Distributed estimation in wireless sensor networks: Physical layer considerations

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Pramod K. Varshney


Distributed estimation, Wireless sensor networks, Cramer-Rao lower bounds

Subject Categories

Electrical and Computer Engineering | Engineering


This dissertation investigates several issues related to distributed estimation in wireless sensor networks (WSNs) with emphasis on physical layer considerations such as effects of channels and demodulation/decoding schemes. We consider both parameter estimation as well as state estimation of moving objects (tracking problems). In the distributed estimation framework, each sensor observes an unknown phenomenon, quantizes its observation and sends its quantized observation to a fusion center via fading and noisy communication channels. Distributed parameter estimation problem is investigated and a maximum-likelihood (ML) estimator is derived incorporating channel statistics into the ML formulation. It is shown that the resulting likelihood function is strictly log-concave almost surely provided that at least one of the communication channels between the sensors and the fusion center has nonzero capacity. The performance bound of the resulting estimator in terms of Cramér-Rao lower bound (CRLB) is derived and a local sensor quantizer design approach is proposed based on expected Fisher Information. Distributed parameter and state estimation problems, in terms of target localization and tracking, are also considered. Channel-aware localization and tracking algorithms are proposed for three different physical layer configurations, namely the hard decoding binary channel, coherent soft decoding in Rayleigh fading channel and noncoherent soft decoding in Rayleigh fading channel. Performance bounds for these estimators in terms of CRLBs and posterior CRLBs (PCRLBs) are also derived.

The design of optimal local sensor quantizers for distributed estimation of dynamic objects, i.e., tracking, is also investigated. A framework is proposed where a feedback mechanism from the fusion center to the local sensors is employed to dynamically adapt local sensor quantizers. A new cost function based on the modified Bayesian CRLB is introduced for the design of local quantizers. For a given particular track, the modified Bayesian CRLB takes into account the measurement history, rather than the measurement statistics as in the case of a classical Bayesian CRLB (BCRLB), so that maximum information about the track can be utilized.

The bandwidth management problem for distributed dynamic estimation is explored. In particular, a methodology is proposed in which the CRLB based quantizer design approach is combined with the generalized Breiman, Friedman, Olshen, and Stone (GBFOS) algorithm to optimally allocate bits in a dynamical manner for a dynamic distributed estimation problem.


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