Distributed algorithms for filtering, estimation, and fault detection over cyber–physical-systems: A tutorial and survey

Abstract

This survey provides a comprehensive overview of distributed estimation, filtering, and fault detection techniques in the context of cyber–physical systems (CPS). Distributed algorithms are crucial for large-scale system monitoring as they enable parallel data processing, local fault identification, and real-time analysis across multiple nodes.

To establish a strong foundation, we first define essential aspects of linear dynamical systems and related graph theoretic concepts, emphasizing observability conditions that are key for local state estimation. We introduce the mathematical framework necessary to understand both the theoretical underpinnings and practical implementations of distributed algorithms in CPS environments.

After discussing consensus algorithms, this survey highlights single-time and double-time-scale consensus-based estimation and filtering approaches. We provide a detailed comparative analysis of these methodologies, examining their computational requirements, communication overhead, and performance characteristics in resource-constrained environments. We further explore different diffusion-based estimation techniques and observationally redundant designs to enhance resilience and robustness against failures and adversarial attacks.

In addition, we investigate distributed fault detection methods that enable local isolation of faults over large-scale CPS. We present both stateless and stateful detection mechanisms, along with threshold-based techniques that balance detection accuracy and false alarm rates. These approaches are essential for maintaining system integrity and preventing cascading failures in critical infrastructure.

This survey concludes with an exploration of diverse real-world applications. We examine implementation challenges and algorithm adaptations in smart grid and power networks, social systems, target tracking and localization, and intelligent transportation systems. Each application domain demonstrates how theoretical advances translate into practical solutions for complex monitoring problems.

By bridging theoretical insights with practical applications, this survey and tutorial provides valuable understanding and research directions in the field of distributed algorithm design for CPS, offering both newcomers and experienced researchers a comprehensive resource for addressing current challenges and future opportunities.