The physical phenomena monitored by sensor networks, for example, forest temperature or water contamination, usually yield sensed data that are strongly correlated in space. With this in mind, researchers have designed a large number of sensor network protocols and algorithms that attempt to exploit such correlations. There is an increasing need to synthetically generate large traces of spatially correlated data representing a wide range of conditions to carefully study the performance of these algorithms. Further, a mathematical model for generating synthetic traces would provide guidelines for designing more efficient algorithms. These reasons motivate us to obtain a simple and accurate model of spatially correlated sensor network data. The proposed model is Markovian in nature and can capture correlation in data irrespective of the node density, the number of source nodes, or the topology. We describe a rigorous mathematical procedure and a simple practical method to extract the model parameters from real traces. We also show how to efficiently generate synthetic traces on a given topology using these parameters. The correctness of the model is verified by statistically comparing synthetic and real data. Further, the model is validated by comparing the performance of algorithms whose behavior depends on the degree of spatial correlation in data, under real and synthetic traces. The real traces are obtained from remote sensing data, publicly available sensor data, and sensor networks that we deploy. We show that the proposed model is more general and accurate than the commonly used jointly Gaussian model. Finally, we create tools that can be easily used by researchers to synthetically generate traces of any size and degree of correlation.
