Networked Multi-sensor Systems Research Articles

Robust fusion filter for networked uncertain descriptor systems with colored noise and cyber-attacks

The robust fusion filtering problem of multi-sensor networked uncertain descriptor systems (NUDSs) with colored noise, uncertain noise variances and cyber-attacks is investigated. During data transmission in unreliable communication networks, the data can be maliciously attacked by attackers. In other words, the local filters (LFs) may receive false data or may not receive data because of the cyber-attacks. By adopting the singular value decomposition (SVD) method, the original NUDSs can be converted into two reduced-order subsystems with uncertain correlated fictitious white noises, and the cyber-attacks are transformed into the fictitious noises. Cross-covariance matrices between local filtering errors are derived. The robust LFs are obtained according to the minimax robust estimation principle. Under the linear unbiased minimum variance criterion, three weighted fusion algorithms are applied to fuse the LFs. For all allowable uncertainties of noise variances and cyber-attacks, the minimal upper bounds of covariance matrices of the local and distributed fusion filters are guaranteed. The proof of their robustness is established through the minimax estimation principle and Lyapunov equation method. Finally, the correctness and effectiveness of the proposed algorithms are verified by a circuit system example.

Distributed nonlinear fusion filtering for multi-sensor networked systems with random varying parameter matrix and missing measurements

This paper is concerned with the distributed fusion filtering algorithm design problem for multi-sensor nonlinear networked systems (MSNNSs) subject to multiplicative noises, random varying parameter matrix and missing measurements (MMs). In particular, we utilize the Bernoulli random variable with certain statistical features to describe and characterize the MMs phenomenon. By introduce a fictitious noise, the effects from process noise as well as random varying parameter matrix are addressed and a new nonlinear stochastic networked system is obtained. The primary purpose of this paper is to develop a novel fusion filtering scheme of the distributed way and provide the corresponding boundedness evaluation criterion. Firstly, specific upper bounds of filtering error covariance (FEC) are identified and locally minimized at each sampling instant. Subsequently, based on the obtained local filters, a distributed fusion filtering algorithm is designed via adopting the inverse covariance intersection (ICI) fusion idea. Furthermore, the analysis with respect to the upper bound of local FEC is discussed and examined by proposing a sufficient condition under certain constraints regarding the related parameters. Eventually, with the help of the simulation experiments, the usefulness of the proposed fusion filtering algorithm is illustrated.

Distributed fusion filtering for multi-sensor nonlinear networked systems with multiple fading measurements via stochastic communication protocol

This paper studies the distributed fusion filtering (DFF) issue for a class of nonlinear delayed multi-sensor networked systems (MSNSs) subject to multiple fading measurements (MFMs) under stochastic communication protocol (SCP). The phenomenon of MFMs occurs randomly in the network communication channels and is characterized by a diagonal matrix with certain statistical information. In order to decrease the overload of communication network and save network resources, the SCP that can regulate the information transmission between sensors and estimators is adopted. The primary aim of the tackled problem is to develop the DFF method for nonlinear delayed MSNSs in the presence of MFMs and SCP based on the inverse covariance intersection fusion rule. In addition, the local upper bound (UB) of the filtering error covariance (FEC) is derived and minimized by means of suitably designing the local filter gain. Moreover, the boundedness analysis regarding the local UB is proposed with corresponding theoretical proof. Finally, two simulation examples with comparative illustrations are given to display the usefulness and feasibility of the derived theoretical results.

Distributed Consensus Estimation for Networked Multi-Sensor Systems under Hybrid Attacks and Missing Measurements.

Cyber-security research on networked multi-sensor systems is crucial due to the vulnerability to various types of cyberattacks. For the development of effective defense measures, attention is required to gain insight into the complex characteristics and behaviors of cyber attacks from the attacker's perspective. This paper aims to tackle the problem of distributed consensus estimation for networked multi-sensor systems subject to hybrid attacks and missing measurements. To account for both random denial of service (DoS) attacks and false data injection (FDI) attacks, a hybrid attack model on the estimator-to-estimator communication channel is presented. The characteristics of missing measurements are defined by random variables that satisfy the Bernoulli distribution. Then a modified consensus-based distributed estimator, integrated with the characteristics of hybrid attacks and missing measurements, is presented. For reducing the computational complexity of the optimal distributed estimation method, a scalable suboptimal distributed consensus estimator is designed. Sufficient conditions are further provided for guaranteeing the stability of the proposed suboptimal distributed estimator. Finally, a simulation experiment on aircraft tracking is executed to validate the effectiveness and feasibility of the proposed algorithm.

