Learning-based inertial odometry has achieved remarkable progress in pedestrian navigation. However, extending these methods to quadruped robots remains challenging due to their distinct and highly dynamic motion patterns. Models that perform well on pedestrian data often experience severe degradation when deployed on legged platforms. To tackle this challenge, we introduce X-IONet, a cross-platform inertial odometry framework that operates solely using a single Inertial Measurement Unit (IMU). X-IONet incorporates a rule-based expert selection module to classify motion platforms and route IMU sequences to platform-specific expert networks. The displacement prediction network features a dual-stage attention architecture that jointly models long-range temporal dependencies and inter-axis correlations, enabling accurate motion representation. It outputs both displacement and associated uncertainty, which are further fused through an Extended Kalman Filter (EKF) for robust state estimation. Extensive experiments on public pedestrian datasets and a self-collected quadruped robot dataset demonstrate that X-IONet achieves state-of-the-art performance, reducing Absolute Trajectory Error (ATE) by 14.3% and Relative Trajectory Error (RTE) by 11.4% on pedestrian data, and by 52.8% and 41.3% on quadruped robot data. These results highlight the effectiveness of X-IONet in advancing accurate and robust inertial navigation across both human and legged robot platforms.

Data-driven inertial sequence learning has revolutionized navigation in GPS-denied environments, offering superior odometric resolution compared to traditional Bayesian methods. However, deep learning-based inertial tracking systems remain vulnerable to privacy breaches that can expose sensitive training data. \hl{Existing differential privacy solutions often compromise model performance by introducing excessive noise, particularly in high-frequency inertial measurements.} In this article, we propose ConvXformer, a hybrid architecture that fuses ConvNeXt blocks with Transformer encoders in a hierarchical structure for robust inertial navigation. We propose an efficient differential privacy mechanism incorporating adaptive gradient clipping and gradient-aligned noise injection (GANI) to protect sensitive information while ensuring model performance. Our framework leverages truncated singular value decomposition for gradient processing, enabling precise control over the privacy-utility trade-off. Comprehensive performance evaluations on benchmark datasets (OxIOD, RIDI, RoNIN) demonstrate that ConvXformer surpasses state-of-the-art methods, achieving more than 40% improvement in positioning accuracy while ensuring $(ε,δ)$-differential privacy guarantees. To validate real-world performance, we introduce the Mech-IO dataset, collected from the mechanical engineering building at KAIST, where intense magnetic fields from industrial equipment induce significant sensor perturbations. This demonstrated robustness under severe environmental distortions makes our framework well-suited for secure and intelligent navigation in cyber-physical systems.

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].

A fundamental requirement for full autonomy in mobile robots is accurate navigation even in situations where satellite navigation or cameras are unavailable. In such practical situations, relying only on inertial sensors will result in navigation solution drift due to the sensors' inherent noise and error terms. One of the emerging solutions to mitigate drift is to maneuver the robot in a snake-like slithering motion to increase the inertial signal-to-noise ratio, allowing the regression of the mobile robot position. In this work, we propose MoRPI-PINN as a physics-informed neural network framework for accurate inertial-based mobile robot navigation. By embedding physical laws and constraints into the training process, MoRPI-PINN is capable of providing an accurate and robust navigation solution. Using real-world experiments, we show accuracy improvements of over 85% compared to other approaches. MoRPI-PINN is a lightweight approach that can be implemented even on edge devices and used in any typical mobile robot application.

This paper presents a novel constrained Factor Graph Optimization (FGO)-based approach for networked inertial navigation in pedestrian localization. To effectively mitigate the drift inherent in inertial navigation solutions, we incorporate kinematic constraints directly into the nonlinear optimization framework. Specifically, we utilize equality constraints, such as Zero-Velocity Updates (ZUPTs), and inequality constraints representing the maximum allowable distance between body-mounted Inertial Measurement Units (IMUs) based on human anatomical limitations. While equality constraints are straightforwardly integrated as error factors, inequality constraints cannot be explicitly represented in standard FGO formulations. To address this, we introduce a differentiable softmax-based penalty term in the FGO cost function to enforce inequality constraints smoothly and robustly. The proposed constrained FGO approach leverages temporal correlations across multiple epochs, resulting in optimal state trajectory estimates while consistently maintaining constraint satisfaction. Experimental results confirm that our method outperforms conventional Kalman filter approaches, demonstrating its effectiveness and robustness for pedestrian navigation.

