Estimation In Sensor Networks Research Articles

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.

A Distributed Implementation of Steady-State Kalman Filter

This paper studies the distributed state estimation in sensor network, where <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$m$</tex></formula> sensors are deployed to infer the <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$n$</tex></formula> -dimensional state of a Linear Time-Invariant (LTI) Gaussian system. By a lossless decomposition of the optimal steady-state Kalman filter, we show that the problem of distributed estimation can be reformulated as that of the synchronization of homogeneous linear systems. Based on such decomposition, a distributed estimator is proposed, where each sensor node runs a local filter using only its own measurement, alongside with a consensus algorithm to fuse the local estimate of every node. We prove that the average of estimates from all sensors coincides with the optimal Kalman estimate, and under certain condition on the graph Laplacian matrix and the system matrix, the consensus error is bounded and the asymptotic error covariance is derived. As a result, the distributed estimator is stable for each single node. We further show that the proposed algorithm has a low message complexity of min( <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$m$</tex></formula> , <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$n$</tex></formula> n). Numerical examples are provided in the end to illustrate the efficiency of the proposed algorithm.

The sensor network estimation with dropouts: Anisotropy-based approach

This paper is concerned with an anisotropy-based estimation problem for a time-varying sensor network with an information theoretic description of statistical uncertainty in the external disturbance. The latter is assumed to be a random sequence with a bounded anisotropy level. The network model involves a number of sensors with a specified communication scheme. The sensors are considered to be non-ideal, and packet dropouts of sensors appear with given probabilities. The estimation problem under consideration is reduced to a partially convex optimization problem. The designed estimation protocol secures boundedness of the anisotropic norm for the system which relates the estimation error to the input. The results are applied to a quadcopter altitude estimation problem as an example.

Distributed Parameter Estimation under Gaussian Observation Noises

In this paper, we consider the problem of distributed parameter estimation in sensor networks. Each sensor makes successive observations of an unknown d-dimensional parameter, which might be subject to Gaussian random noises. They aim to infer true value of the unknown parameter by cooperating with each other. To this end, we first generalize the so-called dynamic regressor extension and mixing (DREM) algorithm to stochastic systems, with which the problem of estimating a d-dimensional vector parameter is transformed to that of d scalar ones: one for each of the unknown parameters. For each of the scalar problem, an estimation scheme is given, where each sensor fuses the regressors and measurements in its in-neighborhood and updates its local estimate by using least-mean squares. Particularly, a counter is also introduced for each sensor, which prevents any (noisy) measurement from being repeatedly used such that the estimation performance will not be greatly affected by certain extreme values. A novel excitation condition termed as local persistent excitation (Local-PE) condition is also proposed, which relaxes the traditional persistent excitation (PE) condition and only requires that the collective signals in each sensor's in-neighborhood are sufficiently excited. With the Local-PE condition and proper step sizes, we show that the proposed estimator guarantee that each sensor infers the true parameter in mean square, even if any individual of them cannot. Numerical examples are finally provided to illustrate the established results.

Event-Triggered Consensus for Continuous-Time Distributed Estimation

Distributed sensor networks have gained interest thanks to the developments in processing power and communications. Event-triggering mechanisms can be useful in reducing communication between the nodes of the network, while still ensuring an adequate behaviour of the system. However, very little attention has been given to continuous-time systems in this context. In this work, we propose a strategy for distributed state estimation in sensor networks, based on average dynamic consensus of the continuous measurements. While communication between nodes is discrete and heavily reduced due to the event-triggering mechanism, our method ensures that the nodes are still able to produce a continuous estimate of the global average measurement and the state of the plant, within some tuneable error bounds.

Two Compensation Strategies for Optimal Estimation in Sensor Networks with Random Matrices, Time-Correlated Noises, Deception Attacks and Packet Losses.

