Distributed State Estimation Problem Research Articles

Finite-time cooperative tracking for high-maneuvering aerial target with sensor network

The finite-time distributed state estimation (DSE) problems based on sensor network for discrete-time nonlinear systems are considered in this paper. Considering the uncertainty of the target maneuvers, the interactive multiple models (IMM) based distributed estimation framework is established by local filter and consensus fusion. In the proposed distributed algorithm, partial of the output of the system can be collected by some sensors and the sensor network is supposed to be collectively observable. According to the consensus protocol, the final estimate results are obtained by fusing local estimate results of each sensor after the consensus fusion stage. The distributed estimate results can be obtained with finite-time when the consensus fusion step is larger than the diameter of the network, and the convergence rate of estimate error of the proposed distributed estimate algorithm can be guaranteed. Besides, the existence of the lower and upper bounds of the error covariance matrix are proved with some necessary assumptions. Finally, numerical simulation example is given for tracking the target with different maneuvers.

Stealthy attacks against distributed state estimation of stochastic multi-agent systems under composite attack detection mechanisms

This paper is concerned with the security problem of distributed state estimation for stochastic multi-agent systems (MASs) under directed topology. First, in the absence of attacks, an optimal distributed filter is proposed to reconstruct the states of MASs by minimizing the mean square error, which makes full use of the measurable local output information and relative state estimates of agents. Moreover, instead of using a single detection mechanism to measure the stealthiness of attacks, based on the structure of the derived filter, a composite attack detection mechanism capable of simultaneously detecting anomalies in the sensor channels of the agents themselves and the network topologies between different agents is utilized in this paper. Then, from the perspective of potential adversaries, two stealthy attack strategies are established through a joint design of sensor and topology attacks, enabling attackers to fulfill diverse attack objectives while evading the given composite detection mechanisms. Finally, simulation results are provided to verify the availability of the designed filter and attack generation schemes.

Distributed consensus filtering in sensor networks considering correlated estimation errors

This paper focuses on the distributed state estimation (DSE) problem in sensor networks through the application of a consensus-based methodology. In practical scenarios, the estimation errors within the sensor network exhibit inherent correlation, primarily arising from the consideration of same prior estimate and process noise in a distributed estimation system. However, prevailing distributed approaches, particularly those embedded within consensus-based DSE frameworks, simply assume independence among estimation errors or utilize a suboptimal strategy that neglect cross-covariance matrix, which may lead to a degraded estimation results. To address this limitation, we propose the fusion algorithm Weighted Average Consensus considering Correlated Estimates Errors, abbreviated as WACCEE. The algorithm improves DSE performance by integrating the correlation among local estimation errors as indicated by the cross-covariance matrix into the fusion process. Furthermore, we prove that the proposed WACCEE fusion algorithm exhibits consensus. Additionally, the stability of the WACCEE filters is guaranteed through an analysis of mean-square exponential boundedness of the estimation error using stochastic stability theory. Finally, the effectiveness of the proposed algorithm substantiated by its application to a target tracking case study and a connected undirected sensor network.

Collaborative Parameter Estimation of Multiple Unmanned Surface Vessels: A Robust Distributed Estimator-Based Approach

In this paper, the collaborative parameter estimation of multiple unmanned surface vessels (USVs) with model structure uncertainties is studied. The considered parameter estimation problem is first converted into a distributed state and parameter joint estimation problem. Then, the robust distributed estimator is constructed to handle the inevitable model structure uncertainties, and the upper bounds of prediction and estimation error covariance matrices are derived respectively. Additionally, the upper bound of the estimation error covariance matrix is minimized by designing appropriate estimator gains. Finally, the advantages of the proposed distributed parameter estimation approach from the perspectives of information interaction and consideration of model structure uncertainties are verified via simulations and practical experiments.

