The objective of this dissertation is the development of a solid theoretical and algorithmic framework for three of the most important aspects of autonomous/artificial- intelligence (AI) systems, namely data quality assurance, localization, and communications. In the era of AI and machine learning (ML), data reign supreme. During learning tasks, we need to ensure that the training data set is correct and complete. During operation, faulty data need to be discovered and dealt with to protect from - potentially catastrophic- system failures. With our research in data quality assurance, we develop new mathematical theory and algorithms for outlier-resistant decomposition of high-dimensional matrices (tensors) based on L1-norm principal-component analysis (PCA). L1-norm PCA has been proven to be resistant to irregular data-points and will drive critical real-world AI learning and autonomous systems operations in the future. At the same time, one of the most important tasks of autonomous systems is self-localization. In GPS-deprived environments, localization becomes a fundamental technical problem. State-of-the-art solutions frequently utilize power-hungry or expensive architectures, making them difficult to deploy. In this dissertation work, we develop and implement a robust, variable-precision localization technique for autonomous systems based on the direction-of-arrival (DoA) estimation theory, which is cost and power-efficient. Finally, communication between autonomous systems is paramount for mission success in many applications. In the era of 5G and beyond, smart spectrum utilization is key. In this work, we develop physical (PHY) and medium-access-control (MAC) layer techniques that autonomously optimize spectrum usage and minimizes intra and internetwork interference.