Due to its great importance in several applied and theoretical fields, the signal estimation problem in multisensor systems has grown into a significant research area. Networked systems are known to suffer random flaws, which, if not appropriately addressed, can deteriorate the performance of the estimators substantially. Thus, the development of estimation algorithms accounting for these random phenomena has received a lot of research attention. In this paper, the centralized fusion linear estimation problem is discussed under the assumption that the sensor measurements are affected by random parameter matrices, perturbed by time-correlated additive noises, exposed to random deception attacks and subject to random packet dropouts during transmission. A covariance-based methodology and two compensation strategies based on measurement prediction are used to design recursive filtering and fixed-point smoothing algorithms. The measurement differencing method-typically used to deal with the measurement noise time-correlation-is unsuccessful for these kinds of systems with packet losses because some sensor measurements are randomly lost and, consequently, cannot be processed. Therefore, we adopt an alternative approach based on the direct estimation of the measurement noises and the innovation technique. The two proposed compensation scenarios are contrasted through a simulation example, in which the effect of the different uncertainties on the estimation accuracy is also evaluated.

Robustness Analysis of Distributed Kalman Filter for Estimation in Sensor Networks.

Motivated by the guaranteed stability margins of linear quadratic regulators (LQRs) and standard Kalman filter (KF) in the frequency domain, this article extends these results to the distributed Kalman-consensus filter (DKCF) for distributed estimation in sensor networks. In particular, we study the robustness margins of DKCF in two cases, one of which is based on the direct target observation while the other uses estimates from neighbor sensors in the network. The loop transfer functions of the two cases are established, and gain and phase margin robustness results are derived for both. The robustness margins of DKCF are improved compared to the single-agent KF. Furthermore, as communication topology varies in sensor networks, graph overall coupling strengths change. We also analyze the correlation between overall coupling strengths and the robustness margins of DKCF.

Probabilistic Transmission Scheme for Distributed Filtering Over Randomly Lossy Sensor Networks in the Presence of Eavesdropper

This paper studies distributed secure estimation in sensor networks with packet losses and an eavesdropper. The message is transmitted through communication channels between sensors, which can be overheard by the eavesdropper with a certain probability. Two types of sensor networks under two cooperative filtering algorithms are considered and probabilistic transmission schemes to defend against the eavesdropper are proposed. For collectively detectable sensor networks under consensus Kalman filter, a sufficient distributed detectability condition on the transmission probabilities is identified to guarantee that the estimation errors of sensors are statistically bounded. Furthermore, a necessary and sufficient security condition is obtained to guarantee unboundedness of the eavesdroppers estimation error. For neighborhood-detectable nodes under standard Kalman filter, a sufficient distributed detectability condition and a necessary security condition are provided on the transmission probabilities. Simulation examples are given to illustrate the results.

Event-Based Control for Synchronization of Stochastic Linear Systems with Application to Distributed Estimation

This paper studies the synchronization of stochastic linear systems which are subject to a general class of noises, in the sense that the noises are bounded in covariance but might be correlated with the states of agents and among each other. We propose an event-based control protocol for achieving the synchronization among agents in the mean square sense and theoretically analyze the performance of it by using a stochastic Lyapunov function, where the stability of c-martingales is particularly developed to handle the challenges brought by the general model of noises and the event-triggering mechanism. The proposed event-based synchronization algorithm is then applied to solve the problem of distributed estimation in sensor network. Specifically, by losslessly decomposing the optimal Kalman filter, it is shown that the problem of distributed estimation can be resolved by using the algorithms designed for achieving the synchronization of stochastic linear systems. As such, an event-based distributed estimation algorithm is developed, where each sensor performs local filtering solely using its own measurement, together with the proposed event-based synchronization algorithm to fuse the local estimates of neighboring nodes. With the reduced communication frequency, the designed estimator is proved to be stable under the minimal requirements of network connectivity and collective system observability.

Distributed Subgradient Algorithm for Multi-Agent Optimization With Dynamic Stepsize

In this paper, we consider distributed convex optimization problems on multi-agent networks. We develop and analyze the distributed gradient method which allows each agent to compute its dynamic stepsize by utilizing the time-varying estimate of the local function value at the global optimal solution. Our approach can be applied to both synchronous and asynchronous communication protocols. Specifically, we propose the distributed subgradient with uncoordinated dynamic stepsizes (DS-UD) algorithm for synchronous protocol and the AsynDGD algorithm for asynchronous protocol. Theoretical analysis shows that the proposed algorithms guarantee that all agents reach a consensus on the solution to the multi-agent optimization problem. Moreover, the proposed approach with dynamic stepsizes eliminates the requirement of diminishing stepsize in existing works. Numerical examples of distributed estimation in sensor networks are provided to illustrate the effectiveness of the proposed approach.

