On the complexity of energy efficient pairwise calibration in embedded sensors

Technological advances in nanotechnology enabled the use of microelectromechanical systems (MEMS) in various application areas. With the integration of various sensor devices into MEMS, autonomously calibrating these sensors become a major research problem. When performing calibration on real-world embedded sensor network deployments, random errors due to internal and external factors alter the calibration parameters and eventually effect the calibration quality in a negative way. Therefore, during autonomous calibration, calibration paths which has low cost and low error values are preferable. To tackle the calibration problem on embedded wireless sensor networks, we present an energy efficient and minimum error calibration model, and also prove that due to random errors the problem turns into an NP-complete problem. To the best of our knowledge this is the first time a formal proof is presented on the complexity of an iterative calibration based problem when random errors are present in the measurements. We also conducted heuristic tests using genetic algorithm to solve the optimization version of the problem, on various graphs. The NP-completeness result also reveals that more research is needed to examine the complexity of calibration in a more general framework in real-world sensor network deployments.