Robust Distributed Parameter Estimation in Wireless Sensor Networks

abstract: Fully distributed wireless sensor networks (WSNs) without fusion center have advantages such as scalability in network size and energy efficiency in communications. Each sensor shares its data only with neighbors and then achieves global consensus quantities by in-network processing. This dissertation considers robust distributed parameter estimation methods, seeking global consensus on parameters of adaptive learning algorithms and statistical quantities. Diffusion adaptation strategy with nonlinear transmission is proposed. The nonlinearity was motivated by the necessity for bounded transmit power, as sensors need to iteratively communicate each other energy-efficiently. Despite the nonlinearity, it is shown that the algorithm performs close to the linear case with the added advantage of power savings. This dissertation also discusses convergence properties of the algorithm in the mean and the mean-square sense. Often, average is used to measure central tendency of sensed data over a network. When there are outliers in the data, however, average can be highly biased. Alternative choices of robust metrics against outliers are median, mode, and trimmed mean. Quantiles generalize the median, and they also can be used for trimmed mean. Consensus-based distributed quantile estimation algorithm is proposed and applied for finding trimmed-mean, median, maximum or minimum values, and identification of outliers through simulation. It is shown that the estimated quantities are asymptotically unbiased and converges toward the sample quantile in the mean-square sense. Step-size sequences with proper decay rates are also discussed for convergence analysis. Another measure of central tendency is a mode which represents the most probable value and also be robust to outliers and other contaminations in data. The proposed distributed mode estimation algorithm achieves a global mode by recursively shifting conditional mean of the measurement data until it converges to stationary points of estimated density function. It is also possible to estimate the mode by utilizing grid vector as well as kernel density estimator. The densities are estimated at each grid point, while the points are updated until they converge to a global mode.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Energy-Efficient Distributed Estimation by Utilizing a Nonlinear Amplifier

abstract: Distributed estimation uses many inexpensive sensors to compose an accurate estimate of a given parameter. It is frequently implemented using wireless sensor networks. There have been several studies on optimizing power allocation in wireless sensor networks used for distributed estimation, the vast majority of which assume linear radio-frequency amplifiers. Linear amplifiers are inherently inefficient, so in this dissertation nonlinear amplifiers are examined to gain efficiency while operating distributed sensor networks. This research presents a method to boost efficiency by operating the amplifiers in the nonlinear region of operation. Operating amplifiers nonlinearly presents new challenges. First, nonlinear amplifier characteristics change across manufacturing process variation, temperature, operating voltage, and aging. Secondly, the equations conventionally used for estimators and performance expectations in linear amplify-and-forward systems fail. To compensate for the first challenge, predistortion is utilized not to linearize amplifiers but rather to force them to fit a common nonlinear limiting amplifier model close to the inherent amplifier performance. This minimizes the power impact and the training requirements for predistortion. Second, new estimators are required that account for transmitter nonlinearity. This research derives analytically and confirms via simulation new estimators and performance expectation equations for use in nonlinear distributed estimation. An additional complication when operating nonlinear amplifiers in a wireless environment is the influence of varied and potentially unknown channel gains. The impact of these varied gains and both measurement and channel noise sources on estimation performance are analyzed in this paper. Techniques for minimizing the estimate variance are developed. It is shown that optimizing transmitter power allocation to minimize estimate variance for the most-compressed parameter measurement is equivalent to the problem for linear sensors. Finally, a method for operating distributed estimation in a multipath environment is presented that is capable of developing robust estimates for a wide range of Rician K-factors. This dissertation demonstrates that implementing distributed estimation using nonlinear sensors can boost system efficiency and is compatible with existing techniques from the literature for boosting efficiency at the system level via sensor power allocation. Nonlinear transmitters work best when channel gains are known and channel noise and receiver noise levels are low.Dissertation/ThesisPh.D. Electrical Engineering 201

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Gravitational Clustering: A Simple, Robust and Adaptive Approach for Distributed Networks

Distributed signal processing for wireless sensor networks enables that different devices cooperate to solve different signal processing tasks. A crucial first step is to answer the question: who observes what? Recently, several distributed algorithms have been proposed, which frame the signal/object labelling problem in terms of cluster analysis after extracting source-specific features, however, the number of clusters is assumed to be known. We propose a new method called Gravitational Clustering (GC) to adaptively estimate the time-varying number of clusters based on a set of feature vectors. The key idea is to exploit the physical principle of gravitational force between mass units: streaming-in feature vectors are considered as mass units of fixed position in the feature space, around which mobile mass units are injected at each time instant. The cluster enumeration exploits the fact that the highest attraction on the mobile mass units is exerted by regions with a high density of feature vectors, i.e., gravitational clusters. By sharing estimates among neighboring nodes via a diffusion-adaptation scheme, cooperative and distributed cluster enumeration is achieved. Numerical experiments concerning robustness against outliers, convergence and computational complexity are conducted. The application in a distributed cooperative multi-view camera network illustrates the applicability to real-world problems.Comment: 12 pages, 9 figure

Distributed Cooperative Localization in Wireless Sensor Networks without NLOS Identification

In this paper, a 2-stage robust distributed algorithm is proposed for cooperative sensor network localization using time of arrival (TOA) data without identification of non-line of sight (NLOS) links. In the first stage, to overcome the effect of outliers, a convex relaxation of the Huber loss function is applied so that by using iterative optimization techniques, good estimates of the true sensor locations can be obtained. In the second stage, the original (non-relaxed) Huber cost function is further optimized to obtain refined location estimates based on those obtained in the first stage. In both stages, a simple gradient descent technique is used to carry out the optimization. Through simulations and real data analysis, it is shown that the proposed convex relaxation generally achieves a lower root mean squared error (RMSE) compared to other convex relaxation techniques in the literature. Also by doing the second stage, the position estimates are improved and we can achieve an RMSE close to that of the other distributed algorithms which know \textit{a priori} which links are in NLOS.Comment: Accepted in WPNC 201

Improved Distributed Estimation Method for Environmental\ud time-variant Physical variables in Static Sensor Networks

In this paper, an improved distributed estimation scheme for static sensor networks is developed. The scheme is developed for environmental time-variant physical variables. The main contribution of this work is that the algorithm in [1]-[3] has been extended, and a filter has been designed with weights, such that the variance of the estimation errors is minimized, thereby improving the filter design considerably\ud and characterizing the performance limit of the filter, and thereby tracking a time-varying signal. Moreover, certain parameter optimization is alleviated with the application of a particular finite impulse response (FIR) filter. Simulation results are showing the effectiveness of the developed estimation algorithm