Zero-mean White Gaussian Noise Research Articles

Identification of time-varying inertia tensor parameters of a space solar power satellite based on a robust weighted recursive algorithm under impulsive disturbance

Considering changes in the structural size and mass caused by the on-orbit assembly process in a planar space solar power satellite, this study proposes an improved robust recursive algorithm to identify the time-varying inertia tensor parameters of the system. In this algorithm, to decrease the effect of impulsive disturbance on inertial parameter identification during the on-orbit assembly and improve computational accuracy, robust weighted factor and multi-innovation theory are involved. Then, the time-varying inertia tensor parameters of this large flexible structure are identified based on the distributed measurement results of multiple attitude sensors. The simulation results indicate that the proposed algorithm improves the identification accuracy and has better robustness than the original method under the impulsive disturbance. The relative values of the average relative error caused by the impulsive disturbance under the proposed algorithm are approximately 27.8–73.0% less than those under the original method. Additionally, the results also demonstrate that the proposed algorithm has higher noise immunity than the classical recursive least-squares method in a time-varying system. When the impulsive disturbance and zero-mean Gaussian white noise are applied to the system, compared with the conventional recursive least-squares method, the proposed algorithm yields lower absolute and relative values of the average relative error by approximately 4.2% and 44.9%, respectively.

Constrained profile estimation for distributed parameter system in one dimension using orthogonal collocation

Several industrial processes fall under the category of Distributed parameter systems (DPS) which are represented as coupled partial differential equations (PDEs). Obtaining accurate and physically meaningful profile estimates of states despite only a limited number of spatially distributed measurements, is a pre-requisite for adequately controlling such systems. In this work, we propose an online constrained state profile estimation approach for DPS. The approach is based on reduced-dimension model represented by differential and algebraic equations (DAE) which in turn is developed by discretization of the PDEs along the spatial coordinate using the orthogonal collocation (OC) method. A profile prediction error based approach is proposed for systematically fixing the dimension of the OC model to be used. Further, to compensate for the inevitable model plant mismatch (MPM) arising in the process of the dimensionality reduction, additive zero mean Gaussian white noise processes are introduced in both state dynamics as well as measurement model. Statistics of these noises are obtained based on simulation based realizations of approximation errors at collocation points and measurement locations. To incorporate the identified correlation between the resulting state and measurement noises in the estimation method, we propose a constrained DAE-EKF (extended Kalman Filter) extension to deal with such correlations. The estimation approach also involves an appropriately formulated optimization based update step to ensure constraint satisfaction over the entire spatial profile leading to physically meaningful state profile estimates. The constrained profile estimator is also integrated with an online moving window based parameter estimation, which enables tracking of both time varying parameters and state profiles. The efficacy of the proposed approach is demonstrated by conducting stochastic simulation studies using two tubular reactor systems. The results show that the proposed constrained online state estimation approach is able to obtain accurate profile estimates at low computational cost, while ensuring that the profile estimates satisfy the given constraints.

Robust Matrix Completion Based on Factorization and Truncated-Quadratic Loss Function

Robust matrix completion refers to recovering a low-rank matrix given a subset of the entries corrupted by gross errors, and has various applications since many real-world signals can be modeled as low-rank matrices. Most of the existing methods only perform well for noise-free data or those with zero-mean white Gaussian noise, and their performance will be degraded in the presence of outliers. In this paper, based on the factorization framework, we propose a novel robust matrix completion scheme via using the truncated-quadratic loss function, which is non-convex and non-smooth, and half-quadratic theory is adopted for its optimization. By introducing an auxiliary variable, half-quadratic optimization (HO) can transform the loss function into two tractable forms, that is, additive and multiplicative formulations. Block coordinate descent method is then exploited as their solver. Compared with the additive form, the multiplicative variant has lower computational cost since we attempt to take the observations contaminated by outliers as missing entries. Numerical simulations and experimental results based on image inpainting and hyperspectral image recovery demonstrate that our algorithms are superior to the state-of-the-art methods in terms of restoration accuracy and runtime. MATLAB code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/bestzywang</uri> .

Numerical optimisation of a classical stochastic system for targeted energy transfer

The paper studies stochastic dynamics of a two-degree-of-freedom system, where a primary linear system is connected to a nonlinear energy sink with cubic stiffness nonlinearity and viscous damping. While the primary mass is subjected to a zero-mean Gaussian white noise excitation, the main objective of this study is to maximise the efficiency of the targeted energy transfer in the system. A surrogate optimisation algorithm is proposed for this purpose and adopted for the stochastic framework. The optimisations are conducted separately for the nonlinear stiffness coefficient alone as well as for both the nonlinear stiffness and damping coefficients together. Three different optimisation cost functions, based on either energy of the system’s components or the dissipated energy, are considered. The results demonstrate some clear trends in values of the nonlinear energy sink coefficients and show the effect of different cost functions on the optimal values of the nonlinear system’s coefficients.

