Zero-mean Noise Research Articles

Networked LQG control over lossy channels with computational/packet-transmission delays and coarsely quantised packets

This article addresses the linear quadratic Gaussian (LQG) control problem of networked multi-input, multi-output systems where computational delay exists and the measurement and control signals are packetised and transmitted through a network within which random delay and packet loss may occur during transmissions. A transmission control protocol (TCP)-like protocol for the communication network is considered in which acknowledgement is sent from the actuator to the controller if and only if the control packet is received, assuming these acknowledgements always reach the estimator in time and without fail. To minimise the data word-length for transmissions over the network and to maximise control system performance, it is proposed that different quantisation resolutions be used for transmission data encapsulation, and control and output signals A/D-D/A conversions at sensor/actuator. To circumvent the problem of disparity between encapsulation and A/D-D/A quantisation resolutions, a pseudo-stochastic approach via subtractive dither is applied to quantise the transmission packets. This also enables us to model the quantisation errors as uncorrelated independent zero-mean additive white noises and apply standard LQG methodology and separation principle to design the estimator and the controller separately. An example is included to demonstrate the effectiveness of the approach.

Optimal filtering for discrete‐time linear systems with multiplicative and time‐correlated additive measurement noises

The filtering problem for discrete-time linear systems with multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive measurement noise is described by a linear system model with white noise. Using the method of measurement differencing and some results obtained in this study, a novel algorithm for optimal filtering of the system under consideration is proposed in the sense of linear minimum mean-square error. The proposed algorithm is recursive, and does not increase computation and storage load with time. The convergence of the proposed algorithm is investigated. Computer simulations are carried out to demonstrate the performance of the proposed algorithm. The simulation results show the superiority of the proposed algorithm.

Asymptotically Optimum Distributed Estimation in the Presence of Attacks

Distributed estimation of a deterministic mean-shift parameter in additive zero-mean noise is studied when using quantized data in the presence of Byzantine attacks. Several subsets of sensors are assumed to be tampered with by adversaries using different attacks such that the compromised sensors transmit fictitious data. First, we consider the task of identifying and categorizing the attacked sensors into different groups according to distinct types of attacks. It is shown that increasing the number K of time samples at each sensor and enlarging the size N of the sensor network can both ameliorate the identification and categorization, but to different extents. As K→∞, the attacked sensors can be perfectly identified and categorized, while with finite but sufficiently large K, as N→∞, it can be shown that the fusion center can also ascertain the number of attacks and obtain an approximate categorization with a sufficiently small percentage of sensors that are misclassified. Next, in order to improve the estimation performance by utilizing the attacked observations, we consider joint estimation of the statistical description of the attacks and the parameter to be estimated after the sensors have been well categorized. When using the same quantization approach successfully employed without attacks, it can be shown that the corresponding Fisher Information Matrix (FIM) is singular. To overcome this, a time-variant quantization approach is proposed, which will provide a nonsingular FIM, provided that K ≥ 2. Furthermore, the FIM is employed to provide necessary and sufficient conditions under which utilizing the compromised sensors in the proposed fashion will lead to better estimation performance when compared to approaches where the compromised sensors are ignored.

Streamline-based inversion of formation properties from formation-tester measurements acquired in high-angle and horizontal wells

