Team-optimal distributed MMSE estimation in general and tree networks

We construct team-optimal estimation algorithms over distributed networks for state estimation in the finite-horizon mean-square error (MSE) sense. Here, we have a distributed collection of agents with processing and cooperation capabilities. These agents observe noisy samples of a desired state through a linear model and seek to learn this state by interacting with each other. Although this problem has attracted significant attention and been studied extensively in fields including machine learning and signal processing, all the well-known strategies do not achieve team-optimal learning performance in the finite-horizon MSE sense. To this end, we formulate the finite-horizon distributed minimum MSE (MMSE) when there is no restriction on the size of the disclosed information, i.e., oracle performance, over an arbitrary network topology. Subsequently, we show that exchange of local estimates is sufficient to achieve the oracle performance only over certain network topologies. By inspecting these network structures, we propose recursive algorithms achieving the oracle performance through the disclosure of local estimates. For practical implementations we also provide approaches to reduce the complexity of the algorithms through the time-windowing of the observations. Finally, in the numerical examples, we demonstrate the superior performance of the introduced algorithms in the finite-horizon MSE sense due to optimal estimation.     

Two triggered information transmission algorithms for distributed moving horizon state estimation

In this work, we consider the reduction of information transmission frequency of distributed moving horizon estimation (DMHE) for a class of nonlinear systems in which interacting subsystems exchange information with each other through a shared communication network. Specifically, algorithms based on two event-triggered methods are proposed to reduce the number of information transmissions between the subsystems in a DMHE scheme. In the first algorithm, a subsystem sends out its current information when a triggering condition based on the difference between the current state estimate and a previously transmitted one is satisfied; in the second algorithm, the transmission of information from a subsystem to other subsystems is triggered by the difference between the current measurement of the output and its derivatives and a previously transmitted measurement. In order to ensure the convergence and ultimate boundedness of the estimation error, we also propose to redesign the local moving horizon estimator of a subsystem to account for the possible lack of state updates from other subsystems explicitly. A chemical process is utilized to demonstrate the applicability and performance of the proposed approaches.     

Analysis of incremental LMS adaptive algorithm over wireless sensor networks with delayed-links

Wireless sensor networks (WSN) are used for many delay-sensitive applications, e.g. military surveillance, emergency response, city management, etc. Therefore, modeling of delay is very important. This paper presents a study of the impact of sensors' sensing delay, process delay and transmission delay in the estimation of the desired unknown parameter in the WSN. Recently proposed wireless sensor networks, in the literature, assume perfect nodes and links, in view of delay. It means that no consideration has been made about the delay in the sensing, processing and, transmission procedures. The proposed method in this paper analyzes the behavior of the distributed incremental estimation algorithm in the presence of delay in wireless sensor networks. Weighted spatio-temporal energy conservation method is used to evaluate the transient and steady state behavior of the wireless sensor networks with delay without putting any restriction on regressor's distribution. The equations that illustrate mean square deviation (MSD), excess mean square error (EMSE) and mean square error (MSE) behavior of individual nodes, are driven. Also, simulations show that overall delay could be calculated to turn off nodes in some iterations without affecting the performance of the distributed estimation algorithm or adding extra latency to the network, which can improve power management strategies by modifying sleep-wake scheduling protocols. Eventually, it is shown that simulation results have a good match with derived theoretical expressions.     

Simplified adaptive estimation

A simplified adaptive scheme is suggested for the estimation of the state vector of linear systems driven by white process noise that is added to an unknown deterministic signal. The design approach is based on embedding the Kalman filter (KF) within a simplified adaptive control loop that is driven by the innovation process. The simplified adaptive loop is idle during steady-state phases that involve white driving noise only. However, when the deterministic signal is added to the driving noise signal, the simplified adaptive control loop enhances the KF gains and helps in reducing the resulting transients. The stability of the overall estimation scheme is established under strictly passive conditions of a related system. The suggested method is applied to the target acceleration estimation problem in a Theater Missile Defence scenario.     

