Showing papers on "White noise published in 2018"
TL;DR: In this article, a navigation technology based on Adaptive Kalman Filter with attenuation factor is proposed to restrain noise in order to improve the precision of navigation information, and the accuracy of the integrated navigation can be improved due to the reduction of the influence of environment noise.
191 citations
TL;DR: A general and flexible algorithm is proposed based on the majorization-minimization method with guaranteed monotonicity, lower computational complexity per iteration and/or convergence to a B-stationary point and many waveform constraints can be flexibly incorporated into the algorithm with only a few modifications.
Abstract: In this paper, we consider the joint design of both transmit waveforms and receive filters for a colocated multiple-input-multiple-output (MIMO) radar with the existence of signal-dependent interference and white noise. The design problem is formulated into a maximization of the signal-to-interference-plus-noise ratio (SINR), including various constraints on the transmit waveforms. Compared with the traditional alternating semidefinite relaxation approach, a general and flexible algorithm is proposed based on the majorization-minimization method with guaranteed monotonicity, lower computational complexity per iteration and/or convergence to a B-stationary point. Many waveform constraints can be flexibly incorporated into the algorithm with only a few modifications. Furthermore, the connection between the proposed algorithm and the alternating optimization approach is revealed. Finally, the proposed algorithm is evaluated via numerical experiments in terms of SINR performance, ambiguity function, computational time, and properties of the designed waveforms. The experiment results show that the proposed algorithms are faster in terms of running time and meanwhile achieve as good SINR performance as the the existing methods.
166 citations
TL;DR: In this article, the existence and uniqueness of solution for stochastic differential equations with distributional drift was studied by giving a meaning to the Stroock-Varadhan martingale problem associated to such equations.
Abstract: We study the existence and uniqueness of solution for stochastic differential equations with distributional drift by giving a meaning to the Stroock–Varadhan martingale problem associated to such equations. The approach we exploit is the one of paracontrolled distributions introduced in (Forum Math. Pi 3 (2015) e6). As a result, we make sense of the three-dimensional polymer measure with white noise potential.
85 citations
TL;DR: A novel method is proposed called complete ensemble local mean decomposition with adaptive noise (CELMDAN) to solve mode mixing resulting from intermittent signals and can extract more fault characteristic information with less interference than ELMD.
79 citations
TL;DR: In this article, the authors defined the general dilution of precision (GDP) of velocity uncertainties as the ratio of uncertainties of velocities determined from to two different deterministic models while accounting for stochastic noise at the same time.
Abstract: The velocity estimates and their uncertainties derived from position time series of Global Navigation Satellite System stations are affected by seasonal signals and their harmonics, and the statistical properties, i.e., the stochastic noise, contained in the series. If the deterministic model in the form of linear trend and periodic terms is not accurate enough to describe the time series, it will alter the stochastic model, and the resulting effect on the velocity uncertainties can be perceived as a result of a misfit of the deterministic model. The effects of insufficiently modeled seasonal signals will propagate into the stochastic model and falsify the results of the noise analysis, in addition to velocity estimates and their uncertainties. We provide the general dilution of precision (GDP) of velocity uncertainties as the ratio of uncertainties of velocities determined from to two different deterministic models while accounting for stochastic noise at the same time. In this newly defined GDP, the first deterministic model includes a linear trend, while the second one includes a linear trend and seasonal signals. These two are tested with the assumption of white noise only as well as the combinations of power-law and white noise in the data. The more seasonal terms are added to the series, the more biased the velocity uncertainties become. With increasing time span of observations, the assumption of seasonal signals becomes less important, and the power-law character of the residuals starts to play a crucial role in the determined velocity uncertainties. With reference frame and sea level applications in mind, we argue that 7 and 9 years of continuous observations is the threshold for white and flicker noise, respectively, while 17 years are required for random-walk to decrease GDP below 5% and to omit periodic oscillations in the GNSS-derived time series taking only the noise model into consideration.
64 citations
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TL;DR: In this paper, the authors prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a periodic domain.
Abstract: Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a periodic domain. There are two new ingredients as compared to the parabolic setting. (i) In constructing stochastic objects, we have to carefully exploit dispersion at a multilinear level. (ii) We introduce novel random operators and leverage their regularity to overcome the lack of smoothing of usual paradifferential commutators.