A new method is developed based on streamlines to determine the reservoir properties from formation-tester measurements. To do so, a previously developed finite-difference reservoir model is coupled with a streamline method to simulate the near-wellbore dynamic measurements in the presence of invasion and arbitrary fluid distributions. The streamline method is specifically developed to overcome technical challenges in modeling deviated wells in heterogeneous reservoirs efficiently. In this study, synthetic reservoir models are constructed based on measurements acquired in offshore well A with 15o deviation angle. The streamline-based method is then implemented to simulate packer-type formation-tester measurements and to appraise permeability of multi-layer reservoirs. In addition, transient measurements from a focused-sampling probe-type formation tester is modeled with streamline method to estimate relative permeability and anisotropy in offshore well B. Inversion results indicate that the accuracy of estimated formation properties is higher for formations with larger mobility because more streamlines trace flow into probes from large-mobility layers. For offshore well A, in the presence of 5% zero-mean Gaussian additive noise, the uncertainty of permeability varies from 6% to 38% for layers with high and low mobilities, respectively. The uncertainty increases to 8% and 41% for high and low mobility cases, respectively, when 5% skewed-Gaussian noise contaminates the measurements. The coupled finite-difference and streamline-based inversion method (FDSM) is then compared to a previously validated finite-difference reservoir model (FDM). The coupled FDSM is 8 times faster than FDM on an average when estimating properties of heterogeneous reservoirs using inversion on formation-tester measurements acquired in highly deviated wells. Computational advantage of FDSM is due to application of one-dimensional solutions of fluid saturations and concentrations along streamlines instead of three-dimensional FDM numerical calculations. Despite the efficiency, history matching of measurements indicates up to 6% difference between FDSM and FDM in results. In high-angle wells, mud-filtrate invasion causes a non-symmetric distribution of invading fluid around the wellbore perimeter. Moreover, presence of large permeability–porosity contrast among layers increases complexity of numerical computations and uncertainty. This study proposes that the streamline-based inversion method is an excellent candidate to overcome these difficulties efficiently.

Statistical Analysis of Non Linear Least Squares Estimation for Harmonic Signals in Multiplicative and Additive Noise

In this paper we consider the problem of parameter estimation for the multicomponent harmonic signals in multiplicative and additive noise. The nonlinear least squares (NLLS) estimators, NLLS1 and NLLS2 proposed by Ghogho et al. (1999b) to estimate the coherent model parameters for single-component harmonic signal, are generalized to the multicomponent harmonic signals for the cases of nonzero- and zero-mean multiplicative noise, respectively. By statistical analysis, some asymptotic results of the NLLS estimators are derived, including the strong consistency, the strong convergence rate and the asymptotic normality. Furthermore, the NLLS1- and NLLS2- based estimators are proposed to estimate the noncoherent model parameters for the cases of nonzero- and zero-mean multiplicative noise, respectively, meanwhile the strong consistency and the asymptotic normality of the NLLS-based estimators are also derived. Finally some numerical experiments are performed to see how the asymptotic results work for finite sample sizes.

Mean-Square Stability Analysis of a Normalized Least Mean Fourth Algorithm for a Markov Plant

Recently, it has been shown that the stability of the least mean fourth (LMF) algorithm depends on the nonstationarity of the plant. The present paper investigates the possibility of overcoming this problem by normalization of the weight vector update term. A rigorous mean-square stability analysis is provided for a recent normalized LMF algorithm, which is normalized by a term that is second order in the estimation error and fourth order in the regressor. The analysis is done for a Markov plant with a stationary white input with even probability density function and a stationary zero-mean white noise. It is proved that the mean-square deviation (MSD) of the algorithm is bounded for all finite values of the input variance, noise variance, initial MSD, and mean-square plant parameter increment. Analytical results are supported by simulations.

Statistical Analysis of Parameter Estimation for 2-D Harmonics in Multiplicative and Additive Noise

This article considers the problem of parameter estimation for two dimensional (2-D) multi-component harmonics in non zero-mean multiplicative and additive noise. The least squares estimators (LSEs) are proposed to estimate the coherent model parameters, and some statistical results of the LSEs are obtained, including strong consistency, strong convergence rate, and asymptotic normality. Furthermore, the LSEs-based estimators are proposed to estimate the noncoherent model parameters, and the strong consistency and the asymptotic normality are also proved. Finally, some numerical experiments are performed to see how the asymptotic results work for finite sample sizes.