Stochastic sensor activation for distributed state estimation over a sensor network

We consider distributed state estimation over a resource-limited wireless sensor network. A stochastic sensor activation scheme is introduced to reduce the sensor energy consumption in communications, under which each sensor is activated with a certain probability. When the sensor is activated, it observes the target state and exchanges its estimate of the target state with its neighbors; otherwise, it only receives the estimates from its neighbors. An optimal estimator is designed for each sensor by minimizing its mean-squared estimation error. An upper and a lower bound of the limiting estimation error covariance are obtained. A method of selecting the consensus gain and a lower bound of the activating probability is also provided.     

Robust distributed maximum likelihood estimation with dependent quantized data

In this paper, we consider the distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic parameters. The parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe the dependence of observations across sensors. Since MLE with a single quantizer is sensitive to the choice of thresholds due to the uncertainty of pdf, we concentrate on MLE with multiple groups of quantizers (which can be determined by the use of prior information or some heuristic approaches) to fend off against the risk of a poor/outlier quantizer. The asymptotic efficiency of the MLE scheme with multiple quantizers is proved under some regularity conditions and the asymptotic variance is derived to be the inverse of a weighted linear combination of Fisher information matrices based on multiple different quantizers which can be used to show the robustness of our approach. As an illustrative example, we consider an estimation problem with a bivariate non-Gaussian pdf that has applications in distributed constant false alarm rate (CFAR) detection systems. Simulations show the robustness of the proposed MLE scheme especially when the number of quantized measurements is small.     

Sensor-network-based robust distributed control and estimation

This paper proposes a novel distributed estimation and control method for uncertain plants. It is of application in the case of large-scale systems, where each control unit is assumed to have access only to a subset of the plant outputs, and possibly controls a restricted subset of input channels. A constrained communication topology between nodes is considered so the units can benefit from estimates of neighboring nodes to build their own estimates. The paper proposes a methodology to design a distributed control structure so that the system is asymptotically driven to equilibrium with L₂-gain disturbance rejection capabilities. A difficulty that arises is that the separation principle does not hold, as every single unit ignores the control action that other units might be applying. To overcome this, a two-stage design is proposed: firstly, the distributed controllers are obtained to robustly stabilize the plant despite the observation errors in the controlled output. At the second stage, the distributed observers are designed aiming to minimize the effects of the communication noise in the observation error. Both stages are formulated in terms of linear matrix inequalities. The performance is shown on a level-control real plant.     

Distributed linear estimation over sensor networks

We consider a network of sensors in which each node may collect noisy linear measurements of some unknown parameter. In this context, we study a distributed consensus diffusion scheme that relies only on bidirectional communication among neighbour nodes (nodes that can communicate and exchange data), and allows every node to compute an estimate of the unknown parameter that asymptotically converges to the true parameter. At each time iteration, a measurement update and a spatial diffusion phase are performed across the network, and a local least-squares estimate is computed at each node. The proposed scheme allows one to consider networks with dynamically changing communication topology, and it is robust to unreliable communication links and failures in measuring nodes. We show that under suitable hypotheses all the local estimates converge to the true parameter value.     

Scheduler-based state estimation over multiple channels networks

We investigate the remote state estimation problem for networked systems over parallel noise-free communication channels. Due to limited network capabilities in practical network environments, communication schedulers are implemented at the transmit side of each subchannel to promote resource efficiency. Specifically, the processed signals are transmitted only when it is necessary to provide the real-time measurements to the remote estimator. The recursive approximate minimum mean-square error estimator is established to restore the state vector of a target plant by utilizing the scheduled transmission signals. All the information coming from the individual subchannels, even if no measurement is sent, will contribute to improve the estimation performance in an analytical form. Finally, a numerical example is given to illustrate the effectiveness of the main results.     