Security Data-Driven Control for Nonlinear Systems Subject to Deception and False Data Injection Attacks

This paper studies the security data-driven control problem for a class of nonlinear systems with completely unknown dynamics under the deception attacks (DA) and false data injection attacks (FDIA) via faded channels. Firstly, the fading phenomenon is formulated by the Rice fading model, which obeys the Gaussian distribution with a known mathematical expectation and variance. DA could invert the direction of I/O data and FDIA may result in false injection data with zero-mean Gaussian white noise. Then, by employing the compact form dynamic linearization method, the security model free adaptive controller (MFAC) is designed, which does not involve the model or structure information of the system. Next, the system stability is analyzed, and the compensation scheme with an increasing gain is proposed to counteract the adverse effect brought by faded channels. A numerical simulation and a load frequency control (LFC) example for multi-area power systems illustrate the validity of the proposed schemes.

Analytical process noise covariance modeling for absolute and relative orbits

This paper develops new analytical process noise covariance models for both absolute and relative spacecraft states. Process noise is always present when propagating a spacecraft state due to dynamics modeling deficiencies. Accurately modeling this noise is essential for sequential orbit determination and improves satellite conjunction analysis. A common approach called state noise compensation models process noise as zero-mean Gaussian white noise accelerations. The resulting process noise covariance can be evaluated numerically, which is computationally intensive, or through a widely used analytical model that is restricted to an absolute Cartesian state and small propagation intervals. Moreover, mathematically rigorous, analytical process noise covariance models for relative spacecraft states are not currently available. To address these limitations of the state of the art, new analytical process noise covariance models are developed for state noise compensation for both Cartesian and orbital element absolute state representations by leveraging spacecraft relative dynamics models. Two frameworks are then presented for modeling the process noise covariance of relative spacecraft states by assuming either small or large interspacecraft separation. The presented techniques are validated through numerical simulations.

A matrix approach to get the variance of the square of the fluctuation function of the DFA

The fluctuation analysis (FA) and the detrended fluctuation analysis (DFA) make it possible to estimate the Hurst exponent H, which characterizes the self-similarity of a signal. Both are based on the fact that the so-called fluctuation function, which can be seen as an approximation of the standard deviation of the process scaled in time by multiplying the time variable by a positive constant, depends on H. The main novelty of the paper is to provide the expression of the variance of the square of the fluctuation function, by using a matrix formulation. We show that it depends on the correlation function of the signal under study when it is zero-mean and Gaussian. Illustrations are given when dealing with a zero-mean white Gaussian noise. Moving average processes and first-order autoregressive processes are also addressed.

New approach to model‐order selection

A new, direct and practical scheme is proposed for determining the model orders of a system, its signal and disturbance using key properties of Kalman filter (KF). Unlike conventional methods, it enjoys the unique property of being both necessary and sufficient. The system is described by the Box–Jenkins model, whose accessible input and output are corrupted by unknown zero-mean white Gaussian-distributed disturbances and measurement noise. The signal and disturbance are outputs of asymptotically-stable linear time-invariant systems driven by an inaccessible input and a zero-mean white Gaussian noise process, respectively. Predictive analytics is used to estimate the input by exploiting its smoothness and the randomness of the noisy input. The system, signal, and disturbance models and their associated KFs are identified for various selected model orders by minimising the KF residuals so that these become zero-mean white noise processes. The selected model-order corresponds to the minimum-variance residual. Equivalently, the minimum order is selected when the number of poles or the output estimates of the identified models are all identical for all orders equal to, or exceeding the minimal order. The scheme is successfully evaluated and shown to outperform the commonly-used but only sufficient Akaike Information Criterion.

Noisy Galvanic Vestibular Stimulation (Stochastic Resonance) Changes Electroencephalography Activities and Postural Control in Patients with Bilateral Vestibular Hypofunction