Distributed State Estimation Under Jointly Connected Switching Networks: Continuous-Time Linear Systems and Discrete-Time Linear Systems

In this paper, we address the distributed state estimation problem for both continuous-time linear time-invariant (LTI) systems and discrete-time LTI systems under switching networks. The observed system is jointly observable, i.e., each agent can only access a part of the measurement output of the observed system and cannot recover the full state by itself. The full state estimation has to be achieved by network communication of neighboring agents. In contrast to existing works, the salient feature of this work is that the developed approach can deal with the jointly connected switching network and thus is more resilient to unreliable communication. First, we propose a new observability decomposition method for linear systems in modal canonical form. Then, we design distributed observers for both the continuous-time and the discrete-time system. Based on the common Lyapunov function approach, we show that the switched estimation error system is asymptotically stable and thus, the full state estimation can be achieved under jointly connected switching networks.

Distributed State Estimation for Linear Systems in Networks With Antagonistic Interactions.

This article deals with the distributed state estimation problem for linear systems in networks with cooperative interactions and antagonistic interactions, where the cooperative interactions and the antagonistic interactions are characterized by the positive weights and the negative weights, respectively. Due to the coexistence of the cooperative interactions and the antagonistic interactions, the existing methods based on the non-negatively weighted graph become not applicable. First, a partition method of the nodes and a decomposition form of the system matrices are introduced. Then a new form of distributed observers is proposed in the network with cooperative interactions and antagonistic interactions. Necessary and sufficient conditions, which guarantee the existence of proposed distributed observers, are presented. In particular, when the communication network is cooperative, the proposed method is suitable for two cases, that is, the nodes in each independent strongly connected component are jointly detectable, or each node is jointly detectable with its neighbors. Finally, three examples are simulated to illustrate the effectiveness of the proposed methods.

Split-spectrum based distributed state estimation for linear systems

This paper studies a distributed state estimation problem for both continuous- and discrete-time linear systems. A simply structured distributed estimator {comprising interconnected local estimators} is first described for estimating the state of a continuous and multi-channel linear system whose sensed outputs are distributed across a fixed multi-agent network. The estimator is then extended to non-stationary networks whose graphs switch according to a switching signal. The estimator is guaranteed to solve the problem, provided a network-widely shared high gain condition achieving a form of spectrum separation is satisfied. As an alternative to sharing a common gain across the network, a fully distributed version of the estimator is also studied in which each agent adaptively adjusts a local gain, though the practicality of this approach is subject to a robustness issue common to adaptive control. A discrete-time version of the distributed state estimation problem is also studied, and a corresponding estimator based again on spectrum separation, but not high gain, is proposed for time-varying networks. For each scenario, it is explained how to construct the estimator so that the state estimation errors in the local estimators all converge to zero exponentially fast at a fixed but arbitrarily chosen rate, provided the network’s graph is strongly connected for all time. The proposed estimators are inherently resilient to abrupt changes in the number of agents and communication links in the inter-agent communication graph upon which the algorithms depend, provided the network is redundantly strongly connected and redundantly jointly observable.

Covariance intersection based event-triggered distributed state estimation under channel independent DoS attacks

This paper investigates the event-triggered distributed state estimation problem for a class of discrete time-varying systems in the presence of denial-of-service (DoS) attacks, where each sensor node selectively shares its local information with neighbors. In contrast to the previous studies where the DoS attacks are considered on sensor-to-filter channels, we deal with the situation that DoS attacks jam each filter-to-filter communication channel independently. To reduce the communication rate and save network resources, a novel event-triggered communication strategy is presented that takes into account the impact of DoS attacks and is specialized for each communication channel. Based on the covariance intersection fusion rule and weight rearrangement method, a distributed state estimation algorithm is proposed. Further, the consistency of estimates and mean-square boundedness of estimation errors are proved under system collective observability and some other mild assumptions. Lastly, a numerical simulation is conducted to demonstrate the developed results and the effectiveness of the proposed algorithm.

