Theoretical Foundations of Multi-Sensor Fusion for UAV State Estimation: From Observability to Filter Design

R. Dhivya, Hemawathi Somasundaram

Abstract


Accurate state estimation is critical for UAV autonomy, relying heavily on the fusion of heterogeneous sensor data. This paper presents a comprehensive conceptual treatment of multi-sensor fusion for UAV state estimation, focusing on the theoretical underpinnings that govern observability, filter design, and error propagation. We begin by formalizing the observability conditions for nonlinear systems equipped with inertial, GPS, vision, and barometric sensors, highlighting scenarios where certain states become unobservable due to sensor limitations or environmental factors. The paper then explores the design principles of Extended Kalman Filters (EKF), Unscented Kalman Filters (UKF), and factor graph optimization, emphasizing their respective strengths and weaknesses in handling nonlinearities and measurement noise. We introduce the concept of “fusion consistency,” a metric to evaluate the reliability of fused estimates over time, and discuss strategies to mitigate filter divergence. Additionally, the paper examines the role of sensor calibration and time synchronization in maintaining filter accuracy. By bridging theoretical insights with practical design considerations, this work provides a foundational guide for researchers developing robust UAV state estimation systems capable of operating in complex, dynamic environments.

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