62 citations
TL;DR: In this paper, a closed-form image reconstruction method for single-pixel imaging based on the generalized inverse of the measurement matrix is presented, which regularizes the inverse problem by minimizing the norms of the convolution between the reconstructed image and a set of spatial filters.
Abstract: We present a closed-form image reconstruction method for single-pixel imaging based on the generalized inverse of the measurement matrix. Its numerical cost scales proportionally with the number of measured samples. Regularization of the inverse problem is obtained by minimizing the norms of the convolution between the reconstructed image and a set of spatial filters. The final reconstruction formula can be expressed in terms of matrix pseudoinverse. At high compression, this approach is an interesting alternative to the methods of compressive sensing based on l1-norm optimization, which are too slow for real-time applications. For instance, we demonstrate experimental single-pixel detection with real-time reconstruction obtained in parallel with measurement at a frame rate of 11 Hz for highly compressive measurements with a resolution of 256 × 256. To this end, we preselect the sampling functions to match the average spectrum obtained with an image database. The sampling functions are selected from the Walsh-Hadamard basis, from the discrete cosine basis, or from a subset of Morlet wavelets convolved with white noise. We show that by incorporating the quadratic criterion into the closed-form reconstruction formula, we can use binary rather than continuous sampling and reach similar reconstruction quality as is obtained by minimizing the total variation. This makes it possible to use cosine- or Morlet-based sampling with digital micromirror devices without advanced binarization methods.
56 citations
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TL;DR: In this paper, an explicit temporal splitting numerical scheme for the stochastic Allen-Cahn equation driven by additive noise was proposed, where the splitting strategy was combined with an exponential Euler scheme of an auxiliary problem.
Abstract: This article analyzes an explicit temporal splitting numerical scheme for the stochastic Allen-Cahn equation driven by additive noise, in a bounded spatial domain with smooth boundary in dimension $d\le 3$. The splitting strategy is combined with an exponential Euler scheme of an auxiliary problem.
When $d=1$ and the driving noise is a space-time white noise, we first show some a priori estimates of this splitting scheme. Using the monotonicity of the drift nonlinearity, we then prove that under very mild assumptions on the initial data, this scheme achieves the optimal strong convergence rate $\OO(\delta t^{\frac 14})$. When $d\le 3$ and the driving noise possesses some regularity in space, we study exponential integrability properties of the exact and numerical solutions. Finally, in dimension $d=1$, these properties are used to prove that the splitting scheme has a strong convergence rate $\OO(\delta t)$.
53 citations
TL;DR: In this article, the Edwards-Wilkinson model was used to describe large scale random fluctuations in the heat equation with additive white noise, and the renormalized solution converges to the solution of a deterministic diffusion equation with an effective diffusivity.
Abstract: We consider the heat equation with a multiplicative Gaussian potential in dimensions d ≥ 3. We show that the renormalized solution converges to the solution of a deterministic diffusion equation with an effective diffusivity. We also prove that the renormalized large scale random fluctuations are described by the Edwards–Wilkinson model, that is, the stochastic heat equation (SHE) with additive white noise, with an effective variance.
52 citations
TL;DR: A more general form of DFT interpolation based frequency estimator based on interpolation of three discrete Fourier transform spectral lines based on sinusoid signal is proposed.
TL;DR: In this paper, a time-delayed feedback tristable system driven by Gaussian white noise is investigated by simulating the potential function, mean first-passage time (MFPT), and signal-to-noise ratio (SNR) of the system.
TL;DR: In this article, the 2D Euler equations with random initial condition distributed as a Gaussian measure are considered and the theory developed by S. Albeverio and A.-B. Cruzeiro is revisited.
Abstract: The 2D Euler equations with random initial condition distributed as a certain Gaussian measure are considered. The theory developed by S. Albeverio and A.-B. Cruzeiro is revisited, following the ap...
TL;DR: In this paper, Biercuk et al. investigated the effect of correlated noise on randomised benchmarking (RB) and gate-set tomography (GST), and found that the performance of standard benchmarking techniques is strongly influenced by the statistical properties of the noise affecting the hardware, complicating direct comparisons between experiments.