Identification and distributed fusion filter for multi-sensor networked systems with stochastic deception attacks

In the multi-sensor networked systems, each sensor produces its local state estimate based on its own observations, and then sends it to a fusion center (FC) for fusion estimation. During transmitting local state estimates to the fusion center, the data may suffer from stochastic deception attacks from malicious attackers, where the probabilities of attacks and the variances of attack noises are unknown. Using a correlation function method (CFM), the probabilities of attacks and the variances of attack noises in individual channels are identified in parallel. The possibly attacked local state estimate is filtered to reproduce local state estimate in the FC. Using the matrix-weighted fusion algorithm in the linear unbiased minimum variance (LUMV) criterion, a distributed fusion filter is performed based on the reproduced local state estimates. A simulation example illustrates the validity of the algorithms.

Distributed filtering for multi-sensor networked systems with stochastic communication protocol and correlated noises

In multi-sensor networked systems, to solve data conflicts caused by limited bandwidths during measurement data exchange among sensors, a stochastic communication protocol scheduling is employed to ensure that each sensor can only receive one component of measurement vector from neighbor nodes at each instant. The measurement components selected for communication at each instant are indicated by a set of random variables. When each sensor knows which component of the measurement vector from each of its neighbor nodes is passed at each instant, an optimal distributed Kalman filter (ODKF) where both estimator and gain rely on values of random variables is designed in the linear minimum variance sense. To reduce the online computational burden, a suboptimal DKF (SDKF) where the filtering gain relies on probabilities of random variables is designed and its steady-state property is analyzed. When each sensor doesn't know which component of the measurement vector is passed at each instant, a probability-dependent DKF (PDKF) where both estimator and gain rely on probabilities of random variables is designed and its steady-state property is analyzed. Finally, the performances of the proposed three DKF algorithms are compared. Two simulation examples verify the effectiveness of algorithms.

Distributed variational Bayesian adaptive filtering for randomly delayed measurements and unknown noise statistics in multi-sensor networked systems

To deal with randomly delayed measurements and unknown noise statistics in multi-sensor networked systems, a distributed variational Bayesian adaptive cubature Kalman filtering algorithm (DVB_ACKF) is presented in this paper. To compensate for the effects induced by randomly delayed measurements, a refined measurement reorganization method is designed via a two-stage estimation strategy. Specifically, we first estimate the time delay step. The measurements are then rearranged based on the estimated results from the first stage. Then, a novel noise estimator with the sliding-window and variational Bayesian method is developed to estimate the mean and covariance of the unknown noise. The network topology attribute and measurement accuracy have been combined to eliminate the distributed fusion error. The tuning parameter and forgetting factor as well as their bounds are analyzed. Furthermore, numerical simulations are carried out to verify the superior performance of the developed algorithm.

Robust weighted fusion Kalman estimators for systems with uncertain noise variances, multiplicative noises, missing measurements, packets dropouts and two‐step random measurement delays

AbstractFor multisensor networked systems with uncertain noise variances, multiplicative noises and multiple networked‐induced uncertainties including missing measurements, packets dropouts and two‐step random measurement delays, the robust weighted fusion estimation problem is addressed in this article. More precisely, the system noise variances are assumed to be uncertain but bounded, the other four uncertainties are compensated into fictitious white noise by the proposed model transformation method, which includes the augmented method and extended fictitious noise technique. Then local multi‐model system is obtained, for which robust local Kalman estimator is obtained based on the minimax robust estimation principle and unified estimation method. Based on this, the six robust weighted fusion time‐varying Kalman estimators are presented in a unified form, which include robust weighted fusers weighted by matrices, diagonal, scalars, and a robust covariance intersection (CI) fuser and two fast CI (FCI) fusers. The robustness proving method, including the extended Lyapunov equation approach with two kinds of generalized Lyapunov equations, non‐negative matrix factorization and elementary transformation of matrix, is presented to prove that the actual estimation error variances are guaranteed to have minimal upper bounds for all admissible uncertainties. The accuracy relations are proved. Further, the robust local and fused steady‐state Kalman estimators are presented. Finally, a simulation example applied to Internet‐based three tank water system is given to demonstrate effectiveness of the proposed results.

