As the demand for spectrum sharing between radar and communications systems is steadily increasing, the coexistence between the two systems is a growing and very challenging problem. Radar tracking in the presence of strong communications interference can result in low probability of detection even when sequential Monte Carlo

tracking methods such as the particle filter (PF) are used that better match the target kinematic model. In particular, the tracking performance can fluctuate as the power level of the communications interference can vary dynamically and unpredictably.

This work proposes to integrate the interacting multiple model (IMM) selection approach with the PF tracker to allow for dynamic variations in the power spectral density of the communications interference. The model switching allows for a necessary transition between different communications interference power spectral density (CI-PSD) values in order to reduce prediction errors. Simulations demonstrate the high performance of the integrated approach with as many as six dynamic CI-PSD value changes during the target track. For low signal-to-interference-plus-noise ratios, the derivation for estimating the high power levels of the communications interference is provided; the estimated power levels would be dynamically used in the IMM when integrated with a track-before-detect filter that is better matched to low SINR tracking applications.

This dissertation introduces stochastic ordering of instantaneous channel powers of fading channels as a general method to compare the performance of a communication system over two different channels, even when a closed-form expression for the metric may not be available. Such a comparison is with respect to a variety of performance metrics such as error rates, outage probability and ergodic capacity, which share common mathematical properties such as monotonicity, convexity or complete monotonicity. Complete monotonicity of a metric, such as the symbol error rate, in conjunction with the stochastic Laplace transform order between two fading channels implies the ordering of the two channels with respect to the metric. While it has been established previously that certain modulation schemes have convex symbol error rates, there is no study of the complete monotonicity of the same, which helps in establishing stronger channel ordering results. Toward this goal, the current research proves for the first time, that all 1-dimensional and 2-dimensional modulations have completely monotone symbol error rates. Furthermore, it is shown that the frequently used parametric fading distributions for modeling line of sight exhibit a monotonicity in the line of sight parameter with respect to the Laplace transform order. While the Laplace transform order can also be used to order fading distributions based on the ergodic capacity, there exist several distributions which are not Laplace transform ordered, although they have ordered ergodic capacities. To address this gap, a new stochastic order called the ergodic capacity order has been proposed herein, which can be used to compare channels based on the ergodic capacity. Using stochastic orders, average performance of systems involving multiple random variables are compared over two different channels. These systems include diversity combining schemes, relay networks, and signal detection over fading channels with non-Gaussian additive noise. This research also addresses the problem of unifying fading distributions. This unification is based on infinite divisibility, which subsumes almost all known fading distributions, and provides simplified expressions for performance metrics, in addition to enabling stochastic ordering.

Structural integrity is an important characteristic of performance for critical components used in applications such as aeronautics, materials, construction and transportation. When appraising the structural integrity of these components, evaluation methods must be accurate. In addition to possessing capability to perform damage detection, the ability to monitor the level of damage over time can provide extremely useful information in assessing the operational worthiness of a structure and in determining whether the structure should be repaired or removed from service. In this work, a sequential Bayesian approach with active sensing is employed for monitoring crack growth within fatigue-loaded materials. The monitoring approach is based on predicting crack damage state dynamics and modeling crack length observations. Since fatigue loading of a structural component can change while in service, an interacting multiple model technique is employed to estimate probabilities of different loading modes and incorporate this information in the crack length estimation problem. For the observation model, features are obtained from regions of high signal energy in the time-frequency plane and modeled for each crack length damage condition. Although this observation model approach exhibits high classification accuracy, the resolution characteristics can change depending upon the extent of the damage. Therefore, several different transmission waveforms and receiver sensors are considered to create multiple modes for making observations of crack damage. Resolution characteristics of the different observation modes are assessed using a predicted mean squared error criterion and observations are obtained using the predicted, optimal observation modes based on these characteristics. Calculation of the predicted mean square error metric can be computationally intensive, especially if performed in real time, and an approximation method is proposed. With this approach, the real time computational burden is decreased significantly and the number of possible observation modes can be increased. Using sensor measurements from real experiments, the overall sequential Bayesian estimation approach, with the adaptive capability of varying the state dynamics and observation modes, is demonstrated for tracking crack damage.

