Secure MARG Sensor-Based Attitude Estimation on SO(3) Under Randomly Occurring False Data Injection Attacks

In many applications, attitude estimation algorithms rely on Magnetic field, Angular Rate, and Gravity measurements from a triad of sensors known as MARG sensors. Attitude estimation of rigid bodies is crucial for navigation systems which can be vulnerable to cyber-attacks. Several works in the literature focus on secure state estimation against randomly occurring false data injection (FDI) attacks on output measurements for both linear and nonlinear systems. However, no studies address this problem when the state belongs to the special orthogonal group SO(3), which provides a structured mathematical framework for attitude representation. Given the importance of SO(3) for attitude estimation, this paper proposes a secure MARG sensor-based attitude estimation on SO(3), subject to randomly occurring FDI attacks. A novel Kalman gain of the invariant extended Kalman filter (IEKF), which is typically used for attitude estimation under noisy measurements, is designed. The objective of the proposed design is to minimize the upper bound of the estimation error covariance matrix. The proposed algorithm is validated through Monte Carlo simulations.