Abstract: Growth in the capabilities of quantum information hardware mandates access to techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). Our analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped 171Yb+ ion-qubit and inject engineered noise $$\left( { \propto \hat \sigma _z} \right)$$
to probe protocol performance. Experiments on RB validate predictions that measured fidelities over sequences are described by a gamma distribution varying between approximately Gaussian, and a broad, highly skewed distribution for rapidly and slowly varying noise, respectively. Similarly we find a strong gate set dependence of default experimental GST procedures in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlated $$\hat \sigma _z$$
errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlated $$\hat \sigma _x$$
or $$\hat \sigma _y$$
errors or depolarising noise processes, highlighting the impact of the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments. Experiments reveal that the presence of correlated noise may compromise the interpretation of techniques for the validation of quantum hardware. A team led by Michael Biercuk at Australia’s University of Sydney and National Measurement Institute, carried out experiments on a single trapped 171Yb+ ion to test the reliability of widespread techniques for characterisation, validation and verification of quantum hardware. Although error processes are often assumed to be statistically independent, in practice slowly varying external fields may introduce temporal correlations in noise. The experiments revealed that the outcome of randomised benchmarking and gate-set tomography differ substantially in presence of correlated noise, and reveal an unexpected sequence-dependent behaviour. These results demonstrate that the reliability of standard performance benchmarking techniques is strongly influenced by the statistical properties of the noise affecting the hardware, complicating direct comparisons between experiments.
TL;DR: Two-level denoised framework with singular value decomposition and adaptive wavelet denoising is proposed, and the improved method of selecting singular value based on curvature spectrum is proposed.
TL;DR: In this paper, the presence of a periodic component in a time series of functions is investigated in both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general setting of a weakly dependent contaminating process.
Abstract: We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general setting of a weakly dependent contaminating process. Several forms of the periodic component are considered. Our tests are motivated by the likelihood principle and fall into two broad categories, which we term multivariate and fully functional. Generally, for the functional series that motivate this research, the fully functional tests exhibit a superior balance of size and power. Asymptotic null distributions of all tests are derived and their consistency is established. Their finite sample performance is examined and compared by numerical studies and application to pollution data.
TL;DR: An adaptive extended Kalman filter based on the maximum likelihood is proposed to estimate the instantaneous amplitudes of the travelling waves and the effectiveness of exacting mutation feature using the proposed method has been demonstrated by a simulated instantaneous pulse.
Abstract: The fault location in transmission systems remains a challenging problem, primarily due to the fault location near the substation ends or the weak fault signals. In this study, an adaptive extended Kalman filter (EKF) based on the maximum likelihood (ML) is proposed to estimate the instantaneous amplitudes of the travelling waves. In this method, the EKF algorithm is used to estimate the optimal states (the clean travelling waves) with additive white noise while ML is used to adaptively optimise the error covariance matrices and the initial conditions of the EKF algorithm. Using the proposed method, the singularity points of travelling waves can be detected, and the exact arrival time of the initial wave head at the substations M and N can be easily yielded. Thus the fault distance can be calculated precisely. The effectiveness of exacting mutation feature using the proposed method has been demonstrated by a simulated instantaneous pulse. Also, the proposed method has been tested with different types of faults, such as different fault locations, different fault resistances and different fault inception angles using ATP simulation. The accuracy of fault location using the proposed method has been compared with conventional wavelet transformation scheme.
TL;DR: Permutation Entroy Optimization (PEO) is proposed in this paper and shows that the algorithm can not only improve the signal to noise ratio (SNR) of the signal effectively, but can also extract the multiple fault features of the gear box in the strong noise environment.
Abstract: Variational Mode Decomposition (VMD) can decompose signals into multiple intrinsic mode functions (IMFs). In recent years, VMD has been widely used in fault diagnosis. However, it requires a preset number of decomposition layers K and is sensitive to background noise. Therefore, in order to determine K adaptively, Permutation Entroy Optimization (PEO) is proposed in this paper. This algorithm can adaptively determine the optimal number of decomposition layers K according to the characteristics of the signal to be decomposed. At the same time, in order to solve the sensitivity of VMD to noise, this paper proposes a Modified VMD (MVMD) based on the idea of Noise Aided Data Analysis (NADA). The algorithm first adds the positive and negative white noise to the original signal, and then uses the VMD to decompose it. After repeated cycles, the noise in the original signal will be offset to each other. Then each layer of IMF is integrated with each layer, and the signal is reconstructed according to the results of the integrated mean. MVMD is used for the final decomposition of the reconstructed signal. The algorithm is used to deal with the simulation signals and measured signals of gearbox with multiple fault characteristics. Compared with the decomposition results of EEMD and VMD, it shows that the algorithm can not only improve the signal to noise ratio (SNR) of the signal effectively, but can also extract the multiple fault features of the gear box in the strong noise environment. The effectiveness of this method is verified.
