Distributed prediction of time series data with kernels and adaptive filtering techniques in sensor networks

Wireless sensor networks are becoming versatile tools for learning a physical phenomenon, monitoring its variations and predicting its evolution. They rely on low-cost tiny devices which are deployed in the region under scrutiny and collaborate with each other. Limited computation and communication resources require special care in designing distributed prediction algorithms for sensor networks. In this communication, we propose a nonlinear prediction technique that takes advantage of recent developments in kernel machines and adaptive filtering for online nonlinear functional learning. Conventional methods, however, are inappropriate for large-scale sensor networks, as the resulting model corresponds to the number of deployed sensors. To circumvent these drawbacks, we consider a distributed control of the model order. The model parameters are transmitted from sensor to sensor and updated by each sensor based the measurement information. The model order is incremented whenever this increment is relevant compared to a fixed-order model. The proposed approach is naturally adapted for predicting a time-varying phenomenon, as model order increases are governed by the novelty of the new observation at each sensor node. We illustrate the applicability of the proposed technique by some simulations on establishing the temperature map in an region heated by sources.