Uniform Quantization Effects Research Articles

Distributed adaptive moving horizon estimation for multi-sensor networks subject to quantization effects

This paper investigates the distributed state estimation problem for multi-sensor networks with quantized measurements. Within the Bayesian framework, a distributed adaptive moving horizon estimation algorithm is developed. Unlike the existing methods regarding quantized errors roughly as bounded uncertainties, the posterior distributions of the errors are demanded to be derived. To overcome the difficulty of evaluating the posterior distributions for series of the states and quantized errors jointly, the variational Bayesian methodology is adopted to approximate the true distributions. Based on the fixed-point iteration method, the update rules are analytically derived, with the convergence criterion provided. Furthermore, by incorporating the average consensus algorithm into the prediction process, all sensors can achieve consensus on their estimates in a distributed manner. Finally, a numerical example of target tracking under logarithmic and uniform quantization effects is given to illustrate the validity of the proposed algorithm.

Sequential Fusion Estimation for Multirate Complex Networks With Uniform Quantization: A Zonotopic Set-Membership Approach.

In this article, the sequential fusion estimation problem is investigated for multirate complex networks (MRCNs) with uniformly quantized measurements. The process and measurement noises, which are unknown-yet-bounded (UYB), are restrained into a family of zonotopes, and the multiple sensors are allowed to have different sampling periods. To facilitate digital transmissions, the sensor measurements are uniformly quantized before being sent to the remote estimator. The purpose of this article is to design a sequential set-membership estimator such that, in the simultaneous presence of UYB noises, multirate samplings, and uniform quantization effects, the estimation error (after each measurement update) is confined to a zonotope with minimum F -radius at each time instant. By introducing certain virtual measurements, the MRCNs are first transformed into single-rate ones exhibiting a switching phenomenon. Then, by utilizing the properties of zonotopes, the desired zonotopes are derived, which contain the estimation error dynamics after each measurement update. Subsequently, the gain matrices of the sequential estimator are derived by minimizing the F -radii of these zonotopes, and the uniform boundedness is analyzed for the F -radius of the zonotope containing the estimation error after all measurement updates. Furthermore, sufficient conditions are derived to ensure the existence of the desired uniform upper/lower bounds. Finally, an illustrated example is proposed to show the effectiveness of the proposed sequential fusion estimation method.

Set-membership filtering for two-dimensional shift-varying systems with stochastic communication protocol and uniform quantization

This paper is concerned with the set-membership filtering problem for the two-dimensional shift-varying systems subject to the stochastic communication protocol and uniform quantization effects. To prevent the data transmission from collisions, only one sensor can transmit the measured information to the filter at each sampling shift instant, and the selected sensor is determined by the scheduling strategy of the stochastic communication protocol. On the contrary, the uniform quantization mechanism has been employed to mitigate the influence of quantization error on filtering performance. Incorporating the stochastic communication protocol and uniform quantization mechanism, this paper proposes a set-membership filter design framework for the two-dimensional shift-varying systems with unknown-but-bounded noises. Sufficient conditions are derived for the existence of desired set-membership filter by utilizing double mathematical induction, such that the estimation error resides within the ellipsoidal set. Moreover, the optimal filtering algorithm is given by minimizing the ellipsoidal constraints. Finally, several examples are provided to illustrate the effectiveness of the proposed filter design algorithm.

Quantized recursive filtering for networked systems with stochastic transmission delays

This paper investigates the recursive filtering problem for a class of networked systems subject to the uniform quantization effects and stochastic transmission delays. The system output is quantized according to a uniform quantization mechanism, and then sent to the remote filter via a communication network undergoing stochastic transmission delays (which are modeled by a sequence of independent and identically distributed variables). To deal with the stochastic transmission delays, an indicator function is delicately designed to ensure that the filtering process is implemented based on the quantized measurement with the newest timestamp available for the filter. With the aid of the indicator function, a free-delay system is obtained by using the augmented system method. The aim of this paper is to design a Kalman-type filter for the augmented system such that an upper bound of the filtering error covariance is guaranteed and minimized. With the aid of the stochastic analysis method, the desired upper bound of the filtering error covariance is derived by recursively solving two Riccati-like difference equations. Then, the upper bound is minimized by properly selecting the filter parameters. Finally, a numerical example is provided to illustrate the validity of the developed filtering scheme.

