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IONet: Learning to Cure the Curse of Drift in Inertial Odometry

Changhao Chen, Xiaoxuan Lu, Andrew Markham, Niki Trigoni

arXiv:1802.02209v1cs.ROcs.AIcs.CV

TL;DR

Low-cost smartphone IMUs suffer rapid drift because integration amplifies sensor and state-estimation errors. The paper breaks continuous integration into windows, treats latent motion states as sequence-learning variables, and reports that IONet outperforms traditional PDR and SINS across extensive tests, including trolley tracking.

Abstract

from arXiv · show

Inertial sensors play a pivotal role in indoor localization, which in turn lays the foundation for pervasive personal applications. However, low-cost inertial sensors, as commonly found in smartphones, are plagued by bias and noise, which leads to unbounded growth in error when accelerations are double integrated to obtain displacement. Small errors in state estimation propagate to make odometry virtually unusable in a matter of seconds. We propose to break the cycle of continuous integration, and instead segment inertial data into independent windows. The challenge becomes estimating the latent states of each window, such as velocity and orientation, as these are not directly observable from sensor data. We demonstrate how to formulate this as an optimization problem, and show how deep recurrent neural networks can yield highly accurate trajectories, outperforming state-of-the-art shallow techniques, on a wide range of tests and attachments. In particular, we demonstrate that IONet can generalize to estimate odometry for non-periodic motion, such as a shopping trolley or baby-stroller, an extremely challenging task for existing techniques.

Related Work

Related work spans model-based inertial navigation, step-based pedestrian dead reckoning, and sequential deep learning. IONet is positioned as inertial-data-only learning for odometry, contrasting with traditional and primarily visual approaches.

Strapdown Inertial Navigation System

  • SINS integrates inertial measurements directly but low-cost MEMS IMUs make accurate open-loop navigation difficult.Recent MEMS advances enabled deployment on mobile devices, while accuracy limitations remain a central challenge.Source: Related Work · p. 2

Pedestrian Dead Reckoning

  • PDR detects steps, estimates stride length and heading, and updates locations per step, but requires tuned parameters and still accumulates errors.Prior work also fused PDR with external references such as floor plans and WiFi fingerprinting.Source: Related Work · p. 2

Sequential Deep Learning

  • Deep learning has shown strong performance on sequential data, including speech, translation, visual tracking, and video description.The cited examples motivate sequential learning as a relevant methodological direction.Source: Related Work · p. 2
  • IONet is presented as the first neural-network framework to achieve inertial odometry using inertial data only.The paper distinguishes its sensor-only approach from prior learning-based work using visual or visual-inertial observations.Source: Related Work · p. 2

Existing Methods

  • Figure 2 compares the architectures of existing SINS and PDR methods.The figure is identified as an overview of these two existing method families.Source: Figure 2 · p. 2

The Curse of Inertial Tracking

Traditional inertial navigation updates attitude, velocity, and location through sequential integration from IMU measurements. With low-cost MEMS sensors, noise, orientation initialization errors, and state coupling cause rapid drift and make pedestrian use impractical.

State Updates

  • SINS transforms gyroscope and accelerometer measurements through attitude, velocity, and location updates based on Newtonian mechanics.Gyroscope angular velocities update orientation; accelerations are transformed, gravity is removed, and velocity is integrated into location.Source: The Curse of Inertial Tracking · pp. 2–3

The Curse of Inertial Tracking

  • High-precision INS depends on costly accurate sensors and time-consuming initialization, requirements unsuitable for everyday pedestrian tracking.Orientation initialization is especially problematic because small orientation errors strongly affect gravity projection.Source: The Curse of Inertial Tracking · p. 3
  • Consumer-phone IMU errors are amplified by open-loop integration, causing the inertial system to collapse within seconds.The error sources include scale factor, axis misalignment, white noise, and random walking noise.Source: The Curse of Inertial Tracking · p. 3
  • A 1 degree attitude error adds 0.1712 m/s2 horizontal acceleration, producing 1.7 m/s velocity error and 8.56 m location error within 10 seconds.The error arises from incorrect gravity projection after orientation initialization.Source: The Curse of Inertial Tracking · p. 3
  • Applying a deep neural network directly to the physical state-space model would not remove the system’s intrinsic problems.The underlying curse remains tied to the model’s continuous state propagation and integration.Source: The Curse of Inertial Tracking · p. 3

Tracking Down A Cure

The proposed cure breaks continuous integration into windows and reformulates inertial tracking as sequential estimation of latent states. A batch window predicts displacement and heading changes, enabling a neural-network formulation while acknowledging that true window independence is impossible.