Distributed resilient fusion filtering for nonlinear systems with multiple missing measurements via dynamic event-triggered mechanism

This paper investigates the distributed resilient fusion filtering (DRFF) issue under inverse covariance intersection (ICI) fusion criterion and dynamic event-triggered mechanisms (DETMs), where the physical plant is described by stochastic nonlinear multi-sensor networked systems (MSNSs) with time-varying system parameters and multiple missing measurements (MMMs). The measurements from various sensor nodes to the fusion center may undergo the missing data, where this phenomenon is depicted by means of random variables governed by certain statistical principles. In addition, the DETM is adopted to regulate the communication process from each sensor node to fusion center, which can alleviate the network transmission situations with communication overload and energy consumption limitation. The purpose of the addressed issue is to construct a set of local resilient filters (LRFs) for stochastic nonlinear MSNSs with MMMs via the DETM, which can guarantee that the minimized upper bounds are derived and the desirable filter gain with easy-to-implementation form is given. Subsequently, via the obtained LRFs, a unified framework of the DRFF approach is formulated through using the ICI fusion criterion. In addition, the monotonicity analysis of the obtained upper bound in regard to the triggered parameter is examined by providing rigorous theoretical proof. Finally, the simulations with comparison experiment are provided to illustrate the validity of presented DRFF technique.

Protocol-Based Optimal Stealthy Data-Injection Attacks via Compromised Sensors in Cyber-Physical Systems

This article concentrates on designing a strictly stealthy attack strategy from the adversarial perspective against the multisensor cyber-physical systems (CPSs) under the round-robin protocol (RRP). The aim is to maximize the attack performance and remain strictly stealthy at the same time. Different from the existing attacks against the single-sensor application scenario, we propose a stealthy attack strategy for multisensor networked systems. In addition, due to the scheduling effects of the RRP, only incomplete transmitted data can be corrupted at each time step. Thus, a novel protocol-based attack model is developed, and then the corrupted error covariance at the remote side is derived to quantify the attack performance. Next, a convex optimization problem is formulated to solve the optimal attack parameters, which leads to the worst filtering performance. Moreover, the analytical expression of the optimal attack parameters is presented and proved. Finally, the experiments on a permanent magnet synchronous machine monitoring system are conducted to verify our results.

Distributed H∞ fusion filtering for multi-sensor networked systems with DoS attacks and sensor saturations

The design problem of a distributed H∞ fusion filter is investigated for multi-sensor networked systems subject to denial of service (DoS) attacks and sensor saturations. The prediction compensation strategy is adopted to solve the problem of packet losses caused by DoS attacks. The local H∞ filter based on single-sensor measurements is obtained via a linear matrix inequality (LMI) method such that the local filtering error system is exponentially stable in the mean square sense and possesses a specified H∞ performance. According to the different H∞ performance levels of local filters, a distributed scalar-weighted fusion filter is constructed. The proposed distributed fusion filter is low complex in computation and has better H∞ performance than the average of all local filters. Simulation studies verify the effectiveness of the proposed algorithms.