Recursive Fault Estimation With Energy Harvesting Sensors and Uniform Quantization Effects

In this letter, the recursive fault estimation issue is considered for nonlinear time-varying systems subject to the effects induced by energy harvesting sensors and uniform quantization. Based on the energy harvesting mechanism and stochastic distribution of the absorbed energy, the real-time occurrence probability of missing measurements is calculated recursively. This research intends to develop a recursive estimator for the considered nonlinear time-varying system with energy harvesting sensors, such that, under uniform quantization effects, the state and fault can be jointly estimated. By adopting the induction approach, an upper bound is firstly calculated for the estimation error covariances (EECs) of the state and fault. Then, the value of the time-varying estimator parameter is computed through minimizing such calculated upper bound. In the end, an illustrative example is presented to verify the availability of the developed fault estimation method.

Robust ellipsoidal set-membership fault estimation for time-varying systems with uniform quantization effects over sensor networks.

This article is concerned with the robust set-membership fault estimation problem for a class of uncertain discrete time-varying systems over sensor networks. The system measurements are subject to the uniform quantization which results in the unknown-but-bounded noises. Attention is focused on the design of a set-membership fault estimator such that, in the simultaneous presence of uncertain parameters, unknown-but-bounded noises and uniform quantization effects, the estimation errors are confifined to a certain ellipsoidal region. By using the mathematical induction, a suffificient condition is derived for the existence of the desired fault estimator at each time step in terms of a set of recursive matrix inequalities. Moreover, an optimization problem is formulated by minimizing the ellipsoid of the estimation error. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed fault estimator design scheme.

Ultimately Bounded Filtering for Time-Delayed Nonlinear Stochastic Systems with Uniform Quantizations under Random Access Protocol.

This paper investigates the ultimately bounded filtering problem for a kind of time-delay nonlinear stochastic systems with random access protocol (RAP) and uniform quantization effects (UQEs). In order to reduce the occurrence of data conflicts, the RAP is employed to regulate the information transmissions over the shared communication channel. The scheduling behavior of the RAP is characterized by a Markov chain with known transition probabilities. On the other hand, the measurement outputs are quantized by the uniform quantizer before being transmitted via the communication channel. The objective of this paper is to devise a nonlinear filter such that, in the simultaneous presence of RAP and UQEs, the filtering error dynamics is exponentially ultimately bounded in mean square (EUBMS). By resorting to the stochastic analysis technique and the Lyapunov stability theory, sufficient conditions are obtained under which the desired nonlinear filter exists, and then the filter design algorithm is presented. At last, two simulation examples are given to validate the proposed filtering strategy.

Non-fragile consensus control for nonlinear multi-agent systems with uniform quantizations and deception attacks via output feedback approach

In this paper, we handle the non-fragile consensus control problem for a class of discrete time-varying nonlinear multi-agent systems with uniform quantization and randomly occurring deception attacks. The quantization error is described by a noise distributed uniformly in certain interval, and the phenomenon of the randomly occurring deception attacks is depicted by the Bernoulli distributed random variables with known probabilities. Here, the measurement output utilized in the controller side is not only from a single agent itself, but also from its adjacent agents, where the corresponding transmissions are carried out under a given topology. In particular, the controller gain perturbations are characterized by the multiplicative noises. We focus on the design of non-fragile time-varying output feedback controller such that, when the randomly occurring deception attacks, uniform quantization effects as well as controller gain perturbations exist simultaneously, and the desired consensus performance is guaranteed by designing the controller parameters. Accordingly, a sufficient condition is derived to ensure the existence of the desired control scheme, where the feasibility of conducted problem can be tested by solving a set of matrix inequalities. Moreover, the optimal consensus performance is addressed by employing an optimization problem. Finally, we utilize the simulations to illustrate the feasibility of the proposed output feedback control strategy.

The Effect of Uniform Quantization on Parameter Estimation of Compound Distributions

This letter considers the problem of how uniform quantization affects the maximum likelihood estimation of the parameters of a probability density function representing a compound distribution. As a measure of the information loss due to quantization, the loss of Fisher information is used. The main contribution of this letter is the approximation which characterizes the asymptotic behavior of the loss allowing a significant reduction of the computational complexity. We further investigate how to choose the quantization interval to guarantee a predefined loss of Fisher information. An extensive numerical simulation demonstrates the efficiency of the approximation.

