ABSTRACT Inertial odometry (IO) relies exclusively on signals from an inertial measurement unit (IMU) for localization and offers a promising avenue for consumer-grade positioning. However, accurate modeling of the nonlinear motion patterns present in IMU signals remains the principal limitation on IO accuracy. To address this challenge, we propose CKANIO, an IO framework that integrates Chebyshev-based Kolmogorov-Arnold Networks (Chebyshev KAN). To the best of our knowledge, this work represents the first application of an interpretable KAN model to IO. Experimental results on five publicly available datasets demonstrate the effectiveness of CKANIO. Index T erms-- Chebyshev KAN, Inertial Odometry, Inertial Measurement Unit signals 1. INTRODUCTION Inertial odometry (IO) estimates the position and orientation of an IMU-equipped platform using acceleration and angular velocity signals provided by the inertial measurement unit (IMU) [1].

Accurate approximation of complex nonlinear functions is a fundamental challenge across many scientific and engineering domains. Traditional neural network architectures, such as Multi-Layer Perceptrons (MLPs), often struggle to efficiently capture intricate patterns and irregularities present in high-dimensional functions. This paper presents the Chebyshev Kolmogorov-Arnold Network (Chebyshev KAN), a new neural network architecture inspired by the Kolmogorov-Arnold representation theorem, incorporating the powerful approximation capabilities of Chebyshev polynomials. By utilizing learnable functions parametrized by Chebyshev polynomials on the network's edges, Chebyshev KANs enhance flexibility, efficiency, and interpretability in function approximation tasks. We demonstrate the efficacy of Chebyshev KANs through experiments on digit classification, synthetic function approximation, and fractal function generation, highlighting their superiority over traditional MLPs in terms of parameter efficiency and interpretability. Our comprehensive evaluation, including ablation studies, confirms the potential of Chebyshev KANs to address longstanding challenges in nonlinear function approximation, paving the way for further advancements in various scientific and engineering applications.