Sequential Decentralized Parameter Estimation under Randomly Observed Fisher Information

Abstract: We consider the problem of decentralized estimation using wireless sensor networks. 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 under non-fading listening channels (through which sensors collect their observations), 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 under fading listening channels. We show that the optimal centralized estimator under Gaussian noise is characterized by two processes, namely the observed Fisher information U_t, and the observed correlation V_t. It is noted that under non-fading listening channels only V_t is random, whereas under fading listening channels both U_t and V_t are random. In the proposed scheme, each sensor computes its local random process(es), and sends a single bit to the fusion center (FC) whenever the local random process(es) pass(es) 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 the observed Fisher information (or the approximation to it) reaches a target value. We provide an asymptotic analysis for the proposed estimator and also the one based on conventional uniform-in-time sampling under both non-fading and fading channels; 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.