Patients with bilateral vestibular hypofunction (BVH) often suffer from imbalance, gait problems, and oscillopsia. Noisy galvanic vestibular stimulation (GVS), a technique that non-invasively stimulates the vestibular afferents, has been shown to enhance postural and walking stability. However, no study has investigated how it affects stability and neural activities while standing and walking with a 2 Hz head yaw turning. Herein, we investigated this issue by comparing differences in neural activities during standing and walking with a 2 Hz head turning, before and after noisy GVS. We applied zero-mean gaussian white noise signal stimulations in the mastoid processes of 10 healthy individuals and seven patients with BVH, and simultaneously recorded electroencephalography (EEG) signals with 32 channels. We analyzed the root mean square (RMS) of the center of pressure (COP) sway during 30 s of standing, utilizing AMTI force plates (Advanced Mechanical Technology Inc., Watertown, MA, USA). Head rotation quality when walking with a 2 Hz head yaw, with and without GVS, was analyzed using a VICON system (Vicon Motion Systems Ltd., Oxford, UK) to evaluate GVS effects on static and dynamic postural control. The RMS of COP sway was significantly reduced during GVS while standing, for both patients and healthy subjects. During walking, 2 Hz head yaw movements was significantly improved by noisy GVS in both groups. Accordingly, the EEG power of theta, alpha, beta, and gamma bands significantly increased in the left parietal lobe after noisy GVS during walking and standing in both groups. GVS post-stimulation effect changed EEG activities in the left and right precentral gyrus, and the right parietal lobe. After stimulation, EEG activity changes were greater in healthy subjects than in patients. Our findings reveal noisy GVS as a non-invasive therapeutic alternative to improve postural stability in patients with BVH. This novel approach provides insight to clinicians and researchers on brain activities during noisy GVS in standing and walking conditions in both healthy and BVH patients.

Statistical Behavior of Teager-Kaiser Energy Operator in Presence of White Gaussian Noise

In this work we are interested in the behavior of Teager-Kaiser energy operator (TKEO) applied to a zero-mean white Gaussian noise. For this purpose, we analyze the statistical distribution of the outputs of the TKEO under this noise. We show that the probability density function (pdf) characterizing the output of TKEO, is asymmetric and highly skewed pdf with a stronger peak near the mean, and can be fitted by a shifted Log-Laplace distribution. Some useful moments charactering key aspects of the pdf of TKEO are calculated. We prove that the coefficient of variation, skewness and kurtosis are independent on the variance of the noise, while mean and standard deviation are proportional to this variance. Results of simulations show the interest of TKEO moments for signal detection.

The Kalman Filter Uncertainty Concept in the Possibility Domain

The Kalman filter (KF) is one of the most important and common optimal recursive data processing algorithms in many applications characterized by linear dynamical behavior and affected by random zero-mean white Gaussian noise. However, when measurement processes are considered, inaccuracy is not only due to noise but also to several contributions to uncertainty that can be due to both random and uncompensated systematic effects. Therefore, when the KF is used on experimental data, all uncertainty contributions should be considered. While several proposals are available in the literature to modify the KF in order to consider different probability distributions and systematic effects, represented both in probability and possibility domains, they are not fully compliant with the uncertainty concept adopted in metrology. The aim of this paper is, hence, to reformulate the KF theory within the possibility domain in compliance with the measurement uncertainty concept, in order to be able to consider both the random and systematic contributions to uncertainty (regardless of their distribution) that may affect the measurement process. An experimental setup is considered and the results obtained under different assumptions are reported.

Optimal Stochastic Signaling Under Average Power and Bit Rate Constraints

The optimal stochastic signaling based on the joint design of prior distribution and signal constellation is investigated under an average bit rate and power constraints. First, an optimization problem is formulated to maximize the average probability of correct decision over the set of joint distribution functions for prior probabilities and the corresponding constellation symbols. Next, an alternative problem formulation, for which the optimal joint distribution is characterized by a randomization among at most three mass points, is provided, and it is shown that both formulations share the same solution. Three special cases of the problem are investigated in detail. First, in the absence of randomization, the optimal prior probability distribution is analyzed for a given signal constellation and a closed-form solution is provided. Second, the optimal deterministic pair of prior probabilities and the corresponding signal levels are considered. Third, a binary communication system with scalar observations is investigated in the presence of a zero-mean additive white Gaussian noise, and the optimal solution is obtained under practical assumptions. Finally, numerical examples are presented to illustrate the theoretical results. It is observed that the proposed approach can provide improvements in terms of average symbol error rate over the classical scheme for certain scenarios.

Research on Facial Expression Recognition Technology Based on Convolutional-Neural-Network Structure

Human facial expressions change so subtly that recognition accuracy of most traditional approaches largely depend on feature extraction. In this article, the authors employ a deep convolutional neural network (CNN) to devise a facial expression recognition system to discover deeper feature representation of facial expression. The proposed system is composed of the input module, the pre-processing module, the recognition module and the output module. The authors introduce jaffe and ck+ to simulate and evaluate the performance under the influence of different factors (e.g. network structure, learning rate and pre-processing). The authors also examine the anti-noise property of the system with zero-mean gaussian white noise. In addition, they simulate the recognition accuracy on different expression pairs and discuss the confusion issue on similar expression recognition. Finally, they introduce the k-nearest neighbor (KNN) algorithm compared with CNN to make the results more convincing.

