Collaborative Estimation in Distributed Sensor Networks

Networks of smart ultra-portable devices are already indispensable in our lives, augmenting our senses and connecting our lives through real time processing and communication of sensory (e.g., audio, video, location) inputs. Though usually hidden from the user’s sight, the engineering of these devices involves fierce tradeoffs between energy availability (battery sizes impact portability) and signal processing / communication capability (which impacts the "smartness" of the devices). The goal of this dissertation is to provide a fundamental understanding and characterization of these tradeoffs in the context of a sensor network, where the goal is to estimate a common signal by coordinating a multitude of battery-powered sensor nodes. Most of the research so far has been based on two key assumptions –"distributed processing" and "temporal independence" – that lend analytical tractability to the problem but otherwise are often found lacking in practice. This dissertation introduces novel techniques to relax these assumptions – leading to vastly efficient energy usage in typical networks (up to 20% savings) and new insights on the quality of inference. For example, the phenomenon of sensor drift is ubiquitous in applications such as air-quality monitoring, oceanography and bridge monitoring, where calibration is often difficult and costly. This dissertation provides an analytical framework linking the state of calibration to the overall uncertainty of the inferred parameters. In distributed estimation, sensor nodes locally process their observed data and send the resulting messages to a sink, which combines the received messages to produce a final estimate of the unknown parameter. In this dissertation, this problem is generalized and called "collaborative estimation", where some sensors can potentially have access to the observations from neighboring sensors and use that information to enhance the quality of their messages sent to the sink, while using the same (or lower) energy resources. This is motivated by the fact that inter-sensor communication may be possible if sensors are geographically close. As demonstrated in this dissertation, collaborative estimation is particularly effective in "energy-skewed" and "information-skewed" networks, where some nodes may have larger batteries than others and similarly some nodes may be more informative (less noisy) compared to others. Since the node with the largest battery is not necessarily also the most informative, the proposed inter-sensor collaboration provides a natural framework to route the relevant information from low-energy-high-quality nodes to high-energy-low-quality nodes in a manner that enhances the overall power-distortion tradeoff. This dissertation also analyzes how time-correlated measurement noise affects the uncertainties of inferred parameters. Imperfections such as baseline drift in sensors result in a time-correlated additive component in the measurement noise. Though some models of drift have been reported in the literature earlier, none of the studies have considered the effect of drifting sensors on an estimation application. In this dissertation, approximate measures of estimation accuracy (Cramer-Rao bounds) are derived as a function of physical properties of sensors – namely the drift strength, correlation (Markov) factor and the time-elapsed since last calibration. For stationary drift (Markov factor less than one), it is demonstrated that the first order effect of drift is asymptotically equivalent to scaling the measurement noise by an appropriate factor. When the drift is non-stationary (Markov factor equal to one), it is established that the constant part of a signal can only be estimated inconsistently (with non-zero asymptotic variance). The results help quantify the notions that measurements taken sooner after calibration result in more accurate inference. COLLABORATIVE ESTIMATION IN DISTRIBUTED SENSOR NETWORKS