Towards invariant extended Kalman filter-based resilient distributed state estimation for moving robots over mobile sensor networks under deception attacks

This paper studies the resilient distributed state estimation problem for moving robots over wireless sensor networks (WSNs) under deception attacks. The state of a moving robot consists of its position and orientation, evolving according to a nonlinear motion model, and the WSNs are mobile. These settings make the problem more challenging than most existing researches on the resilient distributed state estimation which recover stationary or linear states by static WSNs. To achieve the resilient distributed state estimation for the robot over a mobile sensor network (MSN), we propose a novel invariant extended Kalman filter-based resilient distributed state estimation approach. Specifically, based on the mappings between a Lie group and its Lie algebra, we first define a new type of estimation errors and linearize it. Utilizing the linearization results, the calculation of the current prior estimate based on the last posterior one is achieved by each sensor, which avoids the estimation biases induced by the computation of Jacobian matrices. Then, sensors in the MSN fuse the local prior estimates of their neighbors according to the covariance intersection fusion rule, obtaining more accurate estimates than their local prior ones. Finally, measurements collected by the sensors are used to correct the estimates. In the correction process, an adaptive gain is designed for each sensor to restrict the negative effects of the attacks on the estimates, which is crucial for the accomplishment of the resilient estimation task. We illustrate the performance of the approach by convergence analysis of the estimation errors based on the boundedness of the covariance matrix estimates computed in the state estimation process and verify it by simulation and experimental results.

Distributed Exponential State Estimation for Discrete-Time Linear Systems Over Jointly Connected Switching Networks

The existing results on distributed state estimation problems for discrete-time linear systems were obtained over connected static networks, or every-time connected switching networks by a two-time-scale design. This paper further studies the same problem over jointly connected switching networks which can be disconnected at every time instant by a single-time-scale distributed design. Since the existing distributed designs critically rely on the connectedness assumption on the networks and thus may not apply to jointly connected switching networks, we have to modify the local observers and develop a novel approach which makes use of the uniform complete observability property for a discrete-time time-varying system. Additionally, we establish two exponential stability results for two classes of discrete-time switched systems, which may be of independent interest.

Distributed exponential state estimation of linear systems over jointly connected switching networks

Recently, the distributed state estimation problem for continuous-time linear systems over jointly connected switching networks was solved. Due to the use of the generalized Barbalat’s Lemma, it can only show that the estimation errors asymptotically converge to the origin. By a completely different approach, this paper further studies the distributed state estimation problem with two new features. First, the asymptotic convergence is strengthened to the exponential convergence. This strengthened result not only offers a guaranteed convergence rate, but also renders the error system total stability and thus the capability to withstand small disturbances. Second, the coupling gains of our local observers can be different from each other and thus offers greater design flexibility, while the coupling gains in the existing result were required to be identical. These two new features are achieved by establishing exponential stability for two classes of linear time-varying systems, which may have other applications.

Distributed observer for LTI systems under stochastic impulsive sequential attacks

In this paper, we consider the distributed state estimation problem of continuous-time linear time-invariant (LTI) systems, where communication channels are attacked by stochastic impulsive sequences. In a networked system, the communication channel between an agent and its neighbor is vulnerable to being attacked. Continuous attacks have been widely studied so far, but with the development of attack techniques, intermittent attacks have been emerging, which are more difficult to be identified and detected, and have not been well portrayed and studied. Therefore, this paper investigates a random intermittent injection attack, which leads to abrupt and random changes of the state information transmitted by the neighbors. First, this attack is modeled as a stochastic impulsive sequential attack, where both its impulsive time and impulsive intensity are random. Then a distributed observer under stochastic impulsive sequential attack is proposed. Since the impulsive attack destroys the stability of the system, in order to attenuate the impact of the impulsive attack, a large feedback gain is necessary. By using the graph theory, matrix theory and stochastic analysis, sufficient conditions for the existence of the distributed observer in the sense of mean square and in the sense of almost sure are presented, respectively. Finally, the effectiveness of the proposed distributed observer is verified by numerical simulations.