A cooperative detection and compensation mechanism against Denial-of-Service attack for cyber-physical systems

This paper is concerned with the detection and compensation co-design issue for cyber-physical systems against Denial-of-Service (DoS) attack. First, a novel supervisory strategy is proposed based on the concept of packet reception rate, which can detect the behavior of a DoS attacker during a given time window. A quantitative description of the relationship among attack times, time window, attack success rate and packet reception rate is analyzed. Based on the attack detection information, the current state under attack can be successfully reconstructed by some past available states. Then, a co-design compensation mechanism is also obtained, which can further guarantee the attacked system is stochastically stable (without the zero-mean Gaussian white noise) or mean square exponentially ultimately bounded (with the zero-mean Gaussian white noise). The corresponding design conditions are derived in terms of linear matrix inequalities. Finally, a numerical example and a practical example are given to show the effectiveness and superiority of the presented design method.

Perception of force and stiffness in the presence of low-frequency haptic noise.

ObjectiveThis work lays the foundation for future research on quantitative modeling of human stiffness perception. Our goal was to develop a method by which a human’s ability to perceive suprathreshold haptic force stimuli and haptic stiffness stimuli can be affected by adding haptic noise.MethodsFive human participants performed a same-different task with a one-degree-of-freedom force-feedback device. Participants used the right index finger to actively interact with variations of force (∼5 and ∼8 N) and stiffness (∼290 N/m) stimuli that included one of four scaled amounts of haptically rendered noise (None, Low, Medium, High). The haptic noise was zero-mean Gaussian white noise that was low-pass filtered with a 2 Hz cut-off frequency; the resulting low-frequency signal was added to the force rendered while the participant interacted with the force and stiffness stimuli.ResultsWe found that the precision with which participants could identify the magnitude of both the force and stiffness stimuli was affected by the magnitude of the low-frequency haptically rendered noise added to the haptic stimulus, as well as the magnitude of the haptic stimulus itself. The Weber fraction strongly correlated with the standard deviation of the low-frequency haptic noise with a Pearson product-moment correlation coefficient of ρ > 0.83. The mean standard deviation of the low-frequency haptic noise in the haptic stimuli ranged from 0.184 N to 1.111 N across the four haptically rendered noise levels, and the corresponding mean Weber fractions spanned between 0.042 and 0.101.ConclusionsThe human ability to perceive both suprathreshold haptic force and stiffness stimuli degrades in the presence of added low-frequency haptic noise. Future work can use the reported methods to investigate how force perception and stiffness perception may relate, with possible applications in haptic watermarking and in the assessment of the functionality of peripheral pathways in individuals with haptic impairments.

Cardiac conduction velocity estimation from sequential mapping assuming known Gaussian distribution for activation time estimation error.

In this paper, we study the problem of the cardiac conduction velocity (CCV) estimation for the sequential intracardiac mapping. We assume that the intracardiac electrograms of several cardiac sites are sequentially recorded, their activation times (ATs) are extracted, and the corresponding wavefronts are specified. The locations of the mapping catheter's electrodes and the ATs of the wavefronts are used here for the CCV estimation. We assume that the extracted ATs include some estimation errors, which we model with zero-mean white Gaussian noise values with known variances. Assuming stable planar wavefront propagation, we derive the maximum likelihood CCV estimator, when the synchronization times between various recording sites are unknown. We analytically evaluate the performance of the CCV estimator and provide its mean square estimation error. Our simulation results confirm the accuracy of the proposed method and the error analysis of the proposed CCV estimator.

Transcranial Random Noise Stimulation of Visual Cortex: Stochastic Resonance Enhances Central Mechanisms of Perception.