TL;DR: In this paper, the authors focus on the time domain output-only technique called Data-Driven Stochastic Subspace Identification (DD-SSI), in order to identify modal models (frequencies, damping ratios and mode shapes).
TL;DR: In this article, the authors generalized the Wiener Path Integral (WPI) technique for determining the joint response probability density function of nonlinear systems subject to Gaussian white noise excitation to account for non-white, non-Gaussian, and non-stationary processes.
TL;DR: In this paper, an inverse random source scattering problem in an inhomogeneous background medium is considered, where the wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise.
Abstract: This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.
TL;DR: This paper estimates amplitude of a power distribution systems signal corrupted with white noise and harmonics by using the windowed symmetrical interpolation fast Fourier transform using the polynomial coefficients of amplitude estimation.
Abstract: This paper estimates amplitude of a power distribution systems signal corrupted with white noise and harmonics by using the windowed symmetrical interpolation fast Fourier transform. The polynomial coefficients of amplitude estimation are derived. The influence of harmonic and the spectral interference (leakage) from image parts is analyzed. The analytical expression of the amplitude estimation variance is derived and compared with the unbiased Cramer–Rao lower bound. The proposed methods are validated through computer simulations and experiments.
TL;DR: This paper proposes new insights into the network centrality based not only on the network graph, but also on a more structured model of network uncertainties, where the network uncertainty is modeled by structured additive Gaussian white noise input on the update dynamics of each agent.
Abstract: We propose new insights into the network centrality based not only on the network graph, but also on a more structured model of network uncertainties. The focus of this paper is on the class of uncertain linear consensus networks in continuous time, where the network uncertainty is modeled by structured additive Gaussian white noise input on the update dynamics of each agent. The performance of the network is measured by the expected dispersion of its states in steady state. This measure is equal to the square of the $\mathcal {H}_2$ -norm of the network, and it quantifies the extent by which its state deviates away from the consensus state in steady state. We show that this performance measure can be explicitly expressed as a function of the Laplacian matrix of the network and the covariance matrix of the noise input. We investigate several structures for noise input and provide engineering insights on how each uncertainty structure can be relevant in real-world settings. Then, a new centrality index is defined in order to assess the influence of each agent or link on the network performance. For each noise structure, the value of the centrality index is calculated explicitly, and it is shown how it depends on the network topology as well as the noise structure. Our results assert that agents or links can be ranked according to this centrality index, and their rank can drastically change from the lowest to the highest, or vice versa, depending on the noise structure. This fact hints at emergence of fundamental tradeoffs on network centrality in the presence of multiple concurrent network uncertainties with different structures.
TL;DR: A novel explicit full discrete scheme is proposed to numerically solve the stochastic Allen-Cahn equation with cubic nonlinearity, perturbed by additive space-time white noise, with convergence rates twice as high as existing ones in the literature.
Abstract: In Becker and Jentzen (2019) and Becker et al. (2017), an explicit temporal semi-discretization scheme and a space-time full-discretization scheme were, respectively, introduced and analyzed for the additive noise-driven stochastic Allen-Cahn type equations, with strong convergence rates recovered. The present work aims to propose a different explicit full-discrete scheme to numerically solve the stochastic Allen-Cahn equation with cubic nonlinearity, perturbed by additive space-time white noise. The approximation is easily implementable, performing the spatial discretization by a spectral Galerkin method and the temporal discretization by a kind of nonlinearity-tamed accelerated exponential integrator scheme. Error bounds in a strong sense are analyzed for both the spatial semi-discretization and the spatio-temporal full discretization, with convergence rates in both space and time explicitly identified. It turns out that the obtained convergence rate of the new scheme is, in the temporal direction, twice as high as existing ones in the literature. Numerical results are finally reported to confirm the previous theoretical findings.
20 Aug 2018
TL;DR: A newly proposed method is described, based on generation of a white noise signal, its transformation into the frequency domain, spectral processing and inverse transform back into the time domain, for the generation of power-law, colored digital noise signals (sequences) with arbitrary spectral slope.