Partition‐based distributed extended Kalman filter for large‐scale nonlinear processes with application to chemical and wastewater treatment processes

AbstractIn this article, we address a partition‐based distributed state estimation problem for large‐scale general nonlinear processes by proposing a Kalman‐based approach. First, we formulate a linear full‐information estimation design within a distributed framework as the basis for developing our approach. Second, the analytical solution to the local optimization problems associated with the formulated distributed full‐information design is established, in the form of a recursive distributed Kalman filter algorithm. Then, the linear distributed Kalman filter is extended to the nonlinear context by incorporating successive linearization of nonlinear subsystem models, and the proposed distributed extended Kalman filter approach is formulated. We conduct rigorous analysis and prove the stability of the estimation error dynamics provided by the proposed method for general nonlinear processes consisting of interconnected subsystems. A chemical process example is used to illustrate the effectiveness of the proposed method and to justify the validity of the theoretical findings. In addition, the proposed method is applied to a wastewater treatment process for estimating the full‐state of the process with 145 state variables.

Optimal Distributed Finite-Time Fusion Method for Multi-Sensor Networks under Dynamic Communication Weight.

Aiming at the problem of distributed state estimation in sensor networks, a novel optimal distributed finite-time fusion filtering method based on dynamic communication weights has been developed. To tackle the fusion errors caused by incomplete node information in distributed sensor networks, the concept of limited iterations of global information aggregation was introduced, namely, fast finite-time convergence techniques. Firstly, a local filtering algorithm architecture was constructed to achieve fusion error convergence within a limited number of iterations. The maximum number of iterations was derived to be the diameter of the communication topology graph in the sensor network. Based on this, the matrix weight fusion was used to combine the local filtering results, thereby achieving optimal estimation in terms of minimum variance. Next, by introducing the generalized information quality (GIQ) calculation method and associating it with the local fusion result bias, the relative communication weights were obtained and embedded in the fusion algorithm. Finally, the effectiveness and feasibility of the proposed algorithm were validated through numerical simulations and experimental tests.

Distributed State Estimation Over Wireless Sensor Networks With Energy Harvesting Sensors.

This article is concerned with the distributed state estimation problem over wireless sensor networks (WSNs), where each smart sensor is capable of harvesting energy from the external environment with a certain probability. The data transmission between neighboring nodes is dependent on the energy level of each sensor, and the internode communication is deemed as a failure when the current energy level is inadequate to guarantee the normal data transmission. Considering the intermittent information exchange over WSNs, a novel distributed state estimator is first constructed via introducing a set of indicator functions, and then the evolution of the probability distribution of energy level and its steady-state distribution is systematically discussed by resorting to the eigenvalue analysis approach and the mathematical induction. Furthermore, the optimal estimator gain is derived by minimizing the trace of the estimation error covariance under known communication sequences. In addition, the convergence of the minimized upper bound of the expected estimation error covariance is analyzed under any initial condition. Finally, an illustrative example regarding the target tracking problem is provided to verify the validity of the obtained theoretical results.

Distributed State Estimation With Deep Neural Networks for Uncertain Nonlinear Systems Under Event-Triggered Communication

This work explores the distributed state estimation problem for an uncertain, nonlinear, and continuous-time system. Given a sensor network, each agent is assigned a deep neural network (DNN) which is used to approximate the system's dynamics. Each agent updates the weights of their DNN through a multiple timescale approach, i.e., the outer layer weights are updated online with a Lyapunov-based gradient descent update law, and the inner layer weights are updated concurrently using a supervised learning strategy. To promote the efficient use of network resources, the distributed observer uses event-triggered communication. A nonsmooth Lyapunov analysis demonstrates that the distributed event-triggered observer achieves uniformly ultimately bounded state reconstruction. A simulation example of a 5-agent sensor network estimating the state of a two-link robotic manipulator tracking a desired trajectory is provided to validate the result and showcase the performance improvements afforded by DNNs.

