Dependent Noises Research Articles

Statistical inference for the first-order autoregressive process with the fractional Gaussian noise

While the statistical inference of first-order autoregressive processes driven by independent and identically distributed noises has a long history, the statistical analysis for first-order autoregressive processes driven by dependent noises is more recent. This paper considers the problem of estimating all the unknown parameters in first-order autoregressive processes driven by the fractional Gaussian noise, which is a self-similar stochastic process used to model persistent or anti-persistent dependency structures in observed time series. The estimation procedure is built upon the marriage of the log-periodogram regression and the method of moments. The usual asymptotic properties, including consistency and asymptotic normality, are established under some mild conditions. Monte Carlo simulations are performed to demonstrate the feasibility and effectiveness of the proposed method. Finally, the estimation methods are applied to model some realized volatility time series, where we find that the realized volatility is rough. Moreover, the proposed model is compared with some alternative models, including the first-order autoregressive process driven by the standard Gaussian noise, the heterogeneous autoregression model with lag structure (1,5,21) (HAR(1,5,21)), the autoregressive fractionally integrated moving average model (ARFIMA(1,d,0)) and the scaled fractional Brownian motion, in forecasting the logarithmic realized volatility.

Consensus of stochastic multi-agent systems with time-delay and Markov jump

In this paper, the H ∞ consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and ( x , u , v ) -dependent noises is studied. Firstly, the H ∞ consensus problem is transformed into a standard H ∞ control problem by model transformation. Then, a dynamic output feedback control protocol is constructed by solving a set of linear matrix inequalities to ensure that the closed-loop system achieves the mean square consensus and meets the specified H ∞ performance level. After that, both delay-independent and delay-dependent stochastic bounded real lemmas are established by taking advantage of the Lyapunov–Krasovskii function method and the generalised It o ^ formula. Finally, we illustrate the validity of the developed method with numerical simulations.

CMW-Net: Learning a Class-Aware Sample Weighting Mapping for Robust Deep Learning.

Modern deep neural networks can easily overfit to biased training data containing corrupted labels or class imbalance. Sample re-weighting methods are popularly used to alleviate this data bias issue. Most current methods, however, require to manually pre-specify the weighting schemes relying on the characteristics of the investigated problem and training data. This makes them fairly hard to be generally applied in practical scenarios, due to their significant complexities and inter-class variations of data bias. To address this issue, we propose a meta-model capable of adaptively learning an explicit weighting scheme directly from data. Specifically, by seeing each training class as a separate learning task, our method aims to extract an explicit weighting function with sample loss and task/class feature as input, and sample weight as output, expecting to impose adaptively varying weighting schemes to different sample classes based on their own intrinsic bias characteristics. Extensive experiments substantiate the capability of our method on achieving proper weighting schemes in various data bias cases, like class imbalance, feature-independent and dependent label noises, and more complicated bias scenarios beyond conventional cases. Besides, the task-transferability of the learned weighting scheme is also substantiated, by readily deploying the weighting function learned on relatively smaller-scale CIFAR-10 dataset on much larger-scale full WebVision dataset. The general availability of our method for multiple robust deep learning issues, including partial-label learning, semi-supervised learning and selective classification, has also been validated. Code for reproducing our experiments is available at https://github.com/xjtushujun/CMW-Net.

Genetic Algorithm to Solve Optimal Sensor Placement for Underwater Vehicle Localization with Range Dependent Noises.

In source localization problems, the relative geometry between sensors and source will influence the localization performance. The optimum configuration of sensors depends on the measurements used for the source location estimation, how these measurements are affected by noise, the positions of the source, and the criteria used to evaluate the localization performance. This paper addresses the problem of optimum sensor placement in a plane for the localization of an underwater vehicle moving in 3D. We consider sets of sensors that measure the distance to the vehicle and model the measurement noises with distance dependent covariances. We develop a genetic algorithm and analyze both single and multi-objective problems. In the former, we consider as the evaluation metric the arithmetic average along the vehicle trajectory of the maximum eigenvalue of the inverse of the Fisher information matrix. In the latter, we estimate the Pareto front of pairs of common criteria based on the Fisher information matrix and analyze the evolution of the sensor positioning for the different criteria. To validate the algorithm, we initially compare results with a case with a known optimal solution and constant measurement covariances, obtaining deviations from the optimal less than 0.1%. Posterior, we present results for an underwater vehicle performing a lawn-mower maneuver and a spiral descent maneuver. We also present results restricting the allowed positions for the sensors.

