Fault diagnosis is crucial for complex autonomous mobile systems, especially for modern-day autonomous driving (AD). Different actors, numerous use cases, and complex heterogeneous components motivate a fault diagnosis of the system and overall system integrity. AD systems are composed of many heterogeneous components, each with different functionality and possibly using a different algorithm (e.g., rule-based vs. AI components). In addition, these components are subject to the vehicle's driving state and are highly dependent. This paper, therefore, faces this problem by presenting the concept of a modular fault diagnosis framework for AD systems. The concept suggests modular state monitoring and diagnosis elements, together with a state- and dependency-aware aggregation method. Our proposed classification scheme allows for the categorization of the fault diagnosis modules. The concept is implemented on AD shuttle buses and evaluated to demonstrate its capabilities.