Observability Analysis Based on QR Decomposition and Adaptive Information Fusion Mechanism for Low-Cost Multi-Rotor UAVs

Abstract

This paper proposes a novel observability analysis method with less computation, which is based on QR decomposition and is suitable for low-cost devices with limited computing power. On this basis, an adaptive information fusion mechanism (AIFM) based on the criteria from the degree of observability (DOO) for the traditional extended Kalman filter (EKF) is designed to improve the tolerance of the integrated navigation system against time-varying observation conditions. Theoretical analysis and experimental results illustrate that the proposed observability analysis method can effectively evaluate each state variable’s observability, whose computational complexity is significantly reduced by 93.07% (the size of stripped observability matrix is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$105\times15$ </tex-math></inline-formula> ) compared with the conventional method based on singular value decomposition (SVD). Moreover, the simulation and real-world experiment results show that the AIFM makes the navigation system more robust by automatically updating the state variables’ weights according to their observability, which also enhances the reliability of the horizontal attitude angle estimation with excellent efficiency since they are given top priority in our fusion mechanism. In conclusion, our method is practical to improve the integrated navigation system’s accuracy, robustness, and fault-tolerance ability in complex and dynamic environments, suggesting that this technique is viable for multi-rotor navigation and control applications.