the parameter estimation algorithms. Recently, studies dedicated to the estimation of synchronization parameters, such as clock offset and skew, have begun to emerge in the literature. The aim of this article is to provide an overview of the state-of-the-art clock synchronization algorithms for WSNs from a statistical signal processing point of view. This article focuses on describing the key features of the class of clock synchronization algorithms that exploit the traditional two-way message (signal) exchange mechanism. Upon introducing the two-way message exchange mechanism, the main clock offset estimation algorithms for pairwise synchronization of sensor nodes are first reviewed, and their performance is compared. The class of fully-distributed clock offset estimation algorithms for network-wide synchronization is then surveyed. The paper concludes with a list of open research problems pertaining to clock synchronization of WSNs.

Normality and Correlation Coefficient in Estimation of Insulators’ Spectral Signature

This work aims to classify the contamination state in insulators using statistical signal processing approaches. When subjected to high voltage, insulators can radiate radio frequency signals (corona effect). The histograms, normality, and correlation coefficient statistical methods are used to estimate the pollution state in glass insulators when subjected to 8 kV. It is shown that in particular situations the histograms can be used to distinguish clean and dirty insulators. The histogram limitation analysis can be improved using the correlation coefficient and the normality or Gaussianity test. Indeed, it is shown that using these parameters into an analysis per sub-bands, it is possible to estimate the pollution state of the insulators. That is, the analysis using these tools checks if the insulators spectra under test are noticeably different from the clean one, used as reference. It is achieved eliminating the fast variation of the correlation coefficient based on the amplitude and width of the peaks. The tests were done up to the frequency of 1 GHz using measured data.

Empirical Non-Parametric Estimation of the Fisher Information

The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM require estimating the probability distribution function (PDF), or its parameters, along with its gradient or Hessian. However, in many practical situations the PDF of the data is not known but the statistician has access to an observation sample for any parameter value. Here we propose a method of estimating the FIM directly from sampled data that does not require knowledge of the underlying PDF. The method is based on non-parametric estimation of an $f$-divergence over a local neighborhood of the parameter space and a relation between curvature of the $f$-divergence and the FIM. Thus we obtain an empirical estimator of the FIM that does not require density estimation and is asymptotically consistent. We empirically evaluate the validity of our approach using two experiments.

Analysis, Blind Identification, and Correction of Frequency Response Mismatch in Two-Channel Time-Interleaved ADCs

In this paper, novel blind identification and compensation architectures for the frequency response mismatch of a two-channel time-interleaved analog-to-digital-converter (TI-ADC) are proposed. First, detailed modeling of the frequency response mismatch is carried out, establishing a direct connection and similarity to the well-known in-phase/quadrature mismatch problem. Stemming from this modeling, the proposed blind mismatch identification and compensation architectures are then developed building on complex statistical signal processing. Compared to the existing methods in the literature, the proposed solutions can identify and correct the frequency response mismatch in a fully blind manner for the full digital bandwidth (BW) of the ADC system, and are also applicable in sub-sampling TI-ADC devices and RF sampling. The efficiency of the proposed solutions is verified and demonstrated using comprehensive measurements of actual RF-sampling TI-ADC hardware with gigahertz-scale instantaneous BW.

Multi-scale statistical signal processing of cutting force in cutting tool condition monitoring

In a machining system, accurate tool wear condition monitoring is paramount for guaranteeing the quality of the workpiece and tool life. The cutting force signal has been proved to be the most sensitive signal to depict the tool wear variation during the machining process. This paper introduces a data-driven modeling framework for tool wear monitoring in a machining process, which is based on statistical processing of cutting force wavelet transform by a hidden Markov tree. As a kind of data-driven prognostic approach, this method exploits the tool wear states feature from a deeply data mining perspective while the Markov dependence of wavelet transformation at different frequencies or scales is captured. With lathe turning as the research object, a detailed study on the statistical analysis of cutting force in different tool conditions is presented. A two phases monitoring process that assesses the tool wear conditions from generated model by using the statistical features of cutting force wavelet transform is built. Compared to the traditional classifiers, which usually have a difficult condition in distinguishing tool wear states when given a limited amount of samples, the proposed approach make more efficient use of the training data with high sensitivity to the tool wear conditions. Experimental studies of Inconel 718 cutting show that this approach is robust and makes the cutting force information exploited effectively in data mining. Based on the experimental results, the proposed method for tool condition monitoring outperforms the traditional used Hidden Markov model and Gaussian mixture model approach.