Adaptive denoising hyperspectral data for visualization enhancement of intraoperative tissue.

The vast amount of reflectance information obtained from the hyperspectral imaging devices offers great opportunities for investigating the function and structure of human tissue. However, the captured hyperspectral data often contain various noises due to the intrinsic imperfection of associated electrical and optical imaging components. This work proposed an automatic total variation algorithm to suppress the noises while preserving the details of the spectral and spatial information. The variation of spectral images at neighboring bands was calculated for regulating the total variation of hyperspectral data so that the spectral-dependent noises can be treated differentially across all bands. Experimental results demonstrated that the proposed method could effectively remove the spectral noises, especially near the ends of those extreme bands. The noise suppressed hyperspectral data could then be used for the visualization enhancement on pathophysiological conditions of intraoperative observed anatomies such as the vessels of brain tissues.

Capacity analysis of underwater visible light communication systems over a lossy channel in the presence of noises.

Absorption and scattering losses due to impurities and turbidity in the water affect the transmission quality of underwater visible light communication links, restricting the channel capacity. For the first time to our knowledge, this paper analytically studies the channel capacity of a point-to-point underwater visible light communication link in the presence of input-independent and -dependent noises along with absorption and scattering losses. This way, novel lower and upper bound expressions on channel capacity are derived when average and peak-intensity constraints are imposed on the channel input. Our proposed upper and lower bounds are tight at high optical signal-to-noise ratio. The derived analytic expression of capacity also helps to evaluate the available data rate in the presence of different types of noise and water. From the results, we can say that input-dependent noise causes more system capacity degradation than input-independent noise. The results show that good water quality is crucial for high-capacity communication links. Furthermore, it is shown that the attenuation of the optical signal is more in water when compared to air as a medium, and channel capacity decreases as the link range increases. The results reported in this paper provide valuable insight into the design of underwater visible light communication systems.

Shot noise processes with randomly delayed cluster arrivals and dependent noises in the large-intensity regime

AbstractWe study shot noise processes with cluster arrivals, in which entities in each cluster may experience random delays (possibly correlated), and noises within each cluster may be correlated. We prove functional limit theorems for the process in the large-intensity asymptotic regime, where the arrival rate gets large while the shot shape function, cluster sizes, delays, and noises are unscaled. In the functional central limit theorem, the limit process is a continuous Gaussian process (assuming the arrival process satisfies a functional central limit theorem with a Brownian motion limit). We discuss the impact of the dependence among the random delays and among the noises within each cluster using several examples of dependent structures. We also study infinite-server queues with cluster/batch arrivals where customers in each batch may experience random delays before receiving service, with similar dependence structures.

Rao-Blackwellized Particle Filter for Asynchronously Dependent Noises

This paper develops Rao-Blackwellized particle filter with asynchronous dependence between system noise and measurement noise. It is pointed out that this dependence affects both the particle filter update step for the nonlinear sub-system and the Kalman filter update step for the conditionally linear sub-system in Rao-Blackwellized particle filter. A de-correlation method is suggested to deal with such influence. The optimal importance density function for sampling the nonlinear sub-state is found out, and a suboptimal one for approximating the optimal importance density function is proposed. The proposed methods are applied to target tracking to testify their effectiveness and superiority.

Moderate deviation principles for unbounded additive functionals of distribution dependent SDEs

<p style='text-indent:20px;'>By comparing the original equations with the corresponding stationary ones, the moderate deviation principle (MDP) is established for unbounded additive functionals of several different models of distribution dependent SDEs, with non-degenerate and degenerate noises.</p>

Robust centralized and integrated covariance intersection fusion Kalman estimators for networked mixed‐uncertain systems

SummaryFor networked mixed uncertain time‐varying systems with uncertain noise variances, random one‐step measurement delay, state‐dependent and noise‐dependent multiplicative noises, and linearly dependent additive white noises, the robust local, centralized, and distributed fusion estimation problems are addressed. Three new approaches are presented, which include a new augmented state approach with fictitious white noises, an extended Lyapunov equation approach with two Lyapunov equations, and a universal integrated covariance intersection (ICI) fusion approach of integrating the minimax robust local Kalman estimators and their conservative cross‐covariances. They constitute a new important methodology of solving robust fusion estimation problems. Applying them, the local, centralized, and distributed ICI fusion time‐varying and steady‐state robust Kalman estimators (predictor, filter, and smoother) are presented in the sense that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, convergence, and accuracy relations are proved. Specially, the proposed ICI fusers improve the robust accuracies of the original covariance intersection fusers, and overcome their drawbacks, such that the local estimators and their conservative variances are assumed to be known, and the conservative cross‐variances are ignored. A simulation example with application to a vehicle suspension system shows the effectiveness of the proposed approaches and results.

