Consistent distributed state estimation with global observability over sensor network

This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter, since it requires each sensor to have global information which is usually forbidden in large networks. Then, a sub-optimal distributed Kalman filter (DKF) is proposed by employing the covariance intersection (CI) fusion strategy. It is proven that the proposed DKF is of consistency, that is, the upper bound of error covariance matrix can be provided by the filter in real time. The consistency also enables the design of adaptive CI weights for better filter precision. Furthermore, the boundedness of covariance matrix and the convergence of the proposed filter are proven based on the strong connectivity of directed network topology and the global observability which permits the sub-system with local sensor's measurements to be unobservable. Meanwhile, to keep the covariance of the estimation error bounded, the proposed DKF does not require the system matrix to be nonsingular at each moment, which seems to be a necessary condition in the main DKF designs under global observability. Finally, simulation results of two examples show the effectiveness of the algorithm in the considered scenarios.Comment: 11 pages, 9 figure

Distributed Filtering for Uncertain Systems Under Switching Sensor Networks and Quantized Communications

This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and interval-quantized messages from neighboring sensors successively, an extended state based distributed Kalman filter (DKF) is proposed for simultaneously estimating both system state and uncertain dynamics. To alleviate the effect of observation biases, an event-triggered update based DKF is presented with a tighter mean square error bound than that of the time-driven one by designing a proper threshold. Both the two DKFs are shown to provide the upper bounds of mean square errors online for each sensor. Under mild conditions on systems and networks, the mean square error boundedness and asymptotic unbiasedness for the proposed two DKFs are proved. Finally, the numerical simulations demonstrate the effectiveness of the developed filters

Distributed Parameter Estimation Under Event-triggered Communications

In this paper, we study a distributed parameter estimation problem with an asynchronous communication protocol over multi-agent systems. Different from traditional time-driven communication schemes, in this work, data can be transmitted between agents intermittently rather than in a steady stream. First, we propose a recursive distributed estimator based on an event-triggered communication scheme, through which each agent can decide whether the current estimate is sent out to its neighbors or not. With this scheme, considerable communications between agents can be effectively reduced. Then, under mild conditions including a collective observability, we provide a design principle of triggering thresholds to guarantee the asymptotic unbiasedness and strong consistency. Furthermore, under certain conditions, we prove that, with probability one, for every agent the time interval between two successive triggered instants goes to infinity as time goes to infinity. Finally, we provide a numerical simulation to validate the theoretical results of this paper

Distributed Kalman Filters with State Equality Constraints: Time-based and Event-triggered Communications

In this paper, we investigate a distributed estimation problem for multi-agent systems with state equality constraints (SEC). First, under a time-based consensus communication protocol, applying a modified projection operator and the covariance intersection fusion method, we propose a distributed Kalman filter with guaranteed consistency and satisfied SEC. Furthermore, we establish the relationship between consensus step, SEC and estimation error covariance in dynamic and steady processes, respectively. Employing a space decomposition method, we show the error covariance in the constraint set can be arbitrarily small by setting a sufficiently large consensus step. Besides, we propose an extended collective observability (ECO) condition based on SEC, which is milder than existing observability conditions. Under the ECO condition, through utilizing a technique of matrix approximation, we prove the boundedness of error covariance and the exponentially asymptotic unbiasedness of state estimate, respectively. Moreover, under the ECO condition for linear time-invariant systems with SEC, we provide a novel event-triggered communication protocol by employing the consistency, and give an offline design principle of triggering thresholds with guaranteed boundedness of error covariance. More importantly, we quantify and analyze the communication rate for the proposed event-triggered distributed Kalman filter, and provide optimization based methods to obtain the minimal (maximal) successive non-triggering (triggering) times. Two simulations are provided to demonstrate the developed theoretical results and the effectiveness of the filters.Comment: 16 pages, 11 figure

Distributed control under compromised measurements:Resilient estimation, attack detection, and vehicle platooning

We study how to design a secure observer-based distributed controller such that a group of vehicles can achieve accurate state estimates and formation control even if the measurements of a subset of vehicle sensors are compromised by a malicious attacker. We propose an architecture consisting of a resilient observer, an attack detector, and an observer-based distributed controller. The distributed detector is able to update three sets of vehicle sensors: the ones surely under attack, surely attack-free, and suspected to be under attack. The adaptive observer saturates the measurement innovation through a preset static or time-varying threshold, such that the potentially compromised measurements have limited influence on the estimation. Essential properties of the proposed architecture include: 1) The detector is fault-free, and the attacked and attack-free vehicle sensors can be identified in finite time; 2) The observer guarantees both real-time error bounds and asymptotic error bounds, with tighter bounds when more attacked or attack-free vehicle sensors are identified by the detector; 3) The distributed controller ensures closed-loop stability. The effectiveness of the proposed methods is evaluated through simulations by an application to vehicle platooning

