On the interdependence of sensing and estimation complexity in sensor networks

Computing the exact maximum likelihood or maximum a posteriori estimate of the environment is computationally expensive in many practical distributed sensing settings. We argue that this computational difficulty can be overcome by increasing the number of sensor measurements. Based on our work on the connection between error correcting codes and sensor networks, we propose a new algorithm, which extends the idea of sequential decoding used to decode convolutional codes to estimation in a sensor network. In a simulated distributed sensing application, this algorithm provides accurate estimates at a modest computational cost given a sufficient number of sensor measurements. Above a certain number of sensor measurements this algorithm exhibits a sharp transition in the number of steps it requires in order to converge, leading to the potentially counter-intuitive observation that the computational burden of estimation can be reduced by taking additional sensor measurements.