Optimal Sensor Collaboration for Parameter Tracking Using Energy Harvesting Sensors

In this paper, we design an optimal sensor collaboration strategy among neighboring nodes while tracking a time-varying parameter using wireless sensor networks in the presence of imperfect communication channels. The sensor network is assumed to be self-powered, where sensors are equipped with energy harvesters that replenish energy from the environment. In order to minimize the mean square estimation error of parameter tracking, we propose an online sensor collaboration policy subject to real-time energy harvesting constraints. The proposed energy allocation strategy is computationally light and only relies on the second-order statistics of the system parameters. For this, we first consider an offline non-convex optimization problem, which is solved exactly using semidefinite programming. Based on the offline solution, we design an online power allocation policy that requires minimal online computation and satisfies the dynamics of energy flow at each sensor. We prove that the proposed online policy is asymptotically equivalent to the optimal offline solution and show its convergence rate and robustness. We empirically show that the estimation performance of the proposed online scheme is better than that of the online scheme when channel state information about the dynamical system is available in the low SNR regime. Numerical results are conducted to demonstrate the effectiveness of our approach

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\u27s 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

Resource Management for Distributed Estimation via Sparsity-Promoting Regularization

Recent advances in wireless communications and electronics have enabled the development of low-cost, low-power, multifunctional sensor nodes that are small in size and communicate untethered in a sensor network. These sensor nodes can sense, measure, and gather information from the environment and, based on some local processing, they transmit the sensed data to a fusion center that is responsible for making the global inference. Sensor networks are often tasked to perform parameter estimation; example applications include battlefield surveillance, medical monitoring, and navigation. However, under limited resources, such as limited communication bandwidth and sensor battery power, it is important to design an energy-efficient estimation architecture. The goal of this thesis is to provide a fundamental understanding and characterization of the optimal tradeoffs between estimation accuracy and resource usage in sensor networks. In the thesis, two basic issues of resource management are studied, sensor selection/scheduling and sensor collaboration for distributed estimation, where the former refers to finding the best subset of sensors to activate for data acquisition in order to minimize the estimation error subject to a constraint on the number of activations, and the latter refers to seeking the optimal inter-sensor communication topology and energy allocation scheme for distributed estimation systems. Most research on resource management so far has been based on several key assumptions, a) independence of observation, b) strict resource constraints, and c) absence of inter-sensor communication, which lend analytical tractability to the problem but are often found lacking in practice. This thesis introduces novel techniques to relax these assumptions and provide new insights into addressing resource management problems. The thesis analyzes how noise correlation affects solutions of sensor selection problems, and proposes both a convex relaxation approach and a greedy algorithm to find these solutions. Compared to the existing sensor selection approaches that are limited to the case of uncorrelated noise or weakly correlated noise, the methodology proposed in this thesis is valid for any arbitrary noise correlation regime. Moreover, this thesis shows a correspondence between active sensors and the nonzero columns of an estimator gain matrix. Based on this association, a sparsity-promoting optimization framework is established, where the desire to reduce the number of selected sensors is characterized by a sparsity-promoting penalty term in the objective function. Instead of placing a hard constraint on sensor activations, the promotion of sparsity leads to trade-offs between estimation performance and the number of selected sensors. To account for the individual power constraint of each sensor, a novel sparsity-promoting penalty function is presented to avoid scenarios in which the same sensors are successively selected. For solving the proposed optimization problem, we employ the alternating direction method of multipliers (ADMM), which allows the optimization problem to be decomposed into subproblems that can be solved analytically to obtain exact solutions. The problem of sensor collaboration arises when inter-sensor communication is incorporated in sensor networks, where sensors are allowed to update their measurements by taking a linear combination of the measurements of those they interact with prior to transmission to a fusion center. In this thesis, a sparsity-aware optimization framework is presented for the joint design of optimal sensor collaboration and selection schemes, where the cost of sensor collaboration is associated with the number of nonzero entries of a collaboration matrix, and the cost of sensor selection is characterized by the number of nonzero rows of the collaboration matrix. It is shown that a) the presence of sensor collaboration smooths out the observation noise, thereby improving the quality of the signal and eventual estimation performance, and b) there exists a trade-off between sensor selection and sensor collaboration. This thesis further addresses the problem of sensor collaboration for the estimation of time-varying parameters in dynamic networks that involve, for example, time-varying observation gains and channel gains. Impact of parameter correlation and temporal dynamics of sensor networks on estimation performance is illustrated from both theoretical and practical points of view. Last but not least, optimal energy allocation and storage control polices are designed in sensor networks with energy-harvesting nodes. We show that the resulting optimization problem can be solved as a special nonconvex problem, where the only source of nonconvexity can be isolated to a constraint that contains the difference of convex functions. This specific problem structure enables the use of a convex-concave procedure to obtain a near-optimal solution