Measuring effective area of spots from pulsed laser beams

The effective area of a laser spot is an important quantity used to characterize the laser-induced damage threshold of optical materials according to ISO 21254-1:2011 standard. A method for measuring the effective area/diameter of spots from pulsed laser beams using charge-coupled device camera-based beam profilers is presented. Factors affecting the measurement’s accuracy, as the background noise and the size of the summation area, were evaluated using MATLAB®. To minimize the noise contribution, we use an iterative method similar to the one used to measure the second-moment-based spot sizes. We find that the two analyzed components of the background noise, its zero-mean noise and its offset, have an opposite effect on the measurements of the effective area/diameter as compared with the second-moment-based measurements. We prove that there is an upper limit of the relative error of such iterative measurements of effective area, the iteration limit parameter, and that it is a measurable quantity. We measure the effective area/diameter of laser spots with different sizes from a Nd:YAG laser at 1064 nm, 6 ns pulse duration, 10 Hz repetition frequency, and estimate the standard uncertainty of the measurements. Further, we generalize the effective area/diameter concept to include elongated (elliptical/rectangular) spots.

A New Application of Kalman Filtering Algorithm Based on Interval Calculation in Navigation System

In traditional Kalman filtering algorithm, the system noise and observation noise should be assumed as zero-mean Gaussian white noise, meanwhile need the state-space model and relevant references be given and accurate. However, the white noise is just an ideal noise model that doesnt exist in real environment. This paper analyzed the effect to filtering result from the statistical estimation in traditional Kalman filtering algorithm and brought interval calculation into traditional Kalman filtering algorithm, which based on the concept of interval and could improve the robustness of the system, decrease the error caused by the statistical estimation of noise model.

Noisy vestibular stimulation improves body balance in bilateral vestibulopathy

To examine the effect of an imperceptible level of galvanic vestibular stimulation (GVS), delivered as zero-mean current noise (noisy GVS), on postural performance in healthy subjects as well as in patients with bilateral peripheral vestibular dysfunction. White noise GVS with an amplitude ranging from 0 to 1,000 μA was applied in 21 healthy subjects and 11 patients with bilateral vestibular dysfunction. Two-legged stance tasks were performed with the eyes closed during a 60-second period, which consisted of a baseline period without stimulation and a stimulation period with GVS. We examined 3 parameters: the velocity, the envelopment area, and the root mean square (RMS) of the center of pressure. White noise GVS improved all 3 parameters in 76% of healthy subjects. The amplitude of the optimal stimulus was 281 ± 40 μA, and it improved the velocity, area, and RMS by 18.4% ± 2%, 37.9% ± 3.5%, and 20.4% ± 2.2%, respectively (p < 0.01). The GVS improved all 3 parameters in 91% of patients. The amplitude of the optimal stimulus was 456 ± 82 μA, and it improved the velocity, area, and RMS by 29.4% ± 4.9%, 45.6% ± 4.7%, and 22% ± 3.3%, respectively (p < 0.01). Noisy GVS is effective in improving postural stability in healthy subjects as well as in patients with bilateral vestibular dysfunction. This study provides Class IV evidence that in patients with bilateral vestibular dysfunction, an imperceptible level of noisy GVS may improve postural stability.

Estimation of the parameters of a railway vehicle suspension using model-based filters with uncertainties

This paper presents two types of extended Kalman filter (EKF) and two types of unscented Kalman filter (UKF) based on vertical railway vehicle models for parameters estimation of secondary suspensions. Due to track irregularities, the random vertical velocity of the track can be approximated as a zero-mean Gaussian white noise and it is used to excite the dynamic model of the railway vehicle. Under this approximation, the variance of the vertical velocity of the track, which is affected by the track roughness level and vehicle velocity, can introduce uncertainty into the system. Based on the random track irregularity, two cases are proposed to determine how the track irregularities enter the system. One case uses the vertical velocity and displacement of the track as inputs of the system and assumes that the state variables are corrupted by the Gaussian noises. The other case assumes that the vertical velocity of the track is the process noise of the system. Based on these two cases, two types of EKF and UKF are developed to estimate the parameters of the secondary suspensions. In order to study the performances of the proposed EKFs and UKFs, several simulation experiments using linear and nonlinear model are carried out that consider the uncertainties of the random track.