Betweenness estimation in OLSR-based multi-hop networks for distributed filtering

In traditional networks special efforts are put to secure the perimeter with firewalls: particular routers that analyze and filter the traffic to separate zones with different levels of trust. In wireless multi-hop networks the perimeter is a concept extremely hard to identify, thus, it is much more effective to enforce control on the nodes that will route more traffic. But traffic filtering and traffic analysis are costly activities for the limited resources of mesh nodes, so a trade-off must be reached limiting the number of nodes that enforce them. This work shows how, using the OLSR protocol, the centrality of groups of nodes with reference to traffic can be estimated with high accuracy independently of the network topology or size. We also show how this approach greatly limits the impact of an attack to the network using a number of firewalls that is only a fraction of the available nodes.     

Event‐triggered robust state estimation for wireless sensor networks

Robust state estimation problem subject to a communication constraint is investigated in this paper for a class of wireless sensor networks constituted by multiple remote sensor nodes and a fusion node. An analytical robust fusion estimator using local event‐triggered transmission strategies is derived aiming to reduce energy consumption of the sensor nodes and refrain from network traffic congestion. Some conditions are presented guaranteeing the uniformly bounded estimation errors of the robust state estimator. Several numerical simulations are presented to show the validity of the proposed method.     

A diffusion subband adaptive filtering algorithm for distributed estimation using variable step size and new combination method based on the MSD

This paper proposes a novel diffusion subband adaptive filtering algorithm for distributed networks. To achieve a fast convergence rate and small steady-state errors, a variable step size and a new combination method is developed. For the adaptation step, the upper bound of the mean-square deviation (MSD) of the algorithm is derived and the step size is adaptive by minimizing it in order to attain the fastest convergence rate on every iteration. Furthermore, for a combination step realized by a convex combination of the neighbor-node estimates, the proposed algorithm uses the MSD, which contains information on the reliability of the estimates, to determine combination coefficients. Simulation results show that the proposed algorithm outperforms the existing algorithms in terms of the convergence rate and the steady-state errors.     

Distributed mode-dependent state estimation for semi-Markovian jumping neural networks via sampled data

In this paper, a novel distributed state estimation scheme with sampled data is proposed for the semi-Markovian jumping neural networks (SMJNNs) with time-varying delays. In particular, mode-dependent distributed state estimators are designed to provide more flexibility. Based on the mode-dependent Lyapunov-Krasovskii functional, sufficient criteria are presented for ensuring the existence of the state estimators, based on which the desired mode-dependent estimator gains are further obtained. Finally, an illustrative example is presented for verifying the effectiveness and applicability of our theoretical results.     

传感器网络分布式鲁棒自适应估计算法

从被噪声污染的信号测量值中获得对某一参数的估计,从而确定不同物理量间的相互依赖关系是传感器网络的一个重要应用,然而测量环境可能存在冲击噪声或脉冲干扰,导致获得的测量数据中包含了大大偏离实际范围的离群值(outliers),从而无法获得有效的参数估计.为了解决这个问题,论文提出了一种分布式鲁棒自适应估计算法,该算法基于离群值稀疏性的思想,在代价函数中引入?1范数,对可能的离群值进行识别并剔除,同时利用网络各节点的相互协作,进一步提高参数估计的性能.通过计算机仿真实验,验证了该算法具有较好的鲁棒性.     

Distributed control of multi-agent systems over unknown communication networks using extremum seeking

In this paper, the solution of large-scale real-time optimization problems of multi-agent systems (MAS) is tackled in a distributed and a cooperative manner without the requirement of exact knowledge of network connectivity. Each agent in the communication network measures a local disagreement cost in addition to its local cost. The agents must work collaboratively to ensure that the system's unknown overall cost (i.e., the sum of the local cost of all the agents) is minimized. In order to minimize this cost, the local disagreement cost of all the agents must first be minimized. This minimization requires the solution of a consensus estimation problem and ensures that the agents reach agreement on their decision variables. To address this challenging problem, a distributed proportional-integral extremum seeking control technique is proposed, one that solves both problems simultaneously. Three simulation examples are included, they demonstrate the effectiveness and robustness of the proposed technique.     

