Sequential Decentralized Parameter Estimation Under Randomly Observed Fisher Information

We consider the problem of decentralized scalar parameter estimation using wireless sensor networks with Gaussian noise. Specifically, we propose a novel framework based on level-triggered sampling, a non-uniform sampling strategy, and sequential estimation. The proposed estimator can be used as an asymptotically optimal fixed-sample-size decentralized estimator when the observed Fisher information, i.e., Fisher information without expectation, is deterministic, as an alternative to the one-shot estimators commonly found in the literature. It can also be used as an asymptotically optimal sequential decentralized estimator when the observed Fisher information is random. We show that the optimal centralized estimator under Gaussian noise, which is the maximum likelihood estimator, is characterized by two processes, namely the observed Fisher information Ut and the observed correlation Vt. It is noted that Vt is always random even when Ut is not. In the proposed scheme, each sensor computes its local random processes, and sends a single bit to the fusion center (FC) whenever the local random processes passes certain predefined levels. The FC, upon receiving a bit from a sensor, updates its approximation to the corresponding global random process and, accordingly, its estimate. The sequential estimation process terminates when Ut (or the approximation to it) reaches a target value. We provide an asymptotic analysis for the proposed estimator and the one based on conventional uniform-in-time sampling under both deterministic and random Ut, and determine the conditions under which they are asymptotically optimal, consistent, and asymptotically unbiased. Analytical results, together with simulation results, demonstrate the superiority of the proposed estimator based on level-triggered sampling over the traditional decentralized estimator based on uniform sampling.