Ordering for energy efficient estimation and optimization in sensor networks

A discretized version of a continuous optimization problem is considered for the case where data is obtained from a set of dispersed sensor nodes and the overall metric is a sum of individual metrics computed at each sensor. An example of such a problem is maximum likelihood estimation based on statistically independent sensor observations. By ordering transmissions from the sensor nodes, a method for achieving a saving in the average number of sensor transmissions is described. While the average number of sensor transmissions is reduced, the approach always yields the same solution as the optimum approach where all sensor transmissions occur. Further, for cases with N sufficiently well designed sensors with sufficiently large signal-to-interference-plus-noise ratios, the average percentage of transmissions saved approaches 100 percent as the number of discrete grid points in the optimization problem Q becomes significantly large. In these same cases, the average percentage of transmissions saved approaches (Q−1)/Q×100 percent as the number of sensors N in the network becomes significantly large.