Event-triggered robust distributed state estimation for sensor networks with state-dependent noises

This paper is concerned with the event-triggered distributed state estimation problem for a class of uncertain stochastic systems with state-dependent noises and randomly occurring uncertainties over sensor networks. An event-triggered communication scheme is proposed in order to determine whether the measurements on each sensor should be transmitted to the estimators or not. The norm-bounded uncertainty enters into the system in a random way. Through available output measurements from not only the individual sensor but also its neighbouring sensors, a sufficient condition is established for the desired distributed estimator to ensure that the estimation error dynamics are exponentially mean-square stable. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities, and then the explicit expression is given for the distributed estimator gains. Finally, a simulation example is provided to show the effectiveness of the proposed event-triggered distributed state estimation scheme.     

Suboptimal distributed control and estimation: application to a four coupled tanks system

The paper proposes an innovative estimation and control scheme that enables the distributed monitoring and control of large-scale processes. The proposed approach considers a discrete linear time-invariant process controlled by a network of agents that may both collect information about the evolution of the plant and apply control actions to drive its behaviour. The problem makes full sense when local observability/controllability is not assumed and the communication between agents can be exploited to reach system-wide goals. Additionally, to reduce agents bandwidth requirements and power consumption, an event-based communication policy is studied. The design procedure guarantees system stability, allowing the designer to trade-off performance, control effort and communication requirements. The obtained controllers and observers are implemented in a fully distributed fashion. To illustrate the performance of the proposed technique, experimental results on a quadruple-tank process are provided.     

Distributed estimation for adaptive sensor selection in wireless sensor networks

Wireless sensor networks (WSNs) are usually deployed for monitoring systems with the distributed detection and estimation of sensors. Sensor selection in WSNs is considered for target tracking. A distributed estimation scenario is considered based on the extended information filter. A cost function using the geometrical dilution of precision measure is derived for active sensor selection. A consensus-based estimation method is proposed in this paper for heterogeneous WSNs with two types of sensors. The convergence properties of the proposed estimators are analyzed under time-varying inputs. Accordingly, a new adaptive sensor selection (ASS) algorithm is presented in which the number of active sensors is adaptively determined based on the absolute local innovations vector. Simulation results show that the tracking accuracy of the ASS is comparable to that of the other algorithms.     

Diffusion normalized subband adaptive algorithm for distributed estimation employing signed regressor of input signal

This paper presents a novel diffusion subband adaptive filtering algorithm for distributed estimation over networks. To achieve the low computational load, the signed regressor (SR) approach is applied to normalized subband adaptive filter (NSAF) and two algorithms for diffusion networks are established. The diffusion SR-NSAF (DSR-NSAF) and modified DSR-NSAF (MDSR-NSAF) have fast convergence speed and low steady-state error similar to the conventional DNSAF. In addition, the proposed algorithms have lower computational complexity than DNSAF due to the signed regressor of the network input signals at each node. Also, based on the spatial-temporal energy conservation relation, the mean-square performance of DSR-NSAF is analyzed and the expressions for the theoretical learning curve and steady-state error are derived. The good performance of these algorithms and the validity of the theoretical results are demonstrated by presenting several simulation results.     

Mobility increases the surface coverage of distributed sensor networks

Coverage is a fundamental issue in sensor networks, which usually dictates the overall network performance. Previous studies on coverage issues mainly focused on sensor networks deployed on a 2D plane or in 3D space. However, in many real world applications, the target fields can be complex 3D surfaces where the existing coverage analysis methodology cannot be applied. This paper investigates the coverage of mobile sensor networks deployed over convex 3D surfaces. This setting is highly challenging because this dynamic type of coverage depends on not only sensors’ movement but also the characteristics of the target field. Specifically, we have made three major contributions. First, we generalize the previous analysis of coverage in the 2D plane case. Second, we derive the coverage characterization for the sphere case. Finally, we consider the general convex 3D surface case and derive the coverage ratio as a function of sensor mobility, sensor density and surface features. Our work timely fills the blank of coverage characterization for sensor networks and provides insights into the essence of the coverage hole problem. Numerical simulation and real-world evaluation verify our theoretical results. The results can serve as basic guidelines for mobile sensor network deployment in applications concerning complex sensing fields.