Zonotopic multi-sensor fusion estimation with mixed delays under try-once-discard protocol: A set-membership framework

In this paper, the fusion estimation problem is investigated for a class of multi-sensor networked systems with unknown-but-bounded noises and mixed time-delays under try-once-discard protocols (TODPs). The measurements of multiple sensor nodes are sent to the remote fusion center through individual network channels, where the TODP is implemented in each channel to schedule the signal transmissions for the purpose of avoiding data collisions. To fuse the information collected from all channels, a sequential estimator is proposed whose estimator parameters are designed such that the estimation error (after each measurement update) is restrained into a zonotope with minimum F-radius at each moment. First, by using the properties of zonotopes, desired zonotopes are obtained that contain the estimation errors, and the F-radii of these zonotopes are subsequently minimized by appropriately designing the estimator parameters. It is shown that, under the proposed zonotopes-based fusion rule, the designed sequential estimator leads to the same estimation accuracy as that of the widely utilized parallel estimator. Finally, an illustrative example is provided to verify the validity of the developed fusion estimation method.

Fusion steady‐state robust filtering for uncertain multisensor networked systems with application to autoregressive moving average signal estimates

AbstractThis article is concerned with the centralized fusion (CF) robust steady‐state Kalman filtering problem for a class of multisensor networked systems with mixed uncertainties including state‐dependent and noise‐dependent multiplicative noises, missing measurements, packet dropouts, and uncertain noise variances. By using a model transformation approach, the initial multisensor system under study is transformed into a multi‐model multisensor system only with uncertain noise variances. By introducing an augmented state vector, the CF system is obtained. In the light of the minimax robust estimation method, and based on the worst‐case fusion system with conservative upper bounds of uncertain noise variances, the CF robust steady‐state Kalman estimators (predictor, filter, and smoother) are proposed in a unified form. By means of the permutation matrices and Lyapunov equation method, the robustness of CF estimators is proved. The accuracy relations among the robust local and fusion steady‐state estimators are proved. An example applied to autoregressive moving average signal estimation is put forward, and the robust CF steady‐state signal estimators are proposed. Simulation experiment shows the correctness of the proposed approach.

Recursive distributed fusion estimation for multi-sensor systems with missing measurements, multiple random transmission delays and packet losses

This paper is concerned with the recursive distributed fusion estimation problems for networked multi-sensor systems with missing measurements, multiple random transmission delays, and packet losses. There exist missing measurements in the observation equations due to unpredictable sensor faults. Moreover, there are often random delays and losses during data transmissions from sensors to the fusion center due to limited communication bandwidths of the network. The Kalman-like recursive distributed fusion predictor and filter in the linear unbiased minimum variance (LUMV) sense are, respectively presented based on local estimates, cross-covariance matrices between local estimates, and cross-covariance matrices between the prior fusion estimate and local estimates. The stability and steady-state property of the proposed algorithms are analyzed. Their estimation accuracy is better than that of local estimates and distributed fusion estimates by matrix-weighting local estimates. A simulation example shows the effectiveness of the proposed algorithms.

Distributed resilient fusion filtering for nonlinear systems with random sensor delay under round-robin protocol

In this paper, we address the distributed resilient fusion filtering (DRFF) problem for a class of nonlinear multi-sensor networked systems (MSNSs) with random sensor delay (RSD) under round-robin protocol (RRP). The RSD is depicted by the Bernoulli random variable with known occurrence probability. In order to relieve the network congestion, the RRP that can deal with information overload issue of the transmission process from sensor to the estimator is utilised. The major objective of this paper is that the resilient fusion filter is designed for nonlinear MSNSs with RSD and RRP in the light of the inverse covariance intersection approach, where the local upper bound regarding the filtering error covariance is obtained and then minimised by suitably exploiting the local filter gain. Finally, a simulation example that can show the validity of the provided DRFF algorithm is presented.

Centralized fusion robust filtering for networked uncertain systems with colored noises, one-step random delay, and packet dropouts

This paper studies the estimation problem for multisensor networked systems with mixed uncertainties, which include colored noises, same multiplicative noises in system parameter matrices, uncertain noise variances, as well as the one-step random delay (OSRD) and packet dropouts (PDs). This study utilizes the centralized fusion (CF) algorithm to combing all information received by each sensor, which improve the accuracy of the estimation. By using the augmentation method, de-randomization method and fictitious noise techniques, the original uncertain system is transformed into an augment model with only uncertain noise variances. Then, for all uncertainties within the allowable range, the robust CF steady-state Kalman estimators (predictor, filter, and smoother) are presented based on the worst-case CF system, in light of the minimax robust estimation principle. To demonstrate the robustness of the proposed CF estimators, the non-negative definite matrix decomposition method and Lyapunov equation approach are employed. It is proved that the robust accuracy of CF estimator is higher than that of each local estimator. Finally, the simulation example applied to the uninterruptible power system (UPS) with colored noises and multiple uncertainties illustrates the effectiveness of the proposed CF robust estimation algorithm.

