Source-linked AI summary
RIDI: Robust IMU Double Integration
Hang Yan, Qi Shan, Yasutaka Furukawa
TL;DR
Conventional IMU double integration is attractive for energy-efficient, anytime sensing but is undermined by rapidly accumulating sensor bias and error. RIDI learns human-motion velocities from IMU histories, corrects low-frequency acceleration errors, and then double-integrates them, achieving trajectories comparable to visual-inertial ground truth with mean positional errors below 3%.
Problem
Conventional IMU double integration is energy-efficient and works inside bags or pockets, but small sensor errors and biases rapidly accumulate into unusable position estimates.
Method
RIDI regresses velocity vectors from histories of linear accelerations and angular velocities, corrects low-frequency acceleration errors, and double-integrates the corrected accelerations to estimate positions.
Results
Mean positional errors below 3% were achieved across six subjects and four smartphone placements, producing trajectories comparable to Visual Inertial Odometry ground truth.
Takeaways & Limitations
The paper demonstrates an IMU-only navigation approach that is energy efficient and works in locations such as bags or pockets while achieving comparable accuracy to visual-inertial navigation.
Takeaways & Limitations
The experiments disable the magnetometer, which damages rotation estimation because of unstable magnetic fields, and future work includes collecting more training data.
Abstract
from arXiv · showhide
This paper proposes a novel data-driven approach for inertial navigation, which learns to estimate trajectories of natural human motions just from an inertial measurement unit (IMU) in every smartphone. The key observation is that human motions are repetitive and consist of a few major modes (e.g., standing, walking, or turning). Our algorithm regresses a velocity vector from the history of linear accelerations and angular velocities, then corrects low-frequency bias in the linear accelerations, which are integrated twice to estimate positions. We have acquired training data with ground-truth motions across multiple human subjects and multiple phone placements (e.g., in a bag or a hand). The qualitatively and quantitatively evaluations have demonstrated that our algorithm has surprisingly shown comparable results to full Visual Inertial navigation. To our knowledge, this paper is the first to integrate sophisticated machine learning techniques with inertial navigation, potentially opening up a new line of research in the domain of data-driven inertial navigation. We will publicly share our code and data to facilitate further research.
1. Introduction
RIDI addresses the practical failure of conventional IMU double integration by learning human-motion patterns and correcting acceleration errors. Across subjects and phone placements, it produces trajectories with mean positional errors below 3%.
- Motivation: Conventional IMU double integration is energy-efficient and works in occluded locations, but small sensor errors or biases rapidly accumulate into unusable positions.The method requires gravity removal followed by velocity and position integration; practical deployment otherwise needs military-grade IMUs.
- Motivation: Human motions have repetitive modes, but step-counting fails when phone orientation differs from travel direction or when motion is sideways or backward.These limitations motivate learning motion directly from IMU signals rather than assuming aligned device and walking directions.
- Approach: RIDI learns instantaneous velocity from IMU histories, adjusts arbitrary device rotations relative to the body, and corrects low-frequency acceleration errors before double integration.The corrected accelerations are integrated to estimate the trajectory.
- Evaluation: Mean positional errors below 3% were achieved across data from six subjects and four smartphone placements, with trajectories comparable to ground truth.The dataset contains more than 100 minutes of motion trajectories recorded at 200Hz using Visual Inertial Odometry ground truth.
- Significance: The paper presents machine learning integrated with inertial navigation as a potential new direction using ubiquitous, low-energy IMUs.The authors plan to share code and data to facilitate further research.
2. Related Work
Prior systems provide robust visual-inertial tracking or specialized IMU capabilities, but IMU-only position estimation remains constrained by visibility, orientation, and deployment assumptions. RIDI targets robust inertial navigation without such impractical assumptions.
- Visual-inertial methods: Visual-inertial SLAM resolves scale ambiguity and supports robust tracking, but requires a camera's clear line of sight in well-lit environments.The paper positions IMU-only navigation as a way to avoid this camera-dependent constraint.
- IMU-based methods: IMUs support rotation estimation, gait and activity recognition, and step-counting, yet position estimation still relies on assumptions such as foot placement or map data.Step-counting also struggles when device orientation and motion direction are misaligned.
- Data collection: Figure 2 depicts four phone configurations used for training-data collection: leg pocket, bag, hand-held, and body-mounted.The camera remains visible so Visual Inertial Odometry can provide ground-truth motions.
- RIDI: RIDI is presented as a machine-learning integration with inertial navigation intended to operate without heuristics or impractical assumptions.This distinguishes the proposed approach from the constraints described for prior IMU-based position estimation.
- Related systems: WiFi-based tracking is treated as complementary rather than a competing method, and the paper states that WiFiSlam critically depends on inertial navigation.The authors describe RIDI as directly beneficial to WiFi-based tracking systems.
3. Inertial 3D Motion Database
The paper contributes an inertial motion database pairing smartphone IMU measurements with 3D trajectories across subjects, placements, and varied human motions. Tango Visual Inertial Odometry supplies ground truth while the camera remains visible.
- Database: The database pairs IMU sensor measurements with 3D motion trajectories across multiple human subjects and smartphone placements.Recorded signals include linear accelerations, angular velocities, gravity directions, device orientations, and 3D camera poses.
