LKAN: A Kolmogorov–Arnold Network-Based Framework with Long-History Statistical Regularization for IMU Trajectory Estimation

High-precision indoor trajectory estimation using pure Inertial Measurement Units (IMUs) remains challenging due to severe cumulative drift and the complexity of modeling nonlinear dynamics. This paper proposes LKAN, a novel end-to-end framework that integrates the Kolmogorov–Arnold Network (KAN) with Long-History Statistical Regularization (LHSR). We design the KANmer encoder, which fuses Multi-Head Self-Attention with KAN to explicitly capture long-range temporal dependencies and intricate nonlinear features from IMU data. To enhance model robustness, a training-only Long-History Statistical Regularization mechanism is introduced; it effectively suppresses feature distribution drift by enforcing historical statistical consistency. Extensive evaluations on three public datasets demonstrate that LKAN significantly outperforms state-of-the-art methods in IMU-only pedestrian localization. Specifically, on the iIMU-TD dataset, LKAN achieves an Absolute Trajectory Error (ATE) of 2.04 m and a Relative Trajectory Error (RTE) of 2.72 m, representing a reduction of 33.8% and 31.1%, respectively, compared to the second-best ResT-IMU. Results on the RoNIN dataset further validate the superiority of LKAN. These findings confirm that LKAN effectively mitigates error accumulation, providing a reliable, high-precision solution for real-time IMU-based positioning in complex indoor environments.