Navigating A Mobile Robot Using Switching Distributed Sensor Networks

This paper proposes a method to navigate a mobile robot by estimating its state over a number of distributed sensor networks (DSNs) such that it can successively accomplish a sequence of tasks, i.e., its state enters each targeted set and stays inside no less than the desired time, under a resource-aware, time-efficient, and computation- and communication-constrained setting.We propose a new robot state estimation and navigation architecture, which integrates an event-triggered task-switching feedback controller for the robot and a two-time-scale distributed state estimator for each sensor. The architecture has three major advantages over existing approaches: First, in each task only one DSN is active for sensing and estimating the robot state, and for different tasks the robot can switch the active DSN by taking resource saving and system performance into account; Second, the robot only needs to communicate with one active sensor at each time to obtain its state information from the active DSN; Third, no online optimization is required. With the controller, the robot is able to accomplish a task by following a reference trajectory and switch to the next task when an event-triggered condition is fulfilled. With the estimator, each active sensor is able to estimate the robot state. Under proper conditions, we prove that the state estimation error and the trajectory tracking deviation are upper bounded by two time-varying sequences respectively, which play an essential role in the event-triggered condition. Furthermore, we find a sufficient condition for accomplishing a task and provide an upper bound of running time for the task. Numerical simulations of an indoor robot's localization and navigation are provided to validate the proposed architecture

Distributed Kalman Filter for A Class of Nonlinear Uncertain Systems: An Extended State Method

This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the original state and the nonlinear dynamics is constructed. By analyzing the extended system, we provide a design method for the filtering gain and fusion matrices, leading to the extended state distributed Kalman filter. It is shown that the proposed filter can provide the upper bound of estimation covariance in real time, which means the estimation accuracy can be evaluated online.It is proven that the estimation covariance of the filter is bounded under rather mild assumptions, i.e., collective observability of the system and jointly strong connectedness of network topologies. Numerical simulation shows the effectiveness of the proposed filter

Community Detection for Gossip Dynamics with Stubborn Agents

We consider a community detection problem for gossip dynamics with stubborn agents in this paper. It is assumed that the communication probability matrix for agent pairs has a block structure. More specifically, we assume that the network can be divided into two communities, and the communication probability of two agents depends on whether they are in the same community. Stability of the model is investigated, and expectation of stationary distribution is characterized, indicating under the block assumption, the stationary behaviors of agents in the same community are similar. It is also shown that agents in different communities display distinct behaviors if and only if state averages of stubborn agents in different communities are not identical. A community detection algorithm is then proposed to recover community structure and to estimate communication probability parameters. It is verified that the community detection part converges in finite time, and the parameter estimation part converges almost surely. Simulations are given to illustrate algorithm performance

Secure distributed filtering for unstable dynamics under compromised observations

In this paper, we consider a secure distributed filtering problem for linear time-invariant systems with bounded noises and unstable dynamics under compromised observations. A malicious attacker is able to compromise a subset of the agents and manipulate the observations arbitrarily. We first propose a recursive distributed filter consisting of two parts at each time. The first part employs a saturation-like scheme, which gives a small gain if the innovation is too large. The second part is a consensus operation of state estimates among neighboring agents. A sufficient condition is then established for the boundedness of estimation error, which is with respect to network topology, system structure, and the maximal compromised agent subset. We further provide an equivalent statement, which connects to 2s-sparse observability in the centralized framework in certain scenarios, such that the sufficient condition is feasible. Numerical simulations are finally provided to illustrate the developed results

Recursive Network Estimation From Binary-Valued Observation Data

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which agents exchange and display binary outputs. Sufficient conditions are given to ensure stability of the observation sequence and identifiability of the system parameters. It is shown that stability and identifiability can be guaranteed under the assumption of independent standard Gaussian disturbances. Via a maximum likelihood approach, the estimation problem is transformed into an optimization problem, and it is verified that its solution is the true parameter vector under the independent standard Gaussian assumption. A recursive algorithm for the estimation problem is then proposed based on stochastic approximation techniques. Its strong consistency is established and convergence rate analyzed. Finally, numerical simulations are conducted to illustrate the results and to show that the proposed algorithm is insensitive to small unmodeled factors