In this work, we evaluate the use of aerial drone hover constraints in a multisensor fusion of ground robot and drone data to improve the localization performance of a drone. In particular, we build upon our prior work on cooperative localization between an aerial drone and ground robot that fuses data from LiDAR, inertial navigation, peer-to-peer ranging, altimeter, and stereo-vision and evaluate the incorporation knowledge from the autopilot regarding when the drone is hovering. This control command data is leveraged to add constraints on the velocity state. Hover constraints can be considered important dynamic model information, such as the exploitation of zero-velocity updates in pedestrian navigation. We analyze the benefits of these constraints using an incremental factor graph optimization. Experimental data collected in a motion capture faculty is used to provide performance insights and assess the benefits of hover constraints.

Autonomous mobile robots are widely used for navigation, transportation, and inspection tasks indoors and outdoors. In practical situations of limited satellite signals or poor lighting conditions, navigation depends only on inertial sensors. In such cases, the navigation solution rapidly drifts due to inertial measurement errors. In this work, we propose WMINet a wheel-mounted inertial deep learning approach to estimate the mobile robot's position based only on its inertial sensors. To that end, we merge two common practical methods to reduce inertial drift: a wheel-mounted approach and driving the mobile robot in periodic trajectories. Additionally, we enforce a wheelbase constraint to further improve positioning performance. To evaluate our proposed approach we recorded using the Rosbot-XL a wheel-mounted initial dataset totaling 190 minutes, which is made publicly available. Our approach demonstrated a 66\% improvement over state-of-the-art approaches. As a consequence, our approach enables navigation in challenging environments and bridges the pure inertial gap. This enables seamless robot navigation using only inertial sensors for short periods.

In real world scenarios, due to environmental or hardware constraints, the quadrotor is forced to navigate in pure inertial navigation mode while operating indoors or outdoors. To mitigate inertial drift, end-to-end neural network approaches combined with quadrotor periodic trajectories were suggested. There, the quadrotor distance is regressed and combined with inertial model-based heading estimation, the quadrotor position vector is estimated. To further enhance positioning performance, in this paper we propose a quadrotor neural dead reckoning approach for quadrotors flying on periodic trajectories. In this case, the inertial readings are fed into a simple and efficient network to directly estimate the quadrotor position vector. Our approach was evaluated on two different quadrotors, one operating indoors while the other outdoors. Our approach improves the positioning accuracy of other deep-learning approaches, achieving an average 27% reduction in error outdoors and an average 79% reduction indoors, while requiring only software modifications. With the improved positioning accuracy achieved by our method, the quadrotor can seamlessly perform its tasks.

We present RetailOpt, a novel opt-in, easy-to-deploy system for tracking customer movements in indoor retail environments. The system utilizes information presently accessible to customers through smartphones and retail apps: motion data, store map, and purchase records. The approach eliminates the need for additional hardware installations/maintenance and ensures customers maintain full control of their data. Specifically, RetailOpt first employs inertial navigation to recover relative trajectories from smartphone motion data. The store map and purchase records are then cross-referenced to identify a list of visited shelves, providing anchors to localize the relative trajectories in a store through continuous and discrete optimization. We demonstrate the effectiveness of our system through systematic experiments in five diverse environments. The proposed system, if successful, would produce accurate customer movement data, essential for a broad range of retail applications, including customer behavior analysis and in-store navigation. The potential application could also extend to other domains such as entertainment and assistive technologies.

This paper advances the field of pedestrian localization by introducing a unifying framework for opportunistic positioning based on nonlinear factor graph optimization. While many existing approaches assume constant availability of one or multiple sensing signals, our methodology employs IMU-based pedestrian inertial navigation as the backbone for sensor fusion, opportunistically integrating Ultra-Wideband (UWB), Bluetooth Low Energy (BLE), and WiFi signals when they are available in the environment. The proposed PEOPLEx framework is designed to incorporate sensing data as it becomes available, operating without any prior knowledge about the environment (e.g. anchor locations, radio frequency maps, etc.). Our contributions are twofold: 1) we introduce an opportunistic multi-sensor and real-time pedestrian positioning framework fusing the available sensor measurements; 2) we develop novel factors for adaptive scaling and coarse loop closures, significantly improving the precision of indoor positioning. Experimental validation confirms that our approach achieves accurate localization estimates in real indoor scenarios using commercial smartphones.