Using Alpha Shapes to Approximate Signal Strength Based Positioning Performance

Received signal strength (RSS) is a common tool for locating a transmitter via a sensor network. It is considered common knowledge that RSS performs well if the transmitter is inside the convex hull of the sensor network, and poorly otherwise. However, this positioning rule of thumb is binary, vague, and not always accurate. In this letter, we consider the alpha shape, which is a generalization of the concept of a convex hull. We show that the alpha shape gives a more accurate estimate of localization performance than the convex hull, and we show how to use it to obtain a quasi-continuous and quantitative (rather than binary and qualitative) estimate of a sensor network´s performance. We then compare this rule of thumb to more detailed, computationally intensive performance limits generated by the Cramer-Rao lower bound, with very good agreement.