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

Rajabi, Mohammad Javad; Dehghan, S. M. M.; Mohammad-Hosseini, S.

doi:10.24200/sci.2025.66968.10354

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

Articles in Press

Document Type : Research Article

Authors

Mohammad Javad Rajabi

S. M. M. Dehghan

S. Mohammad-Hosseini

Electrical and Computer Faculty, Malek Ashtar University of Technology, Tehran, Iran

10.24200/sci.2025.66968.10354

Abstract

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.

Keywords

Inertial Navigation System

Initial Alignment

Robust Filtering

Invariant Extended Kalman Filter

Proportional-Integral Innovation

Subjects