Stochastic DoS attack allocation against collaborative estimation in sensor networks

In this paper, denial of service &#x0028 DoS &#x0029 attack management for destroying the collaborative estimation in sensor networks and minimizing attack energy from the attacker perspective is studied. In the communication channels between sensors and a remote estimator, the attacker chooses some channels to randomly jam DoS attacks to make their packets randomly dropped. A stochastic power allocation approach composed of three steps is proposed. Firstly, the minimum number of channels and the channel set to be attacked are given. Secondly, a necessary condition and a sufficient condition on the packet loss probabilities of the channels in the attack set are provided for general and special systems, respectively. Finally, by converting the original coupling nonlinear programming problem to a linear programming problem, a method of searching attack probabilities and power to minimize the attack energy is proposed. The effectiveness of the proposed scheme is verified by simulation examples.

Secure Estimation Under Causative Attacks

This paper considers the problem of secure parameter estimation when an estimation algorithm is prone to causative attacks. Causative attacks, in general, target decision-making algorithms (e.g., inference or learning algorithm) to alter their decisions in specific scenarios (e.g., distort parameter estimates for specific ranges of the parameter of interest). Such attacks influence the decisions via tampering with the mechanisms through which an algorithm acquires the statistical model of the population about which it aims to form a decision. Such attacks are viable, for instance, by contaminating the historical or training data, or by compromising an expert who provides the statistical model. In the presence of causative attacks, inference algorithms operate under a distorted statistical model for the data samples. This paper introduces a notion of secure parameter estimation and formalizes a framework under which secure estimation can be formulated and analyzed. The central premise underlying the secure estimation framework is that forming secure estimates introduces a new dimension to the estimation objective, pertaining to detecting attacks and isolating the true model. Since detection and isolation decisions themselves are imperfect, their inclusion induces an inherent coupling between the desired secure estimation objective and the auxiliary detection and isolation decisions that need to be formed in conjunction with the estimates. This paper establishes the fundamental interplay among these decisions, and characterizes the general decision rules in closed-forms for any desired estimation cost function. Furthermore, to circumvent the computational complexity associated with growing parameter dimension or attack complexity, a scalable estimation algorithm is provided, which is shown to enjoy certain optimality guarantees. Finally, the theory developed is applied to secure parameter estimation in sensor networks.

Distributed High-Degree Cubature Information Filter With Embedded Hybrid Consensus

To settle the problem of distributed nonlinear state estimation in sensor networks with naive nodes, a novel distributed high-degree cubature information filter with embedded hybrid consensus (DHCIF) is proposed. The multi-dimensional Gaussian weighted integrals involved in the filtering process are approximated by the fifth-degree cubature rule. A novel scheme, with consideration for the predicted measurement errors, is applied to compute the information contribution. With parallel consensus performed on both prior and measurement information, the proposed DHCIF is derived. The stability analysis with regard to consistency and boundedness of estimation errors for the proposed DHCIF is also developed. Finally, the effectiveness and advantage of the proposed DHCIF is validated by a typical maneuvering target tracing scenario. The experimental results indicate that the proposed DHCIF outperforms the existing algorithms in the aspects of estimation accuracy, consistency and consensus at the cost of a little more extra computation burden.

Impulsive Control for Target Estimation in Sensor Networks

State estimation of nonlinear systems over sensor networks is a current challenge. This work pertains to the study of the target estimation in sensor networks using impulsive control. We first propose an impulse-based filtering scheme of a class of nonlinear systems over sensor networks. Based on impulsive control theory and a comparison theorem, we then present generic criteria for estimation under the designed impulse-based filter. The performance is illustrated with simulations in a network with four sensor groups.

Hybrid Consensus-Based Cubature Kalman Filtering for Distributed State Estimation in Sensor Networks

In this paper, the high-dimensional distributed state estimation problem is investigated for a class of sensor networks within the cubature Kalman filtering (CKF) framework. The network consists of two types of nodes, i.e., communication ones and sensor ones. First, a hybrid consensus-based cubature Kalman filtering (HCCKF) is developed by blending the two existing approaches, namely, consensus on measurements (CM) and consensus on information (CI). As a result, the proposed filtering algorithm has complementary features of CM and CI, which turns out to be a better solution to the distributed state estimation problem. Secondly, estimation errors in HCCKF are proved to be exponentially bounded in mean square. Finally, a target tracking case-study in an example sensor network is given to demonstrate the effectiveness of the proposed HCCKF.

Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization

In decentralized optimization, nodes cooperate to minimize an overall objective function that is the sum (or average) of per-node private objective functions. Algorithms interleave local computations with communication among all or a subset of the nodes. Motivated by a variety of applications..decentralized estimation in sensor networks, fitting models to massive data sets, and decentralized control of multirobot systems, to name a few..significant advances have been made toward the development of robust, practical algorithms with theoretical performance guarantees. This paper presents an overview of recent work in this area. In general, rates of convergence depend not only on the number of nodes involved and the desired level of accuracy, but also on the structure and nature of the network over which nodes communicate (e.g., whether links are directed or undirected, static or time varying). We survey the state-of-theart algorithms and their analyses tailored to these different scenarios, highlighting the role of the network topology.

Achieving Cramer–Rao Lower Bounds in Sensor Network Estimation

Achievable bounds for parametric estimation using sensor networks are known for some specific problems. In this article, achievable bounds for the general parametric estimation problem with fixed and varying parameters in the network and for various noise conditions on sensor nodes are studied. The general CramerRao lower bounds (CRLBs) of parameter estimates using sensor array network are derived. Procedures for reaching these bounds can be designed based on the obtained results. The accuracy of derived relationships is confirmed by an example. It is shown that it is possible to develop algorithms of moderate complexity and communication cost achieving the CRLB.

Probability density estimation in sensor networks based on distributed mixture of factor analyzers, mobile agents and stochastic sensor selection

This paper considers the problem of distributed probability density estimation of high-dimensional data in sensor networks. In order to describe and analyze high-dimensional observations, a mixture of factor analyzers can be used instead of Gaussian mixture model. Due to high communication costs between sensor nodes in centralized algorithms, use of these algorithms is not affordable. In this paper, a distributed estimation algorithm is presented based on the mixture of factor analyzers, mobile agents and stochastic sensor selection. In the proposed algorithm, at the beginning of each iteration, a mobile agent is assigned to each independent route of the network which consists of several sensor nodes based on a stochastic sensor selection scheme. The mobile agents calculate local sufficient statistics vector in each sensor node and update global sufficient statistics. At the end of each iteration, the parameters of the mixture model are computed by using global sufficient statistics. Convergence analysis of the proposed distributed algorithm is also presented. Finally, the performance of the proposed algorithm is evaluated by using numerical simulations. Simulation results show the promising performance of the proposed distributed algorithm.

An indoor gas leakage source localization algorithm using distributed maximum likelihood estimation in sensor networks

Gas leakage source localization based on sensor networks has an important practical significance in many fields such as environmental monitoring, security protection and pollution control. This paper proposed a gas leakage source localization algorithm using distributed maximum likelihood estimation method for mobile sensor network to improve the lower performance with static sensor network. Firstly, the likelihood function of gas leakage source parameters was deduced based on the gas turbulent diffusion model. Then, the parameters of gas leakage source were estimated based on the likelihood function with the gas concentration measurement in environment. Finally, the gas leakage source location would be achieved through the iterative optimization of the likelihood function. The preliminary experimental results show that the proposed distributed Maximum Likelihood Estimation method could be achieved an acutely gas leakage source location in an indoor environment. And the reasonable path planning and dynamic topology changing could improve the positioning performance.

Mobile‐agent‐based distributed variational Bayesian algorithm for density estimation in sensor networks

This study considers the problem of probability density estimation and model order selection in distributed sensor networks. For this purpose, a mobile-agent-based distributed variational Bayesian algorithm is proposed. It is assumed that the measurements can be statistically modelled by a common Gaussian mixture model. In the proposed algorithm, the problems of model order selection and probability density estimation will be considered simultaneously using mobile agents and the variational concept. Initially, considering a component number greater than the true one, the variational Bayesian algorithm will be executed in different nodes. In other words, the mobile agents move through different routes in the network and compute the local sufficient statistics. Afterwards, the global sufficient statistics will be updated using these values and finally the parameters of the probability density function will be calculated. This procedure will be repeated until convergence is reached. At this moment, the component whose mixture probability is lower than a threshold value will be removed. The mentioned steps will continue until the true component number is reached. Convergence of the proposed method will also be analytically studied. Finally, the proposed algorithm will be applied to synthetic and also real-world data sets to show its promising performance.