Pseudo Two-Hop Distributed Consensus with Noise

In this paper, we analyze the pseudo two-hop distributed consensus algorithm with communication noise. If there is communication noise among agents, the convergence performance of distributed consensus algorithms degrades. Supposing that the communication noises are zero-mean Gaussian white noise, and the noises are irrelevant and independent in time and spatial, we analyze the convergence performance of the pseudo two-hop distributed consensus algorithm with noise, and calculate mean square errors and the upper bound of mean-square error of the pseudo two-hop distributed consensus algorithm. Finally, simulation results are provided to verify these analytical results.

Belief Propagation Algorithms on Noisy Hardware

The wide recognition that emerging nano-devices will be inherently unreliable motivates the evaluation of information processing algorithms running on noisy hardware as well as the design of robust schemes for reliable performance against hardware errors of varied characteristics. In this paper, we investigate the performance of a popular statistical inference algorithm, belief propagation (BP) on probabilistic graphical models, implemented on noisy hardware, and we propose two robust implementations of the BP algorithm targeting different computation noise distributions. We assume that the BP messages are subject to zero-mean transient additive computation noise. We focus on graphical models satisfying the contraction mapping condition that guarantees the convergence of the noise-free BP. We first upper bound the distances between the noisy BP messages and the fixed point of (noise-free) BP as a function of the iteration number. Next, we propose two implementations of BP, namely, censoring BP and averaging BP, that are robust to computation noise. Censoring BP rejects incorrect computations to keep the algorithm on the right track to convergence, while averaging BP takes the average of the messages in all iterations up to date to mitigate the effects of computation noise. Censoring BP works effectively when, with high probability, the computation noise is exactly zero, and averaging BP, although having a slightly larger overhead, works effectively for general zero-mean computation noise distributions. Sufficient conditions on the convergence of censoring BP and averaging BP are derived. Simulations on the Ising model demonstrate that the two proposed implementations successfully converge to the fixed point achieved by noise-free BP. Additionally, we apply averaging BP to a BP-based image denoising algorithm and as a BP decoder for LDPC codes. In the image denoising application, averaging BP successfully denoises an image even when nominal BP fails to do so in the presence of computation noise. In the BP LDPC decoder application, the power of averaging BP is manifested by the reduction in the residual error rates compared with the nominal BP decoder.

Cramer-Rao bounds for synchronization of rotations

Synchronization of rotations is the problem of estimating a set of rotations R_i in SO(n), i = 1, ..., N, based on noisy measurements of relative rotations R_i R_j^T. This fundamental problem has found many recent applications, most importantly in structural biology. We provide a framework to study synchronization as estimation on Riemannian manifolds for arbitrary n under a large family of noise models. The noise models we address encompass zero-mean isotropic noise, and we develop tools for Gaussian-like as well as heavy-tail types of noise in particular. As a main contribution, we derive the Cram\'er-Rao bounds of synchronization, that is, lower-bounds on the variance of unbiased estimators. We find that these bounds are structured by the pseudoinverse of the measurement graph Laplacian, where edge weights are proportional to measurement quality. We leverage this to provide interpretation in terms of random walks and visualization tools for these bounds in both the anchored and anchor-free scenarios. Similar bounds previously established were limited to rotations in the plane and Gaussian-like noise.

Noise subspace approach for frequency estimation of two-dimensional harmonics in zero-mean multiplicative and additive noise

In this paper, a noise subspace (NS) method is proposed for estimating frequencies of two-dimensional harmonics in the presence of zero-mean multiplicative and additive noise. The proposed method is based on a special structured data matrix, the singular vectors of the matrix and a special basis of the NS which is generated by some of these vectors. It is observed that the estimators are consistent and work quite well in terms of biases and mean square errors. It is also observed that the method can be used to estimate accurately the frequencies of the evanescent component of texture.

