Data-Driven Strategies for selective data transmission in sensor networks Giorgio Battistelli, Alessio Benavoli, and Luigi Chisci Abstract— Energy efficiency is a crucial issue for any task involving wireless sensor networks. The present paper addresses nonlinear state estimation over a centralized sensor network, i.e. a set of sensor nodes communicating with a central information fusion unit, and proposes smart data-driven strategies by which sensors decide which data transmit to the central unit so as to reduce data communication, and thus avoid congestion prob- lems as well as prolong the network lifetime, while providing enhanced performance with respect to periodic transmission. Both measurement and estimate transmission strategies are developed. To cope with nonlinear sensors that cannot fully ob- serve the state, suitable nonlinear observability decompositions are employed. A bearing-only tracking simulation case-study is presented in order to demonstrate the effectiveness of the proposed approach. I. I NTRODUCTION The recent and rapid advances in WSN (Wireless Sensor Network) technology pose challenging estimation issues re- lated to the possibility of optimally exploiting the distributed information provided by the WSN while preserving as much as possible the limited energy resources of the wireless sensor nodes and, thus, prolonging the network lifetime. Since, as well known, data communication represents by far, for a sensor node, the most energy-consuming task, the idea of controlling data transmission so as to achieve a trade-off between communication costs and estimation performance has recently received a certain attention in the literature (see [1], [2], [3], [4], [5] and the references therein). This can be done either in a centralized or in a distributed way. In the former setting, the fusion node selects only a subset of the available sensors to receive the information [6], [7]. Conversely, in a distributed setting, each sensor node decides whether or not the data should be transmitted only on the grounds of the locally available information. Recent work [5] has concerned a network architecture, in which the sensor nodes - equipped with processing capabil- ities - transmit data (either raw measurements or computed estimates) to the central fusion node, providing estimation strategies that properly balance data processing in the WSN nodes and data communication from the sensor nodes to the central unit. The idea in [5] is to control transmission in sensor nodes by selectively transmitting data (measurements or estimates) whose distance, in a suitably weighted norm, Alessio Benavoli acknowledges financial support from the Swiss NSF grant n. 200020-137680/1. G. Battistelli and L. Chisci are with Dipartimento di Sistemi e Infor- matica, DSI-Universit` a di Firenze, Via Santa Marta 3, 50139 Firenze, Italy {battistelli, chisci}@dsi.unifi.it A. Benavoli is with Istituto “Dalle Molle” di Studi sull’Intelligenza Artificiale, 6928 Manno-Lugano, Switzerland alessio@idsia.ch from a properly defined prediction computed on the basis of information available to both the sensor node and the fusion unit exceeds a given threshold chosen according to the desired transmission rate. The data-driven selective transmission strategies proposed in [5] provide significant performance improvements with respect to periodic transmis- sion operating at the same rate but are unable to cope with the presence of nonlinear sensors that cannot fully observe the target process (e.g. angle-only or range-only or Doppler-only position sensors employed for target localization/tracking). This paper extends the data-driven measurement and estimate transmission strategies to general nonlinear systems making use of nonlinear observability decompositions at the sensor level. A. Problem Formulation The present paper addresses estimation of the state of a discrete-time dynamical system x k+1 = f (x k )+ w k (1) given measurements collected from multiple sensors y i k = h i (x k )+ v i k , i =1,...,s (2) under a limitation on the communication rate from each remote sensor unit to a central information fusion unit. Each remote sensor collects noisy measurements of the given system, can process them to find filtered estimates and transmits, at a reduced rate, either measurements or estimates to the fusion node. The fusion node, on the basis of the data received from the remote sensors, should provide, in the best possible way, an estimate of the system state. In the foregoing, we formalize the concept of communi- cation strategy (CS) with fixed rate α i for sensor i. To this end, let us introduce for each sensor i binary variables c i k such that c i k =1 if sensor i transmits at time k or c i k =0 otherwise. Then, a decision mechanism with rate α i ∈ (0, 1) can be formally defined as any, deterministic or stochastic, mechanism of generating c i k such that lim t→∞ 1 t t  k=1 E  c i k  = α i (3) where E{·} denotes the expectation operator. This indicates that, for each sensor, the averaged number of data trans- missions per time unit is constrained to take a value α i . Such a constraint can be used to model all those practical situations in which the sensing units and the monitoring unit are remotely dislocated with respect to each other and the communication rate between them is severely limited.