Optimality and Stability of Event Triggered Consensus State Estimation for Wireless Sensor Networks* Xiangyu Meng 1 and Tongwen Chen 1 Abstract— This paper presents distributed state estimation methods through wireless sensor networks with event triggered communication protocols among the sensors. Optimal consensus filters are derived which apply to generic non-uniform and asynchronous information exchange scenarios among neigh- boring sensors. To obtain a scalable covariance propagation algorithm, the optimal filter is approximated by a suboptimal filter. Homogeneous detection criteria are designed on each sensor node to determine the broadcasting instants. Thus, a consensus on state estimates is reached with all estimator sensors for the suboptimal consensus filter. The purpose of event detection is to achieve energy efficient operation by reducing unnecessary interactions among the neighboring sensors. In addition, the performance of the proposed state estimation algorithm is validated using a simulation example. I. INTRODUCTION In recent years, wireless sensor networks have come into prominence with a range of applications [1], [2]. One of the most important applications is trajectory tracking. The Kalman filter and its various extensions are effective algorithms for tracking the state of known dynamic processes [3], [4]; while H ∞ filter is specifically designed for robust- ness [5]. Typically, sensor networks are often deployed in environments with limited computational and communication resources. Communication over radio is the most energy- consuming function performed by these devices, so that the communication frequency needs to be minimized. These constraints dictate that sensor network problems are best approached in a holistic manner, by jointly maintaining estimation performance while reducing the number of trans- missions. One area that has received considerable attention during recent years is the utilization of an event triggered sampling to trade the computation for communication [6]. As pointed out in [7], event triggered state estimation is not a standard problem due to the non-standard information pattern. Infor- mation is obtained precisely only when an event occurs; if no event takes place, the information can only be inferred from the event condition. Currently, most research on event based state estimation focuses on centralized algorithms, either in stochastic [8], [9], [10] or deterministic settings [11], [12], [13]. However, some problems are difficult or impossible for a monolithic system to solve. This necessitates the use of wireless sensor networks [14]. Unfortunately, the current existing filter designs for wireless sensor networks, most of *This work was supported by NSERC and an iCORE PhD Recruitment Scholarship from the Province of Alberta. 1 The authors are with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada xmeng2@ualberta.ca; tchen@ualberta.ca which are based on time triggered sampling, result in high power consumption and network congestion. Based on the above observations, event triggered dis- tributed state estimation approaches having a low transmis- sion frequency are proposed which significantly reduce the overall bandwidth consumption, and increase the lifetime of the network. These approaches are an extension of [15] to the event triggered transmission case. Event triggered trans- missions pose new challenges to existing design method- ologies as novel requirements, like adaptivity, uncertainty, and nonlinearity, arise. Specifically, the sensor node will not receive any information from the neighbors if the events at neighboring sensor nodes are not triggered. In this case, the behavior of neighboring sensors has to be estimated with the aid of the system model and information obtained from neighbors at event instants. After an event has occurred, the sensor broadcasts its predictive state to its neighbors and the state of the internal system models will be re- initialized for both itself and its neighbors. Then, a modified consensus filter is proposed to accommodate the generic uniform and asynchronous information exchange scenario. The optimal filter gain has been given with the corresponding error covariance updating algorithm. But unfortunately the computational cost is not scalable with respect to the number of sensors. Then the optimal consensus filter is approximated by a scalable suboptimal filter. The formal stability analysis of the suboptimal filter is provided, and a specific event trig- gered transmission mechanism is constructed. Additionally, the event conditions can be checked without the knowledge of neighbors’ information. II. PROBLEM FORMULATION Consider a system whose state at time k is x (k) ∈ R n . The time index k of the state evolution will be discrete and identified with N = {0, 1, 2,...}. Let (Ω, F ,P ) be a probability space upon which {w (k) ,k ∈ N} is an independent sequence of Gaussian random variables, having zero mean and covariance matrices {Q (k)}. That is, E  w (k) w T (l)  = Q (k) δ (k,l) , (1) where δ (k,l)=1 if k = l, and δ (k,l)=0, otherwise. The state at the initial time x (0) is a Gaussian random variable with mean x 0 and covariance matrix P 0 . The state of the system satisfies linear dynamics x (k + 1) = A (k) x (k)+ B (k) w (k) , (2) 2014 American Control Conference (ACC) June 4-6, 2014. 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