Ultimate Boundedness Control for Networked Systems With Try-Once-Discard Protocol and Uniform Quantization Effects

This paper is concerned with the ultimate boundedness control problem for a class of networked nonlinear systems subject to the try-once-discard (TOD) protocol scheduling and uniform quantization effects. To prevent the transmission data from collisions, the communication between sensor nodes and the controller is implemented via a constrained communication channel, where only one sensor node is permitted to transmit data at each time instant. The TOD protocol is utilized to regulate the signal transmission over the communication network under which the scheduling behavior is described by a special switching function. On the other hand, the uniform quantization effects of the network are characterized by a round function (i.e., the nearest integer function). The purpose of the addressed problem is to design an observer-based controller for the networked nonlinear systems such that, in the presence of TOD protocol and uniform quantization effects, the closed-loop system is ultimately bounded and the controlled output is locally minimized. Sufficient conditions are established to guarantee the ultimate boundedness of the dynamics of the closed-loop system in mean square by applying the stochastic analysis approach. Furthermore, the desired controller gains are derived by solving a convex optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design scheme.

Set-membership state estimation subject to uniform quantization effects and communication constraints

In this paper, the set-membership state estimation problem is investigated for a class of discrete time-varying nonlinear systems with uniform quantization effects under the Maximum-Error-First (MEF) protocol. The uncertainty parameter is introduced to characterize the errors resulting from the uniform quantization. Meanwhile, a general sector-like nonlinear function is utilized to model the system dynamics. For the MEF protocol, the transmission judgment conditions with regard to relative errors and absolute errors are, respectively, considered to determine which sensor node is granted the access right. The main goal of this paper is to design the set-membership state estimator, for all admissible uniform quantization effects, nonlinearities and bounded noises, such that the estimated ellipsoid containing all possible true states is recursively derived. Then, the performance is quantified by solving the optimization problem with some linear matrix inequality constraints, and several sufficient conditions are established to obtain the suboptimal ellipsoids and the corresponding estimator gains. In the end, via a simulation example, the efficiency of our proposed estimator design scheme is explored.

Distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks

This paper is concerned with the distributed recursive filtering problem for a class of discrete time-delayed stochastic systems subject to both uniform quantization and deception attack effects on the measurement outputs. The target plant is disturbed by the multiplicative as well as additive white noises. A novel distributed filter is designed where the available innovations are from not only the individual sensor but also its neighboring ones according to the given topology. Attention is focused on the design of a distributed recursive filter such that, in the simultaneous presence of time-delays, deception attacks and uniform quantization effects, an upper bound for the filtering error covariance is guaranteed and subsequently minimized by properly designing the filter parameters via a gradient-based method at each sampling instant. Furthermore, by utilizing the mathematical induction, a sufficient condition is established to ensure the asymptotic boundedness of the sequence of the error covariance. Finally, a simulation example is utilized to illustrate the usefulness of the proposed design scheme of distributed filters.

Output-Feedback Control for Nonlinear Stochastic Systems With Successive Packet Dropouts and Uniform Quantization Effects

In this paper, the dynamic output-feedback control problem is studied for a class of discrete-time nonlinear stochastic systems with successive packet dropouts and uniform quantization effects. The stochastic system under investigation involves state-, control-, and disturbance-dependent noises (also called ( ${x}$ , ${u}$ , ${v}$ )-dependent noises) that bring in substantial difficulties in the stability analysis. The phenomenon of successive packet dropouts is governed by a binary switching random sequence. The measurement output is subject to the uniform quantization which results in the norm-bounded disturbances, and the concept of input-to-state stability in probability is introduced to deal with this kind of disturbances. In virtue of intensive stochastic analysis, several sufficient conditions are established to guarantee that the closed-loop system is input-to-state stable in probability under the effects of probabilistic packet dropouts as well as uniform quantizations. As an easy consequence, the design problem with linear output-feedback controllers is discussed for the benefits of practical applications and some simplified conditions are derived. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.

Statistical theory of quantization

The effect of uniform quantization can often be modeled by an additive noise that is uniformly distributed, uncorrelated with the input signal, and has a white spectrum. This paper surveys the theory behind this model, and discusses the conditions of its validity. The application of the model to floating-point quantization is demonstrated.