A comparison of noise models in a hybrid reference spectrum and principal components analysis algorithm for Raman spectroscopy

Raman spectroscopy exploits the Raman scattering effect to analyze chemical compounds with the use of laser light. Raman spectra are most commonly analyzed using the ordinary least squares (LS) method. However, LS is known to be sensitive to variability in the spectra of the analyte and background materials. In a previous paper, we addressed this problem by proposing a novel algorithm that models expected variations in the analyte as well as background signals. The method was called the hybrid LS and principal component analysis (HLP) algorithm and used an unweighted Gaussian distribution to model the noise in the measured spectra. In this paper, we show that the noise in fact follows a Poisson distribution and improve the noise model of our hybrid algorithm accordingly. We also approximate the Poisson noise model by a weighted Gaussian noise model, which enables the use of a more efficient solver algorithm. To reflect the generalization of the noise model, we from hereon call the method the hybrid reference spectrum and principal components analysis (HRP) algorithm. We compare the performance of LS and HRP with the unweighted Gaussian (HRP‐G), Poisson (HRP‐P), and weighted Gaussian (HRP‐WG) noise models. Our experiments use both simulated data and experimental data acquired from a serial dilution of Raman‐enhanced gold‐silica nanoparticles placed on an excised pig colon. When the only signal variability was zero‐mean random noise (as examined using simulated data), HRP‐P consistently outperformed HRP‐G and HRP‐WG, with the latter coming in as a close second. Note that in this scenario, LS and HRP‐G were equivalent. In the presence of random noise as well as variations in the mean component spectra, the three HRP algorithms significantly outperformed LS, but performed similarly among themselves. This indicates that, in the presence of significant variations in the mean component spectra, modeling such variations is more important than optimizing the noise model. It also suggests that for real data, HRP‐WG provides a desirable trade‐off between noise model accuracy and computational speed. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Adaptive Universal Linear Filtering

We consider the problem of online estimation of an arbitrary real-valued signal corrupted by zero-mean noise using linear estimators. The estimator is required to iteratively predict the underlying signal based on the current and several last noisy observations, and its performance is measured by the mean-square-error. We design and analyze an algorithm for this task whose total square-error on any interval of the signal is equal to that of the best fixed filter in hindsight with respect to the interval plus an additional term whose dependence on the total signal length is only logarithmic. This bound is asymptotically tight, and resolves the question of Moon and Wiessman [“Universal FIR MMSE filtering,” IEEE Trans. Signal Process., vol. 57, no. 3, pp. 1068-1083, 2009]. Furthermore, the algorithm runs in linear time in terms of the number of filter coefficients. Previous constructions required at least quadratic time.

Subspace Approach for Estimating the Frequencies of a 2-D Single-tone in Zero-mean Multiplicative and Additive Noise

Subspace Approach for Estimating the Frequencies of a 2-D Single-tone in Zero-mean Multiplicative and Additive Noise

Uncovering phase maps from surface plasmon resonance images: Towards a sub-wavelength resolution

Abstract We present an original method for uncovering phase maps from surface plasmon resonance microscopy images. The phase images obtained from the recording of V ( Z ) maps with a scanning surface plasmon microscope are affected by zero-mean uncorrelated noise and mechanical drifts. We propose to replace standard phase unwrapping methods by the computation of the local derivative of the phase Δ ϕ / Δ Z from the V ( Z ) complex field. Phase unwrapping basically relies on a smoothness constraint of the phase field, which is severely hampered by the noise. Applications of the proposed derivation to interferometric plasmon phase images demonstrate a superior ability of restoring phase maps, preserving their discontinuities, together with an effective noise smoothing performance, irrespective of locally varying coherence characteristics.

가정용 열펌프 시스템의 정상냉방 운전조건에서 기준모델에 의한 잔차의 통계적 분석

. 도와 경계값을 통계적으로 계산함으로써 진단결과의 확률적 신뢰성을 보장할 수 있는 방법론을 제공하였다. Abstract: To approximate the threshold of the fault detection and diagnosis (FDD) system, validation of the measurements is mandatory. Naturally, the system shows uncertainties due to measuring sensors - mostly thermocouples or RTDs - and due to repeatability. The uncertainty of a thermocouple comes from natural variation or a drift of the thermocouple measurement. Considering the natural variation behaves like zero-mean white noise, its natural variation can be characterized closely by the steady-state standard deviation. However, residuals between measurements and no-fault references in FDD systems show a statistical distribution with various uncertainties. In this paper, steady-state variations of measurement residuals were investigated by utilizing built-in temperature sensors in a heat pump for the model development and the final application.