Enhanced Navigation Precision Through Interaction Multiple Filtering: Integrating Invariant and Extended Kalman Filters

High-precision navigation solutions are essential requirements for various industries, especially the autonomous robotics industry. Inertial navigation systems (INS) are the prime source of navigation information for these applications, while global navigation satellite system (GNSS) measurements act as an aided source to bound INS drift and provide global positioning. However, GNSS availability cannot always be guaranteed, leading to degradation in INS performance. Several filters have been used for INS/GNSS fusion, including the invariant extended Kalman filter (IEKF) and extended Kalman filter (EKF). The IEKF uses Lie group mathematics to preserve system symmetries and handles non-linearities effectively but suffers from rapid divergence during GNSS outages due to its reliance on bounding constraints. In contrast, the EKF is valued for its simplicity and efficiency, but it struggles with high non-linearities, causing the degradation of the accuracy over time, especially during GNSS outages. To overcome these issues, we propose a novel interaction multiple filtering (IMF) technique that integrates both filters' state estimations based on the Markov chain instead of switching between their outputs. Experimental results demonstrate the effectiveness of the proposed approach, showing improved navigation accuracy during GNSS availability compared to EKF by 13.5% and 1.8% when compared to the IEKF. The improvement when comparing the proposed algorithm during challenging environments (GNSS unavailability) with EKF reached 93% and 96% compared to IEKF, proving its robustness in challenging environments.