Polynomial filtering for nonlinear stochastic systems with state‐ and disturbance‐dependent noises

SummaryThis article is concerned with the polynomial filtering problem for a class of nonlinear stochastic systems governed by the Itô differential equation. The system under investigation involves polynomial nonlinearities, unknown‐but‐bounded disturbances, and state‐ and disturbance‐dependent noises ((x,d)‐dependent noises for short). By expanding the polynomial nonlinear functions in Taylor series around the state estimate, a new polynomial filter design method is developed with hope to reduce the conservatism of the existing results. In virtue of stochastic analysis and inequality technique, sufficient conditions in terms of parameter‐dependent linear matrix inequalities (PDLMIs) are derived to guarantee that the estimation error system is input‐to‐state stable in probability. Moreover, the desired polynomial matrix can be obtained by solving the PDLMIs via the sum‐of‐squares approach. The effectiveness and applicability of the proposed method are illustrated by two numerical examples with one concerning the permanent magnet synchronous motor.

Functional Limit Theorems for Shot Noise Processes with Weakly Dependent Noises

We study shot noise processes when the shot noises are weakly dependent, satisfying the ρ-mixing condition. We prove a functional weak law of large numbers and a functional central limit theorem for this shot noise process in an asymptotic regime with a high intensity of shots. The deterministic fluid limit is unaffected by the presence of weak dependence. The limit in the diffusion scale is a continuous Gaussian process whose covariance function explicitly captures the dependence among the noises. The model and results can be applied in financial and insurance risks with dependent claims as well as queueing systems with dependent service times. To prove the existence of the limit process, we employ the existence criterion that uses a maximal inequality requiring a set function with a superadditivity property. We identify such a set function for the limit process by exploiting the ρ-mixing condition. To prove the weak convergence, we establish the tightness property and the convergence of finite dimensional distributions. To prove tightness, we construct two auxiliary processes and apply an Ottaviani-type inequality for weakly dependent sequences.

Robust integrated covariance intersection fusion Kalman estimators for networked mixed uncertain time-varying systems

Abstract For the multisensor time-varying networked mixed uncertain systems with random one-step sensor delays and uncertain-variance multiplicative and linearly dependent additive white noises, a new augmented state method with fictitious noises is presented, by which the original system is transformed into a standard system without delays and with uncertain-variance fictitious white noises. According to the minimax robust estimation principle and the Kalman filtering theory, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the local and integrated covariance intersection (ICI) fused robust time-varying Kalman estimators (filter, predictor and smoother) are presented respectively in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their robustness is proved by the extended Lyapunov equation method, and their accuracy relations are compared based on the traces of the variance matrices and the covariance ellipsoids, respectively. Specially, a universal ICI fusion robust Kalman filtering method of integrating the local robust estimators and their conservative cross-covariances is presented. It overcomes the drawbacks of the original covariance intersection (CI) fusion method and improves robust accuracy of the original CI fuser. A simulation example applied to two-mass spring system shows the effectiveness of the proposed methods and results.

Robust H2/H∞ control for a class of time-varying nonlinear stochastic systems with state- and control-dependent noises

ABSTRACTThis paper deals with the problem of robust control for a class of discrete time-varying nonlinear stochastic systems with state- and control-dependent noises (also called -dependent noises). In the addressed system, all system parameters are allowed to be time-varying, parameter uncertainties are supposed to be norm-bounded, and nonlinearities are assumed to satisfy the sector-bounded condition. A robust stochastic bounded real lemma is established for the uncontrolled system by means of the Riccati difference equation (RDE). Moreover, a necessary and sufficient condition is presented for the existence of finite-horizon robust control by virtue of the solvability of coupled RDEs, and an iterative algorithm is designed to solve these RDEs. Finally, a numerical example is utilised to illustrate the effectiveness of the derived results.

Optimal linear quadratic Gaussian control for discrete time‐varying system with simultaneous input delay and state/control‐dependent noises

SummaryThis article focuses on the problem of linear quadratic Gaussian (LQG) control for discrete time‐varying system with input delay and state/control‐dependent noises. When the state variables can be exactly observed, first, we obtain the maximum principle by applying the method of variation. Second, a nonhomogeneous relationship between the state and the costate is developed in virtue of the obtained maximum principle and the mathematical induction. It is noted that the nonhomogeneous relationship is the solution to the forward and backward stochastic difference equations (FBSDEs). Finally, based on the solution to the FBSDEs, a necessary and sufficient condition for the optimal LQG control is derived in terms of coupled Riccati equations. Moreover, the analytical expression of the optimal controller is presented. The derived results are applied in networked control systems with packet dropout. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.