Distributed H$\infty$-Constraint Robust Estimator for Multi-Sensor Networked Hybrid Uncertain Systems

Due to the complex communication channel environment, uncertainties, including random measurement delays, missing measurements and uncertain measurement noise variances, often exist in multi-sensor networked hybrid uncertain systems. These uncertainties will lead to poor accuracy and robustness for traditional information fusion methods. Hence, this paper presents a distributed robust estimator based on the H constraint to solve the mentioned issues in sensor networked systems. The nonlinear pseudomeasurement model is first constructed with Bernoulli distributed random variables to describe the mentioned uncertainties in the communication channels. Then, a sufficient condition with a local optimal upper bound on estimation error covariance is derived rigorously with respect to the robustness definition, which is based on the H constraint inequality to improve the robustness of state estimation. Furthermore, the proposed estimator is proven to be stable through boundedness analysis for the upper bound matrix. The numerical simulation and target tracking experiment are finally applied to evaluate the effectiveness of the novel fusion estimator.

Robust integrated covariance intersection fusion Kalman estimators for networked systems with a unified measurement model including five uncertainties

For networked multisensor systems (NMSs), a soft measurement model with five uncertainties is presented, which can be viewed as a “soft sensor” such that the measurements received by estimators can be obtained via the computations of this model. A novel “soft sensor” concept is presented. Three new approaches are presented, which include a fictitious white noises approach with compensating random uncertainties, an extended Lyapunov equation approach with three kinds of the Lyapunov equations, and a universal integrated covariance intersection (ICI) fusion approach with integrating local estimators and their cross-covariances. Applying them, the universal ICI and two fast ICI (FICI) fusion time-varying and steady-state minimax robust Kalman estimators (predictor, filter and smoother) are presented in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. They improve the robust accuracies of the original covariance intersection (CI) and fast CI(FCI) fusers, and overcome their drawback to require known local estimators and their conservative variances. Their robustness, accuracy relations, stability, steady-state property, and three modes of convergence are proved. The proposed new concept, approaches and results constitute a new methodology, a universal robust fusion Kalman filtering theory and a new filtering stability theory. A simulation example applied to the vehicle suspension system shows their effectiveness and applicability.

Event-Triggered Distributed Fusion Estimation of Networked Multisensor Systems With Limited Information

In this paper, the event-triggered distributed Kalman filtering problem is considered for a class of networked multisensor fusion systems (NMFSs) under sensor energy and network bandwidth constraint. A general event-triggered scheme is employed for the NMFSs to reduce the energy consumption and communication burden between the sensor nodes and fusion center (FC) under the communication bandwidth constraints. Local estimation information is allowed to transmit partial components to FC over the network with limited bandwidth. A group of binary variables are introduced to describe the component transmitting process when the triggering condition is violated. Furthermore, the untransmitted local estimation signals are compensated by the previous transmitted one, and a recursively event-triggered distributed fusion Kalman filter in the linear minimum mean square error sense is designed from the restructured local unbiased estimators. At each time instant, a set of binary variables are determined by an optimal judgement criterion. Finally, a simulation example is provided to illustrate the effectiveness and advantages of the proposed methods.

Robust fusion steady‐state estimators for networked stochastic uncertain systems with packet dropouts and missing measurements

AbstractIn this article, the robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties. The uncertainties include state‐dependent and noise‐dependent multiplicative noises, missing measurements, packet dropouts, and uncertain noise variances, the phenomena of missing measurements and packet dropouts occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, de‐randomization approach and fictitious noise approach, the original multisensor system under study is converted into a multi‐model multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of non‐negative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive moving average (ARMA) signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.