Random noise enhances the detectability of weak signals in nonlinear systems, a phenomenon known as stochastic resonance (SR). Though counterintuitive at first, SR has been demonstrated in a variety of naturally occurring processes, including human perception, where it has been shown that adding noise directly to weak visual, tactile, or auditory stimuli enhances detection performance. These results indicate that random noise can push subthreshold receptor potentials across the transfer threshold, causing action potentials in an otherwise silent afference. Despite the wealth of evidence demonstrating SR for noise added to a stimulus, relatively few studies have explored whether or not noise added directly to cortical networks enhances sensory detection. Here we administered transcranial random noise stimulation (tRNS; 100-640 Hz zero-mean Gaussian white noise) to the occipital region of human participants. For increasing tRNS intensities (ranging from 0 to 1.5 mA), the detection accuracy of a visual stimuli changed according to an inverted-U-shaped function, typical of the SR phenomenon. When the optimal level of noise was added to visual cortex, detection performance improved significantly relative to a zero noise condition (9.7 ± 4.6%) and to a similar extent as optimal noise added to the visual stimuli (11.2 ± 4.7%). Our results demonstrate that adding noise to cortical networks can improve human behavior and that tRNS is an appropriate tool to exploit this mechanism. Our findings suggest that neural processing at the network level exhibits nonlinear system properties that are sensitive to the stochastic resonance phenomenon and highlight the usefulness of tRNS as a tool to modulate human behavior. Since tRNS can be applied to all cortical areas, exploiting the SR phenomenon is not restricted to the perceptual domain, but can be used for other functions that depend on nonlinear neural dynamics (e.g., decision making, task switching, response inhibition, and many other processes). This will open new avenues for using tRNS to investigate brain function and enhance the behavior of healthy individuals or patients.

Cramér–Rao bounds for L‐band digital aeronautical communication system type 1 based passive multiple‐input multiple‐output radar

In this study, of concern is the achievable estimation accuracy for a non-coherent passive multiple-input multiple-output (MIMO) radar employing orthogonal frequency-division multiplexing (OFDM) based signals of opportunity. The motivation behind this investigation is the surveillance aspect of the air trac management modernisation process currently taking place in civil aviation. To this end, the surveillance capability of the OFDM-based L-band digital aeronautical communication system type 1 (LDACS1) is analysed. The extension of the LDACS1 communication system towards surveillance is of great importance since it would enable an alternative, non-cooperative surveillance application, and, together with the already validated navigation extension, establish a fully integrated LDACS1-based communication, navigation, and surveillance technology. The modied Cramer-Rao bound on the joint estimation of target location and velocity for a non-coherent passive MIMO radar, employing the OFDM-based LDACS1 signals as signals of opportunity, is investigated. The analysis is carried out assuming one target, multiple and widely separated transmit and receive antennas, orthogonal waveforms, independent reection coecients, and zero-mean white Gaussian noise. Closed-form expressions for the relevant elements of the modied Fisher information matrix are obtained. The results can be used to assess the estimation accuracy of a multiple antenna passive radar system employing any OFDM-based signals of opportunity.

Multiframe Superresolution of Vehicle License Plates Based on Distribution Estimation Approach

Low-resolution (LR) license plate images or videos are often captured in the practical applications. In this paper, a distribution estimation based superresolution (SR) algorithm is proposed to reconstruct the license plate image. Different from the previous work, here, the high-resolution (HR) image is estimated via the obtained posterior probability distribution by using the variational Bayesian framework. To regularize the estimated HR image, a feature-specific prior model is proposed by considering the most significant characteristic of license plate images; that is, the target has high contrast with the background. In order to assure the success of the SR reconstruction, the models representing smoothness constraints on images are also used to regularize the estimated HR image with the proposed feature-specific prior model. We show by way of experiments, under challenging blur with size 7 × 7 and zero-mean Gaussian white noise with variances 0.2 and 0.5, respectively, that the proposed method could achieve the peak signal-to-noise ratio (PSNR) of 22.69 dB and the structural similarity (SSIM) of 0.9022 under the noise with variance 0.2 and the PSNR of 19.89 dB and the SSIM of 0.8582 even under the noise with variance 0.5, which are 1.84 dB and 0.04 improvements in comparison with other methods.

Image Denoising With Edge-Preserving and Segmentation Based on Mask NHA.

In this paper, we propose a zero-mean white Gaussian noise removal method using a high-resolution frequency analysis. It is difficult to separate an original image component from a noise component when using discrete Fourier transform or discrete cosine transform for analysis because sidelobes occur in the results. The 2D non-harmonic analysis (2D NHA) is a high-resolution frequency analysis technique that improves noise removal accuracy because of its sidelobe reduction feature. However, spectra generated by NHA are distorted, because of which the signal of the image is non-stationary. In this paper, we analyze each region with a homogeneous texture in the noisy image. Non-uniform regions that occur due to segmentation are analyzed by an extended 2D NHA method called Mask NHA. We conducted an experiment using a simulation image, and found that Mask NHA denoising attains a higher peak signal-to-noise ratio (PSNR) value than the state-of-the-art methods if a suitable segmentation result can be obtained from the input image, even though parameter optimization was incomplete. This experimental result exhibits the upper limit on the value of PSNR in our Mask NHA denoising method. The performance of Mask NHA denoising is expected to approach the limit of PSNR by improving the segmentation method.