H∞ consensus control with spectrum constraints for stochastic multi-agent systems subject to (x, u, v)-dependent noises

This paper is concerned with the problem of H∞ consensus control with spectrum constraints for continuous-time multi-agent systems (MASs) with (x, u, v)-dependent noises. By means of the spectrum technique, the definition of (−β,−α)-stability is introduced, and the relationship between the convergence rate of state responses and the (−β,−α)-stability is discussed for the closed-loop system. The aim of the addressed problem is to design a static output feedback controller such that the closed-loop system is (−β,−α)-stable and the prescribed H∞ performance requirement is satisfied. In virtue of the stochastic analysis method and Kronecker product, sufficient conditions are obtained for the existence of H∞ consensus controller. Two examples are provided to illustrate the availability of the proposed techniques.

Unforeseen data estimation in water distribution system

Unforeseen data is a mostly encountered problem in the water distribution system (WDS) application. The WDS is considered to be significant component in the social framework. This paper proposes an improved version of window based Kalman filter known to be customized Kalman filter (CKF). The academic section WDS of National Institute of Technology-Tiruchirappalli, Tamil Nadu, India is considered as the case-study. The flows across the pipes and head level of the reservoir tanks are measurement of interest which has significant data loss due to the randomly varying sampling interval. The available measurements are also corrupted with the state and input dependent noises along with the conventional uncertainties. This is due to the interconnection between the consumers and structural complexity of the considered case-study which causes the direct and indirect impact over the other states due to the propagation of the disturbance occurring at any spatial instance of the interconnected WDS. The proposed CKF is equipped with the necessary remedies to have an optimal estimates of unforeseen data even in the presence of state and input dependent noises. The CKF algorithm is incorporated along with the mean imputation technique as a priori of the estimates, which improves the estimation accuracy. The estimated results are validated through the quantative and qualitative analysis for the considered case-study.

IMPROVED MODEL SELECTION METHOD FOR AN ADAPTIVE ESTIMATION IN SEMIMARTINGALE REGRESSION MODELS

This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally Gaussian distribution. An example of such noise is the non-Gaussian Ornstein-Uhlenbeck-Levy processes. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Under some conditions on the noise distribution, sharp oracle inequality for the robust risk has been proved and the robust efficiency of the model selection procedure has been established. The numerical analysis results are given.

Consensus of double-integrator multi-agent systems without relative states derivative under relative-state dependent measurement noises

ABSTRACTThis paper proposes a consensus protocol for continuous-time double-integrator multi-agent systems under noisy communication in directed topologies. Each agent’s control input relies on its own velocity and the relative positions with neighbours; it does not require the relative velocities. The agent receives its neighbours’ positions information corrupted by time-varying measurement noises whose intensities are proportional to the absolute relative distance that separates the agent from the neighbours. The consensus protocol is mainly based on the velocity damping gain to derive conditions under which the unbiased mean square χ-consensus is achieved in directed fixed topologies, and the unbiased mean square average consensus is achieved in directed switching topologies. The mean square state errors are quantified for both the positions and velocities. Finally, to illustrate the approach presented, some numerical simulations are performed.

On mean‐square H∞ control for discrete‐time nonlinear stochastic systems with (x, u, v)‐dependent noises

SummaryIn this paper, the H∞ control problem is investigated for a general class of discrete‐time nonlinear stochastic systems with state‐, control‐, and disturbance‐dependent noises (also called (x, u, v)‐dependent noises). In the system under study, the system state, the control input, and the disturbance input are all coupled with white noises, and this gives rise to considerable difficulties in the stability and H∞ performance analysis. By using the inequality techniques, a sufficient condition is established for the existence of the desired controller such that the closed‐loop system is mean‐square asymptotically stable and also satisfies H∞ performance constraint for all nonzero exogenous disturbances under the zero‐initial condition. The completing square technique is used to design the H∞ controller with hope to reduce the resulting conservatism, and a special algebraic identity is employed to deal with the cross‐terms induced by (x, u, v)‐dependent noises. Several corollaries with simplified conditions are presented to facilitate the controller design. The effectiveness of the developed methods is demonstrated by two numerical examples with one concerning the multiplier‐accelerator macroeconomic system.