Signal Detection for QPSK Based Cognitive Radio Systems using Support Vector Machines

Cognitive radio based network enables oppor- tunistic dynamic spectrum access by sensing, adopting and utilizing the unused portion of licensed spectrum bands. Cognitive radio is intelligent enough to adapt the commu- nication parameters of the unused licensed spectrum. Spec- trum sensing is one of the most important tasks of the cogni- tive radio cycle. In this paper, the auto-correlation function kernel based Support Vector Machine (SVM) classifier along with Welch's Periodogram detector is successfully imple- mented for the detection of four QPSK (Quadrature Phase Shift Keying) based signals propagating through an AWGN (Additive White Gaussian Noise) channel. It is shown that the combination of statistical signal processing and machine learning concepts improve the spectrum sensing process and spectrum sensing is possible even at low Signal to Noise Ra- tio (SNR) values up to 50 dB.

Blind source separation based interference suppression schemes for OFDM and DS-CDMA

In statistical wireless signal processing, extraction of unobserved signals from observed mixtures can be achieved using Blind Source Separation (BSS) algorithms. Orthogonal Frequency Division Multiplexing (OFDM) and Direct Sequence-Code Division Multiple Access (DS-CDMA) can be pronounced as the well established predominant air interface communication techniques. Consequences of an effort taken and counteractive solutions to diminish the undesirable influences encountered within the wireless air interface of those techniques with aid of BSS schemes are disclosed. Filter coefficients for the receiver are ascertained with the support of a set of energy functions and the iterative fixed point rule. Time correlation properties of the channel are taken advantage for BSS. Performance of the algorithm are evaluated using OFDM and DS-CDMA models under slow fading channel conditions with a receiver containing Equal Gain Combining. The importance is that, this scheme can be promoted as a low computationally complex mechanism.

Ken Steven’s research and influence on automatic speech recognition

This talk will address Dr. Kenneth Steven’s considerable influence in the area of speech recognition. Central to Ken’s model of lexical access is the relationship between acoustics and articulation. Binary distinctive features are identified from the continuous signal based on acoustic cues that are tied to articulation. As such, variability in this parameterization is reduced from that seen in the physical signal. The acoustic features are then matched against the lexicon where there is generally only one representation for each word. This lexical representation consists of a bundle of distinctive features. In contrast, state-of-the-art recognizers use acoustic features that are not tied to articulation. Consequently, they are highly variable, resulting in the recognizer’s over-reliance on sophisticated machine-learning tools and statistical signal processing methodologies that are data intensive and often fail to generalize. Further, multiple lexical representations of each word in terms of acoustic units called tri-phones are needed to cope with pronunciation variability. While Ken’s model has not been fully realized, it has motivated research into extraction of the distinctive features, investigations of alternate articulation-based representations, and marrying these representations with well-established recognition back-ends to study gains in robustness. Examples from studies and their promise relative to state-of-the-art methods will be given.

The random matrix regime of Maronna’s M-estimator with elliptically distributed samples

This article demonstrates that the robust scatter matrix estimator CˆN∈CN×N of a multivariate elliptical population x1,…,xn∈CN originally proposed by Maronna in 1976, and defined as the solution (when existent) of an implicit equation, behaves similar to a well-known random matrix model in the limiting regime where the population N and sample n sizes grow at the same speed. We show precisely that CˆN∈CN×N is defined for all n large with probability one and that, under some light hypotheses, ‖CˆN−SˆN‖→0 almost surely in spectral norm, where SˆN follows a classical random matrix model. As a corollary, the limiting eigenvalue distribution of CˆN is derived. This analysis finds applications in the fields of statistical inference and signal processing.