#### Date

2016

#### Document Type

Dissertation

#### Degree

Doctor of Philosophy

#### Department

Electrical Engineering

#### First Adviser

Blum, Rick S.

#### Other advisers/committee members

Blum, Rick S.; Li, Tiffany Jing; Yan, Zhiyuan; Huang, Wei-Min

#### Abstract

The work in this dissertation investigates selected topics concerning sensor networkswhich focus on solving signal detection and estimation problems. In the interest of complexity reduction or to facilitate efficient distributed computation using consensus, modified versions of the optimal hypothesis test are considered for a canonical multivariate Gaussian problem in the first part. As the optimal test involves all possible products of observations taken at L different times or from L different sensors, the investigations consider truncated tests which maintain only those products involving sensors or times with indices that differ by k or less. Such tests can provide significant complexity and storage reduction and facilitate efficient distributed computation using a consensus algorithm provided k is much smaller than L. The focus is on cases with a large number L of observations or sensors such that significant efficiency results with a truncation rule, k as a function of L, which increases very slowly with L. A key result provides sufficient conditions on truncation rules and sequences of hypothesis testing problems which provide no loss in deflection performance, an accepted performance measure, as L approaches infinity when compared to the optimal detector. Several popular classes of system and process models, including observations from wide-sense stationary limiting processes as L → ∞ after the mean is subtracted, are employed as illustrative classes of examples to demonstrate the sufficient conditions are not overly restrictive. In these examples, we find significant truncation can be employed even when we assume the difficulty of the hypothesis testing problem scales in the least favorable manner, putting the most stringent conditions on the truncation rule. In all the cases considered, numerical results imply the fixed-false-alarm-rate detection probability of the truncated detector converges to the detection probability of the optimal detector for our asymptotically optimal truncation in terms of deflection.In the second part, distributed estimation of a deterministic mean-shift parameter inadditive zero-mean noise is studied when using binary quantized data in the presence ofman-in-the-middle attacks which falsify the data transmitted from sensors to the fusion center. Several subsets of sensors are assumed to be tampered with by adversaries using different attacks such that the compromised sensors transmit fictitious data. First, we consider the task of identifying and categorizing the attacked sensors into different groups according to distinct types of attacks. It is shown that increasing the number K of time samples at each sensor and enlarging the size N of the sensor network can both ameliorate the identification and categorization, but to different extents. As K → ∞, the attacked sensors can be perfectly identified and categorized, while with finite but sufficiently large K, as N → ∞, it can be shown that the fusion center can also ascertain the number of attacks and obtain an approximate categorization with a sufficiently small percentage of sensors that are misclassified. Next, in order to improve the estimation performance by utilizing the attacked observations, we consider joint estimation of the statistical description of the attacks and the parameter to be estimated after the sensors have been well categorized. When using the same quantization approach successfully employed without attacks, it can be shown that the corresponding Fisher Information Matrix (FIM) is singular. To overcome this, a time-variant quantization approach is proposed, which will provide a nonsingular FIM, provided that K ≥ 2. Furthermore, the FIM is employed to provide necessary and sufficient conditions under which utilizing the compromised sensors in the proposed fashion will lead to better estimation performance when compared to approaches where the compromised sensors are ignored.In the last part, estimation of an unknown deterministic vector from possible nonbinary quantized sensor data is considered in the presence of spoofing attacks which alter thedata presented to several sensors. Contrary to previous work, a generalized attack model is employed which manipulates the data using transformations with arbitrary functional forms determined by some attack parameters whose values are unknown to the attacked system. For the first time, necessary and sufficient conditions are provided under which the transformations provide a guaranteed attack performance in terms of Cramer-Rao Bound (CRB) regardless of the processing the estimation system employs, thus defining a highly desirable attack. Interestingly, these conditions imply that, for any such highly desirable attack when the attacked sensors can be perfectly identified by the estimation system, either the Fisher Information Matrix (FIM) for jointly estimating the desired and attack parameters is singular or the attacked system is unable to improve the CRB for the desired vector parameter through this joint estimation even though the joint FIM is nonsingular. It is shown that it is always possible to construct such a highly desirable attack by properly employing a sufficiently large dimension attack vector parameter relative to the number of quantization levels employed, which was not observed previously. For a class of spoofing attacks, a computationally efficient heuristic for the joint identification of the attacked sensors and estimation of the desired vector parameter achieves the CRB when the sensor system can perfectly identify the attacked sensors (a genie bound) for a sufficient number of observations in numerical tests.

#### Recommended Citation

Zhang, Jiangfan, "Selected Topics in Signal Detection and Estimation in Sensor Networking" (2016). *Theses and Dissertations*. 2903.

http://preserve.lehigh.edu/etd/2903