Neural activity tracking using electroencephalography (EEG) and magnetoencephalography (MEG) brain scanning methods has been widely used in the field of neuroscience to provide insight into the nervous system. However, the tracking accuracy depends on the presence of artifacts in the EEG/MEG recordings. Artifacts include any signals that do not originate from neural activity, including physiological artifacts such as eye movement and non-physiological activity caused by the environment.

This work proposes an integrated method for simultaneously tracking multiple neural sources using the probability hypothesis density particle filter (PPHDF) and reducing the effect of artifacts using feature extraction and stochastic modeling. Unique time-frequency features are first extracted using matching pursuit decomposition for both neural activity and artifact signals.

The features are used to model probability density functions for each signal type using Gaussian mixture modeling for use in the PPHDF neural tracking algorithm. The probability density function of the artifacts provides information to the tracking algorithm that can help reduce the probability of incorrectly estimating the dynamically varying number of current dipole sources and their corresponding neural activity localization parameters. Simulation results demonstrate the effectiveness of the proposed algorithm in increasing the tracking accuracy performance for multiple dipole sources using recordings that have been contaminated by artifacts.

Parkinson's disease is a neurodegenerative condition diagnosed on patients with

clinical history and motor signs of tremor, rigidity and bradykinesia, and the estimated

number of patients living with Parkinson's disease around the world is seven

to ten million. Deep brain stimulation (DBS) provides substantial relief of the motor

signs of Parkinson's disease patients. It is an advanced surgical technique that is used

when drug therapy is no longer sufficient for Parkinson's disease patients. DBS alleviates the motor symptoms of Parkinson's disease by targeting the subthalamic nucleus using high-frequency electrical stimulation.

This work proposes a behavior recognition model for patients with Parkinson's

disease. In particular, an adaptive learning method is proposed to classify behavioral

tasks of Parkinson's disease patients using local field potential and electrocorticography

signals that are collected during DBS implantation surgeries. Unique patterns

exhibited between these signals in a matched feature space would lead to distinction

between motor and language behavioral tasks. Unique features are first extracted

from deep brain signals in the time-frequency space using the matching pursuit decomposition

algorithm. The Dirichlet process Gaussian mixture model uses the extracted

features to cluster the different behavioral signal patterns, without training or

any prior information. The performance of the method is then compared with other

machine learning methods and the advantages of each method is discussed under

different conditions.

Continuous monitoring of sensor data from smart phones to identify human activities and gestures, puts a heavy load on the smart phone's power consumption. In this research study, the non-Euclidean geometry of the rich sensor data obtained from the user's smart phone is utilized to perform compressive analysis and efficient classification of human activities by employing machine learning techniques. We are interested in the generalization of classical tools for signal approximation to newer spaces, such as rotation data, which is best studied in a non-Euclidean setting, and its application to activity analysis. Attributing to the non-linear nature of the rotation data space, which involve a heavy overload on the smart phone's processor and memory as opposed to feature extraction on the Euclidean space, indexing and compaction of the acquired sensor data is performed prior to feature extraction, to reduce CPU overhead and thereby increase the lifetime of the battery with a little loss in recognition accuracy of the activities. The sensor data represented as unit quaternions, is a more intrinsic representation of the orientation of smart phone compared to Euler angles (which suffers from Gimbal lock problem) or the computationally intensive rotation matrices. Classification algorithms are employed to classify these manifold sequences in the non-Euclidean space. By performing customized indexing (using K-means algorithm) of the evolved manifold sequences before feature extraction, considerable energy savings is achieved in terms of smart phone's battery life.

Software-defined radio provides users with a low-cost and flexible platform for implementing and studying advanced communications and remote sensing applications. Two such applications include unmanned aerial system-to-ground communications channel and joint sensing and communication systems. In this work, these applications are studied.

In the first part, unmanned aerial system-to-ground communications channel models are derived from empirical data collected from software-defined radio transceivers in residential and mountainous desert environments using a small (< 20 kg) unmanned aerial system during low-altitude flight (< 130 m). The Kullback-Leibler divergence measure was employed to characterize model mismatch from the empirical data. Using this measure the derived models accurately describe the underlying data.

In the second part, an experimental joint sensing and communications system is implemented using a network of software-defined radio transceivers. A novel co-design receiver architecture is presented and demonstrated within a three-node joint multiple access system topology consisting of an independent radar and communications transmitter along with a joint radar and communications receiver. The receiver tracks an emulated target moving along a predefined path and simultaneously decodes a communications message. Experimental system performance bounds are characterized jointly using the communications channel capacity and novel estimation information rate.

Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision: including view-point in activity analysis, articulation in shape analysis, and measurement invariance in non-linear dynamical modeling. The increasing success of these methods is attributed to the complementary information that topology provides, as well as availability of tools for computing topological summaries such as persistence diagrams. However, persistence diagrams are multi-sets of points and hence it is not straightforward to fuse them with features used for contemporary machine learning tools like deep-nets. In this paper theoretically well-grounded approaches to develop novel perturbation robust topological representations are presented, with the long-term view of making them amenable to fusion with contemporary learning architectures. The proposed representation lives on a Grassmann manifold and hence can be efficiently used in machine learning pipelines.

The proposed representation.The efficacy of the proposed descriptor was explored on three applications: view-invariant activity analysis, 3D shape analysis, and non-linear dynamical modeling. Favorable results in both high-level recognition performance and improved performance in reduction of time-complexity when compared to other baseline methods are obtained.

Cognitive radio (CR) and device-to-device (D2D) systems are two promising dynamic spectrum access schemes in wireless communication systems to provide improved quality-of-service, and efficient spectrum utilization. This dissertation shows that both CR and D2D systems benefit from properly designed cooperation scheme.

In underlay CR systems, where secondary users (SUs) transmit simultaneously with primary users (PUs), reliable communication is by all means guaranteed for PUs, which likely deteriorates SUs’ performance. To overcome this issue, cooperation exclusively among SUs is achieved through multi-user diversity (MUD), where each SU is subject to an instantaneous interference constraint at the primary receiver. Therefore, the active number of SUs satisfying this constraint is random. Under different user distributions with the same mean number of SUs, the stochastic ordering of SU performance metrics including bit error rate (BER), outage probability, and ergodic capacity are made possible even without observing closed form expressions. Furthermore, a cooperation is assumed between primary and secondary networks, where those SUs exceeding the interference constraint facilitate PU’s transmission by relaying its signal. A fundamental performance trade-off between primary and secondary networks is observed, and it is illustrated that the proposed scheme outperforms non-cooperative underlay CR systems in the sense of system overall BER and sum achievable rate.

Similar to conventional cellular networks, CR systems suffer from an overloaded receiver having to manage signals from a large number of users. To address this issue, D2D communications has been proposed, where direct transmission links are established between users in close proximity to offload the system traffic. Several new cooperative spectrum access policies are proposed allowing coexistence of multiple D2D pairs in order to improve the spectral efficiency. Despite the additional interference, it is shown that both the cellular user’s (CU) and the individual D2D user's achievable rates can be improved simultaneously when the number of D2D pairs is below a certain threshold, resulting in a significant multiplexing gain in the sense of D2D sum rate. This threshold is quantified for different policies using second order approximations for the average achievable rates for both the CU and the individual D2D user.

Deep learning architectures have been widely explored in computer vision and have

depicted commendable performance in a variety of applications. A fundamental challenge

in training deep networks is the requirement of large amounts of labeled training

data. While gathering large quantities of unlabeled data is cheap and easy, annotating

the data is an expensive process in terms of time, labor and human expertise.

Thus, developing algorithms that minimize the human effort in training deep models

is of immense practical importance. Active learning algorithms automatically identify

salient and exemplar samples from large amounts of unlabeled data and can augment

maximal information to supervised learning models, thereby reducing the human annotation

effort in training machine learning models. The goal of this dissertation is to

fuse ideas from deep learning and active learning and design novel deep active learning

algorithms. The proposed learning methodologies explore diverse label spaces to

solve different computer vision applications. Three major contributions have emerged

from this work; (i) a deep active framework for multi-class image classication, (ii)

a deep active model with and without label correlation for multi-label image classi-

cation and (iii) a deep active paradigm for regression. Extensive empirical studies

on a variety of multi-class, multi-label and regression vision datasets corroborate the

potential of the proposed methods for real-world applications. Additional contributions

include: (i) a multimodal emotion database consisting of recordings of facial

expressions, body gestures, vocal expressions and physiological signals of actors enacting

various emotions, (ii) four multimodal deep belief network models and (iii)

an in-depth analysis of the effect of transfer of multimodal emotion features between

source and target networks on classification accuracy and training time. These related

contributions help comprehend the challenges involved in training deep learning

models and motivate the main goal of this dissertation.