Double-event-triggered cooperative maximum correntropy estimation over wireless sensor networks

This paper is concerned with the distributed state estimation problem for a class of multi-sensor network systems with bandwidth constraints, measurement loss, and shot noises. To tackle these issues, the double-event-triggered cooperative maximum correntropy estimation algorithm is proposed following the proposed double-event-triggered communication mechanism and maximum correntropy criterion. With such an algorithm, measurement errors between adjacent events in the first-event trigger are applied to determine whether the sensor node needs to transmit data, and then current innovation samples in the second-event trigger are to detect measurement anomalies. Compared to existing approaches, the proposed algorithm can significantly reduce communication costs and improve sensors’ service life, accuracy and robustness. A simulation case-study concerning moving target tracking with multiple unmanned aerial vehicles (multi-UAVs) is worked out to demonstrate the effectiveness of the considered algorithm.

The Optimal Distributed Weighted Least-Squares Estimation in Finite Steps for Networked Systems

This brief investigates the distributed state estimation problem for networked systems. Based on the coupled measurements and information exchanged with neighboring nodes, we propose a distributed estimation algorithm for each node to obtain the state estimate, which is equivalent to the centralized weighted least-squares (WLS) one. When the communication network of the system consists of an acyclic graph, the distributed state estimation algorithm converges in finite iterations. Then we demonstrate that the size of the abstract graph determines the number of iterations. Furthermore, we propose an algorithm for detecting false data attacks by distributed calculation. Finally, the numerical results verify the effectiveness of developed algorithms.

Centralized and distributed adaptive cubature information filters for multi-sensor systems with unknown probability of measurement loss

This paper studies the centralized and distributed state estimation problems for nonlinear multi-sensor systems with unknown probability of measurement loss. Based on the variational Bayesian (VB) method and the cubature information filter (CIF), two adaptive filters, namely centralized adaptive CIF (CA-CIF) and distributed adaptive CIF (DA-CIF), are proposed respectively. First, a series of Bernoulli random variables are introduced as the indicators of measurement loss, and the loss probabilities are modeled as Beta distributions. By transforming all distributions into exponential family form, the CA-CIF can approximate the posterior distributions of the state, loss indicators and loss probabilities by the Expectation-Maximization (EM) algorithm. To reduce the computational cost and improve the reliability, the DA-CIF is further derived by utilizing the average consensus algorithm. Compared with the existing results which rely on the knowledge of the loss indicators or the loss probabilities, the proposed two filters require no information about the measurement loss, and are thus more applicable for practical scenarios. Finally, two examples of target tracking and permanent magnet synchronous motor are included to validate the feasibility and superiority of the proposed two filters.

Distributed estimation for multi‐agent systems with relative measurements and quantized communication: A feedback quadratic framework

SummaryIn this paper, the feedback quadratic distributed state estimation problem is investigated for a class of linear discrete time‐varying multi‐agent systems subject to non‐Gaussian noises. For the multi‐agent systems, each agent has access to not only the local measurements but the relative states to its adjacent agents as well. Due to the bandwidth constraints of the digital communication networks, the signals are quantized and then exchanged between two adjacent agents, where the probabilistic uniform quantizations are taken into account. The purpose of the addressed problem is to design a novel quadratic distributed estimator for each agent based on the local information and the predictions received from the neighbors. In particular, an output injection term is introduced to handle the unstable systems. By means of the state/measurement augmentation approach, the underlying system is transformed into an augmented one, which aggregates the original vector and its second‐order Kronecker power. Accordingly, a distributed estimator is constructed such that an upper bound is ensured for the estimation error covariance and the suboptimal estimator parameters, which minimize such an upper bound, are subsequently calculated in terms of the solutions to certain matrix difference equations. Finally, an illustrative example is provided to verify the effectiveness and superiority of the proposed quadratic estimation scheme.