Optimized Fractional-Order Extended Kalman Filtering for IMU-Based Attitude Estimation Using the Hippopotamus Algorithm

The performance of the Fractional-order Extended Kalman Filter (FEKF) is often constrained by the manual tuning of its fractional-order parameter. This paper proposes HO-FEKF, a novel framework that integrates the Hippopotamus Optimization (HO) algorithm to automate and intelligently determine this optimal parameter. Central to our approach is a hierarchical optimization strategy that efficiently minimizes attitude estimation error. In addition to this automated tuning, we enhance the core FEKF model by improving its handling of nonlinear system dynamics, including the effects of time discretization on the Jacobian, cross-factor interactions, and the use of a sliding residual window. We validated our method on both a public benchmark and a custom-collected dataset. Results show that our improved FEKF surpasses the traditional version, and the complete HO-FEKF framework significantly outperforms approaches based on other optimization algorithms (genetic algorithm GA, grey wolf optimizer GWO, Harris hawks optimizer HHO, and HiPPO-LegS algorithm) combined with FEKF. These findings confirm the practical potential of HO-FEKF for achieving adaptive, high-accuracy attitude estimation in real-world sensor fusion scenarios.