- Ground truth: Visual Inertial Odometry from a Google Tango phone provides the camera-pose ground truth for the database.The collection setup keeps the camera's field of view clear throughout recording.
- Coverage: More than 100 minutes of data were collected at 200Hz from six subjects using four smartphone placements.Motion types include forward and backward walking, side motion, and acceleration or deceleration.
- Preprocessing: Asynchronous signals from different sources are synchronized to Tango pose timestamps through linear interpolation during preprocessing.
4. Algorithm
RIDI estimates horizontal velocities from recent IMU signals, then learns low-frequency acceleration corrections whose double integration produces positions. It handles varied phone placements through stabilized coordinates and cascaded placement-specific regressors.
- Algorithm: RIDI first regresses a velocity vector, then estimates low-frequency acceleration corrections so corrected accelerations can be integrated into positions.The correction parameters are fitted by matching integrated corrected velocities to regressed velocities.
- Learning to regress velocities: A cascaded model uses one SVM to classify four phone placements and eight SVRs to predict 2D stabilized-frame velocities.Each placement has two type-specific SVRs, and the vertical direction is ignored.
- Coordinate frames: The stabilized-IMU frame removes device pitch and roll, making velocity regression independent of tilting and rolling.The frame aligns its y-axis with gravity while retaining the horizontal plane for regression.
- Learning to regress velocities: The velocity regressor uses smoothed angular velocities and linear accelerations from the previous 200 frames, forming a 1200-dimensional feature vector.The history spans 1 second of IMU data.
- Learning to regress velocities: SVR hyper-parameters are selected by grid search over C from [0.1, 100.0] and ϵ from [0.001, 1.0], with multiplicative increments of 10.The search is conducted independently for the SVR models.
- Correcting acceleration errors: Direct integration of predicted velocities produces positions but performs worse than the proposed corrected-acceleration integration.RIDI therefore uses predicted velocities as cues for correcting acceleration errors rather than integrating those velocities directly.
5. Implementation
The system is implemented in C++ with OpenCV, Eigen, and Ceres Solver. Although presented as an offline batch method, all experiments use an online two-thread implementation.
- Implementation: The implementation uses C++ with OpenCV, Eigen, and Ceres Solver on a desktop with an Intel I7-4790 CPU and 32GB RAM.Ceres is used for implementation convenience despite the optimization having a closed-form solution.
- Implementation: The online implementation updates correction terms every 200 frames using the latest 1,000 frames.Correction terms are initialized to zero before the first update.
- Implementation: A second online thread performs double integration every frame to produce position estimates.The paper presents the algorithm offline for clarity, while experiments use the online version.
6. Experimental results
Experiments evaluate RIDI against baselines for positional accuracy, scale consistency, velocity regression, and generalization to unseen devices and subjects. RIDI outperforms competing methods in most sequences, while performance depends on training coverage and model design.
- Position evaluations: RIDI outperforms all other baselines in most testing sequences, with mean positional errors below 3.0% of total travel distance.The evaluation uses eight testing sequences and compares RIDI with RAW, STEP, RIDI-MAG, and RIDI-ORI.
- Position evaluations: Only RIDI and RIDI-ORI perform well on sequences mixing walking patterns, including backward motions, because they infer motion directions.STEP and RIDI-MAG fail in these cases because they do not infer velocity directions.
- Scale consistency: RIDI trajectories align with satellite or floorplan imagery after metric-scale adjustment, supporting scale-consistent reconstruction.Figure 6 overlays the system trajectory with Google Maps or a floorplan image; Tango is shown for comparison.
- Parameter λ: Integrating velocity regression with raw IMU acceleration is important: relying on either regressed velocities or naive double integration alone performs poorly.The experiments use λ = 0.1, while λ = 0 corresponds to integrating regressed velocities alone and λ = infinity to naive double integration.
- Velocity evaluations: 0.016 [m2/s2] and 0.015 [m2/s2] are the cascaded velocity regression MSEs on the X and Z axes, versus 0.32 [m2/s2] and 0.54 [m2/s2] for all-in-one SVR.Placement classification achieves 94.70% training accuracy and 93.65% testing accuracy.
- Generalization: The Full model generalizes well to unseen subjects, achieving below 5% MPE in most cases, but some sequences show 8 meter errors after 100 meters.The unseen-device evaluation uses a Google Pixel XL; more data and improved regression methods are identified as future work.
7. Conclusion
The paper presents RIDI as an IMU-only inertial-navigation approach that learns human-motion patterns to correct accelerations before double integration. It reports energy-efficient, anytime-anywhere operation with accuracy comparable to full visual-inertial navigation, while identifying broader data collection and deployment as future work.
- Conclusion: RIDI learns velocity vectors from IMU signals, corrects linear accelerations with linear least squares, and integrates them twice to estimate positions.The approach is designed for natural human motions and arbitrary phone placements.
- Conclusion: The IMU-only system is energy efficient, works inside bags or pockets, and achieves accuracy comparable to a full visual-inertial navigation system.These properties are presented as the paper's central practical outcome.
- Conclusion: Future work includes collecting more data across subjects and devices, learning a universal velocity regressor, and deploying RIDI on less powerful mobile devices.The paper describes these directions as ways to extend generalization and practical deployment.