Abstract: The present paper addresses the generation of power-law, colored digital noise signals (sequences) with arbitrary spectral slope. In the beginning, brief background information is given about some noise features. Further, a newly proposed method is described, based on generation of a white noise signal, its transformation into the frequency domain, spectral processing and inverse transform back into the time domain. Computer simulations are performed to confirm the consistency of the algorithm, including estimation of the power spectral density and the autocorrelation, along with example of its outperformance in comparison with the corresponding in-built Matlab® function.
TL;DR: In this article, the authors proposed a non-local fractional beam model, where nonlocal effects are represented as viscoelastic long-range volume forces and moments exchanged by non-adjacent beam segments depending on their relative motion, while local effects are modelled by elastic classical stress resultants.
Abstract: Non-local viscoelasticity is a subject of great interest in the context of non-local theories. In a recent study, the authors have proposed a non-local fractional beam model where non-local effects are represented as viscoelastic long-range volume forces and moments, exchanged by non-adjacent beam segments depending on their relative motion, while local effects are modelled by elastic classical stress resultants. Long-range interactions have been given a fractional constitutive law, involving the Caputo's fractional derivative. This paper introduces a comprehensive numerical approach to calculate the stochastic response of the non-local fractional beam model under Gaussian white noise. The approach combines a finite-element discretization with a fractional-order state-variable expansion and a complex modal transformation to decouple the discretized equations of motion. While closed-form expressions are derived for the finite-element matrices associated with elastic and fractional terms, fractional calculus is used to solve the decoupled equations of motion, in both time and frequency domain. Remarkably, closed-form expressions are obtained for the power spectral density, cross power spectral density, variance and covariance of the beam response along the whole axis. Time-domain solutions are obtained by time-step numerical integration methods involving analytical expressions of impulse response functions. Numerical examples show versatility of the non-local fractional beam model as well as computational advantages of the proposed solution procedure.
TL;DR: This work proposes an event-triggered control scheme for discrete-time linear systems subject to Gaussian white noise disturbances that outperforms traditional periodic control for the same average transmission rate and does not generate transmissions in the absence of disturbances.
TL;DR: Decomposition results of simulation signals indicate that signals added with white Gaussian noise and non-stationary components can be correctly decomposed using the AR-EWT, which cannot be achieved using the original EWT.
TL;DR: In this article, the stochastic response of monostable vibration energy harvesters with fractional derivative damping under Gaussian white noise excitation was investigated, and the numerical results indicated that the proposed method has a satisfactory level of accuracy.
Abstract: To the best of authors’ knowledge, the dynamical behaviors of vibration energy harvesters with fractional derivative damping have not been discussed by researchers with the help of the stochastic averaging method. As the fractional-order models are more accurate than the classical integer-order models, so it is necessary to investigate the dynamical behaviors of fractional vibration energy harvesters. This paper aims to investigate the stochastic response of monostable vibration energy harvesters with fractional derivative damping under Gaussian white noise excitation. First, we can get the equivalent stochastic system with the help of variable transformation. Then, the approximately analytical solutions of the equivalent stochastic system can be obtained by the stochastic averaging method. Third, the numerical results are considered as the benchmark to prove the effectiveness of the proposed method. The results indicate that the proposed method has a satisfactory level of accuracy. We also discuss the effect of system parameters on the mean square voltage.
TL;DR: This work proposes an EMD-based algorithm assisted by sinusoidal functions with a designed uniform phase distribution with a comprehensive theoretical explanation for the substantial reduction of the mode splitting and the residual noise effects simultaneously.
Abstract: The empirical mode decomposition (EMD) is an established method for the time–frequency analysis of nonlinear and nonstationary signals. However, one major drawback of the EMD is the mode mixing effect. Many modifications have been made to resolve the mode mixing effect. In particular, disturbance-assisted EMDs, such as the noise-assisted EMD and the masking EMD, have been proposed to resolve this problem. These disturbance-assisted approaches have led to a better performance of the EMD in the analysis of real-world data sets, but they may also have two side effects: the mode splitting and residual noise effects. To minimize or eliminate the mode mixing effect while avoiding the two side effects of traditional disturbance-assisted EMDs, we propose an EMD-based algorithm assisted by sinusoidal functions with a designed uniform phase distribution with a comprehensive theoretical explanation for the substantial reduction of the mode splitting and the residual noise effects simultaneously. We examine the performance of the new method and compare it to those of other disturbance-assisted EMDs using synthetic signals. Finally numerical experiments with real-world examples are conducted to verify the performance of the proposed method.