Parameter Estimation from Aggregated Max-Min-Mean Measurements in Sensor Networks

Sensor networks often require accurate parameter estimation, but transmitting raw data is frequently infeasible due to bandwidth-limited communication constraints. Existing distributed methods typically face an efficiency-accuracy trade-off. This paper proposes a novel, communication-efficient parameter estimation strategy based on data aggregation. Instead of raw data, only three aggregated statistics - the maximum, minimum, and mean values of sensor measurements - are transmitted from a relay node to the fusion center per time slot. We formulate the problem using maximum likelihood estimation based on the joint distribution of these statistics under Gaussian noise assumptions. To handle the resulting likelihood's complexity and non-convexity, we develop a majorization-minimization (MM) algorithm using a tractable surrogate function and introduce an extrapolated MM (EMM) algorithm for accelerated convergence. Simulations demonstrate our approach significantly reduces communication overhead, achieving estimation performance comparable to using all raw data under certain conditions and superior performance given the same communication budget. The EMM algorithm also shows significantly faster convergence than standard MM.