Radar systems seek to detect targets in some search space (e.g. volume of airspace, or area on the ground surface) by actively illuminating the environment with radio waves. This illumination yields a return from targets of interest as well as highly reflective terrain features that perhaps are not of interest (called clutter). Data adaptive algorithms are therefore employed to provide robust detection of targets against a background of clutter and other forms of interference. The adaptive matched filter (AMF) is an effective, well-established detection statistic whose exact probability density function (PDF) is known under prevalent radar system model assumptions. Variations of this approach, however, lead to tests whose PDFs remain unknown or incalculable. This project will study the effectiveness of saddlepoint methods applied to approximate the known pdf of the clairvoyant matched filter, using MATLAB to complete the numerical calculations. Specifically, the approximation was used to compute tail probabilities for a range of thresholds, as well as compute the threshold and probability of detection for a specific desired probability of false alarm. This was compared to the same values computed using the known exact PDF of the filter, with the comparison demonstrating high levels of accuracy for the saddlepoint approximation. The results are encouraging, and justify further study of the approximation as applied to more strained or complicated scenarios.

The marked increase in the inflow of remotely sensed data from satellites have trans- formed the Earth and Space Sciences to a data rich domain creating a rich repository for domain experts to analyze. These observations shed light on a diverse array of disciplines ranging from monitoring Earth system components to planetary explo- ration by highlighting the expected trend and patterns in the data. However, the complexity of these patterns from local to global scales, coupled with the volume of this ever-growing repository necessitates advanced techniques to sequentially process the datasets to determine the underlying trends. Such techniques essentially model the observations to learn characteristic parameters of data-generating processes and highlight anomalous planetary surface observations to help domain scientists for making informed decisions. The primary challenge in defining such models arises due to the spatio-temporal variability of these processes.

This dissertation introduces models of multispectral satellite observations that sequentially learn the expected trend from the data by extracting salient features of planetary surface observations. The main objectives are to learn the temporal variability for modeling dynamic processes and to build representations of features of interest that is learned over the lifespan of an instrument. The estimated model parameters are then exploited in detecting anomalies due to changes in land surface reflectance as well as novelties in planetary surface landforms. A model switching approach is proposed that allows the selection of the best matched representation given the observations that is designed to account for rate of time-variability in land surface. The estimated parameters are exploited to design a change detector, analyze the separability of change events, and form an expert-guided representation of planetary landforms for prioritizing the retrieval of scientifically relevant observations with both onboard and post-downlink applications.

Limited spectral access motivates technologies that adapt to diminishing resources and increasingly cluttered environments. A joint positioning-communications system is designed and implemented on \acf{COTS} hardware. This system enables simultaneous positioning of, and communications between, nodes in a distributed network of base-stations and unmanned aerial systems (UASs). This technology offers extreme ranging precision ($<$ 5 cm) with minimal bandwidth (10 MHz), a secure communications link to protect against cyberattacks, a small form factor that enables integration into numerous platforms, and minimal resource consumption which supports high-density networks. The positioning and communications tasks are performed simultaneously with a single, co-use waveform, which efficiently utilizes limited resources and supports higher user densities. The positioning task uses a cooperative, point-to-point synchronization protocol to estimate the relative position and orientation of all users within the network. The communications task distributes positioning information between users and secures the positioning task against cyberattacks. This high-performance system is enabled by advanced time-of-arrival estimation techniques and a modern phase-accurate distributed coherence synchronization algorithm. This technology may be installed in ground-stations, ground vehicles, unmanned aerial systems, and airborne vehicles, enabling a highly-mobile, re-configurable network with numerous applications.

In this paper, the Software Defined Radio (SDR) platform is considered for building a pseudo-monostatic, 100MHz Pulse-Doppler radar. The SDR platform has many benefits for experimental communications systems as it offers relatively cheap, parametrically dynamic, off-the-shelf access to the Radiofrequency (RF) spectrum. For this application, the Universal Software Radio Peripheral (USRP) X310 hardware package is utilized with GNURadio for interfacing to the device and Matlab for signal post- processing. Pulse doppler radar processing is used to ascertain the range and velocity of a target considered in simulation and in real, over-the-air (OTA) experiments. The USRP platform offers a scalable and dynamic hardware package that can, with relatively low overhead, be incorporated into other experimental systems. This radar system will be considered for implementation into existing over-the-air Joint Radar- Communications (JRC) spectrum sharing experiments. The JRC system considers a co-designed architecture in which a communications user and a radar user share the same spectral allocation. Where the two systems would traditionally consider one another a source of interference, the receiver is able to decode communications information and discern target information via pulse-doppler radar simultaneously.

Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels are independent and contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue $\lambda_1$ of the Gram matrix formed from data. This Gram matrix has a Wishart distribution. Although exact expressions for the distribution of $\lambda_1$ are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. This dissertation presents tractable methods for computing the distribution of $\lambda_1$ under both the null and alternative hypotheses through a technique of expanding known expressions for the distribution of $\lambda_1$ as inner products of orthogonal polynomials. These newly presented expressions for the distribution allow for computation of detection thresholds and receiver operating characteristic curves to arbitrary precision in floating point arithmetic. This represents a significant advancement over the state of the art in a problem that could previously only be addressed by Monte Carlo methods.

Power spectral analysis is a fundamental aspect of signal processing used in the detection and \\estimation of various signal features. Signals spaced closely in frequency are problematic and lead analysts to miss crucial details surrounding the data. The Capon and Bartlett methods are non-parametric filterbank approaches to power spectrum estimation. The Capon algorithm is known as the "adaptive" approach to power spectrum estimation because its filter impulse responses are adapted to fit the characteristics of the data. The Bartlett method is known as the "conventional" approach to power spectrum estimation (PSE) and has a fixed deterministic filter. Both techniques rely on the Sample Covariance Matrix (SCM). The first objective of this project is to analyze the origins and characteristics of the Capon and Bartlett methods to understand their abilities to resolve signals closely spaced in frequency. Taking into consideration the Capon and Bartlett's reliance on the SCM, there is a novelty in combining these two algorithms using their cross-coherence. The second objective of this project is to analyze the performance of the Capon-Bartlett Cross Spectra. This study will involve Matlab simulations of known test cases and comparisons with approximate theoretical predictions.

As the demand for wireless systems increases exponentially, it has become necessary

for different wireless modalities, like radar and communication systems, to share the

available bandwidth. One approach to realize coexistence successfully is for each

system to adopt a transmit waveform with a unique nonlinear time-varying phase

function. At the receiver of the system of interest, the waveform received for process-

ing may still suffer from low signal-to-interference-plus-noise ratio (SINR) due to the

presence of the waveforms that are matched to the other coexisting systems. This

thesis uses a time-frequency based approach to increase the SINR of a system by estimating the unique nonlinear instantaneous frequency (IF) of the waveform matched

to the system. Specifically, the IF is estimated using the synchrosqueezing transform,

a highly localized time-frequency representation that also enables reconstruction of

individual waveform components. As the IF estimate is biased, modified versions of

the transform are investigated to obtain estimators that are both unbiased and also

matched to the unique nonlinear phase function of a given waveform. Simulations

using transmit waveforms of coexisting wireless systems are provided to demonstrate

the performance of the proposed approach using both biased and unbiased IF estimators.

Machine learning (ML) has played an important role in several modern technological innovations and has become an important tool for researchers in various fields of interest. Besides engineering, ML techniques have started to spread across various departments of study, like health-care, medicine, diagnostics, social science, finance, economics etc. These techniques require data to train the algorithms and model a complex system and make predictions based on that model. Due to development of sophisticated sensors it has become easier to collect large volumes of data which is used to make necessary hypotheses using ML. The promising results obtained using ML have opened up new opportunities of research across various departments and this dissertation is a manifestation of it. Here, some unique studies have been presented, from which valuable inference have been drawn for a real-world complex system. Each study has its own unique sets of motivation and relevance to the real world. An ensemble of signal processing (SP) and ML techniques have been explored in each study. This dissertation provides the detailed systematic approach and discusses the results achieved in each study. Valuable inferences drawn from each study play a vital role in areas of science and technology, and it is worth further investigation. This dissertation also provides a set of useful SP and ML tools for researchers in various fields of interest.