Improving Inertial Navigation System Alignment using a Proportional-Integral Left-Invariant Extended Kalman Filter: A Robust Approach Against Inertial Sensors Errors

Alignment is a critical pre-processing step before initiating inertial navigation operations. The extended Kalman filter (EKF), commonly employed for aligning strap-down inertial navigation systems (SINS), faces challenges due to linearization limitations. In response to some of these challenges, the invariant extended Kalman filter (IEKF) was developed. A key requirement for utilizing IEKF is that the system dynamics must exhibit a group affine property. However, considering inertial measurement unit (IMU) errors as state variables violates this condition. This paper introduces an improved version of IEKF, named the proportional-integral invariant Extended Kalman Filter (PI-IEKF). This approach initially ignores IMU bias and drift to preserve the group affine property. To compensate for these uncertainties, the Kalman filter's innovation term is reformulated into a proportional-integral (PI) structure. The PI gains are tuned based on Lyapunov stability criteria by solving a Linear Matrix Inequality (LMI). The PI-IEKF not only addresses the uncertainties but also enhances alignment accuracy. The proposed approach was evaluated through simulations and field tests. Simulations addressed the nonlinear alignment problem in marine environment with typical wave disturbances, while field tests used an open-source dataset from vehicle-mounted sensors. Comparative results with conventional IEKF demonstrated significant improvements in convergence speed and robustness.