Sensor networks are commonly adopted to collect a variety of measurements in indoor and outdoor settings. However, collecting such measurements from every node in the network, although providing high accuracy and resolution of the phenomena of interest, may easily cause sensors' battery depletion. In this article, we show that measurement correlation can be successfully exploited to reduce the amount of data collected in the network without significantly sacrificing the monitoring accuracy. In particular, we propose an online adaptive measurement technique with which a subset of nodes are dynamically chosen as monitors while the measurements of the remaining nodes are estimated using the computed correlations. We propose an estimation framework based on jointly Gaussian distributed random variables, and we formulate an optimization problem to select the monitors under a total cost constraint. We show that the problem is NP-Hard and propose three efficient heuristics. We also develop statistical approaches that automatically switch between learning and estimation phases to take into account the variability occurring in real networks. Simulations carried out on real-world traces show that our approach outperforms previous solutions based on compressed sensing, and it can be successfully applied to the real application of solar irradiance prediction of photovoltaics systems.