Gradient calculation in sensor networks

Sensor networks are comprised of devices having the ability to communicate, compute and sense the environment. A wide range of information processing tasks has been studied for such networks, including operating systems, issues, architecture optimization, and distributed data processing. In this paper, we analyze and compare four different techniques to estimate the gradient of the function represented by the sensor samples. These include: (GA1) a simple device ID defined direction, (GA2) directional derivative, (GA3) polynomial approximation with a plane, and (GA4) polynomial approximation with a quadratic. We compare these based on density of devices per unit area, and noise in the position and sensed data. The interesting result is that GA3 significantly outperforms the other algorithms, although GA1 performs very well and is much easier to compute than the others.