Prediction of time series using wavelet Gaussian process for wireless sensor networks

The detection and transmission of a physical variable over time, by a node of a sensor network to its sink node, represents a significant communication overload and consequently one of the main energy consumption processes. In this article we present an algorithm for the prediction of time series, with which it is expected to reduce the energy consumption of a sensor network, by reducing the number of transmissions when reporting to the sink node only when the prediction of the sensed value differs in certain magnitude, to the actual sensed value. For this end, the proposed algorithm combines a wavelet multiresolution transform with robust prediction using Gaussian process. The data is processed in wavelet domain, taking advantage of the transform ability to capture geometric information and decomposition in more simple signals or subbands. Subsequently, the decomposed signal is approximated by Gaussian process one for each subband of the wavelet, in this manner the Gaussian process is given to learn a much simple signal. Once the process is trained, it is ready to make predictions. We compare our method with pure Gaussian process prediction showing that the proposed method reduces the prediction error and is improves large horizons predictions, thus reducing the energy consumption of the sensor network.