Tracking Down A Cure

  • The method segments inertial data into independent windows to break continuous error propagation, analogous to resetting an integrator to prevent windup.This is the paper’s central strategy for addressing accumulated integration error.Source: Tracking Down A Cure · p. 3
  • Windowed data remain coupled because attitude, velocity, and location are unobservable states propagated from previous states and measurements.The method therefore targets pseudoindependence rather than true independence.Source: Tracking Down A Cure · p. 3
  • For horizontal indoor positioning, zero mean vertical displacement removes the z component, and distance is represented as ∆l = ∥∆L∥2.The assumption can be relaxed with a barometer for floor changes caused by stairs or elevators.Source: Tracking Down A Cure · p. 3
  • The window output is a polar vector of distance and heading change, while initial velocity and gravity in the body frame become latent quantities to estimate.The formulation uses raw sensor sequences and ultimately projects window displacements from the starting location and heading.Source: Tracking Down A Cure · p. 4
  • The sequence formulation processes a raw inertial-data window in batch to estimate displacement and angle change instead of step-by-step pose updates.Both formulations still depend on initial attitude and velocity, but the windowed formulation supports the proposed neural-network approach.Source: Tracking Down A Cure · pp. 3–4

Deep Neural Network Framework

  • The proposed neural-network framework replaces explicit estimation of initial velocity and body-frame gravity with sequence learning from observed sensor data.This transition is grounded in the constrained motion patterns available within a window.Source: Tracking Down A Cure · p. 4

Deep Neural Network Framework

IONet reformulates inertial tracking over independent windows and uses recurrent networks to infer window-level polar displacement from raw IMU data. A stacked bidirectional LSTM learns motion-dependent latent structure while training minimizes displacement and heading errors.

Windowed inertial estimation

  • Independent IMU windows are treated as sequences whose latent states include initial velocity and gravity rather than being explicitly estimated.The window outputs a polar vector describing the transformation over the processed sequence.Source: Deep Neural Network Framework · p. 4
  • A deep recurrent network maps temporally dependent sensor measurements to polar displacement while preventing latent-state propagation between windows.This breaks continuous error propagation across the full trajectory.Source: Deep Neural Network Framework · p. 4

Network architecture

  • A 2-layer bidirectional LSTM exploits long-term dependencies and both preceding and following frames to model orientation-sensitive inertial transformations.LSTM is used instead of vanilla RNNs to address exploding and vanishing problems.Source: Deep Neural Network Framework · pp. 4, 6

Window and training design

  • Training minimizes a loss based on Euclidean distances between ground-truth and estimated polar displacement components, with κ regulating the weights of distance and heading.The network parameters are recovered by minimizing this loss over the training dataset.Source: Deep Neural Network Framework · p. 6

Experiments

IONet was evaluated across users, devices, attachments, environments, and motion types. It generally outperformed traditional SINS and PDR, while matching Tango on trolley tracking and showing robustness across consumer phones.

Tests Involving Multiple Users and Devices

Comparison with Other DNN Frameworks

  • The 2-layer bidirectional LSTM achieved lower and smoother validation loss than the alternative RNN, CNN, and LSTM frameworks.The comparison evaluated vanilla RNN, vanilla CNN, 1-layer LSTM, and non-bidirectional 2-layer LSTM models.Source: Training Details · p. 6

Tests Involving Multiple Users and Devices

  • 30%-40% improvement over traditional PDR was reported, with IONet’s maximum error staying around 2 meter within 90% testing time.These tests involved four participants walking randomly for two minutes with phones in hand, pocket, and handbag attachments.Source: Tests Involving Multiple Users and… · p. 6
  • IONet showed good robustness across iPhone 7, iPhone 6, and iPhone 5 despite their distinct IMU sensors.The model was tested on devices whose IMU properties differed from the training phone.Source: Tests Involving Multiple Users and… · p. 7

Large-scale Indoor Localization

  • In large-scale indoor tests, IONet trajectories were closer to Tango than those of the other approaches, while producing continuous trajectories at 10 Hz.The tests covered two office-building floors, long straight lines, slopes, and three phone attachments.Source: Large-scale Indoor Localization · p. 7

Trolley Tracking

  • For trolley tracking, IONet showed almost the same accuracy as Tango and greater robustness because the pure inertial approach is less affected by environmental factors.Tango could collapse when visual features were wrong or unavailable, leaving a large distance error after recovery.Source: Trolley Tracking · pp. 7–8

Conclusion and Future Work

The paper presents IONet as a recurrent neural framework for inertial odometry and reports performance gains over traditional PDR and SINS. Future work targets transferability across sensor units, users, environments, and attachments.

Conclusion

  • IONet learns inertial odometry directly from raw IMU data using a sequential physical model and deep recurrent neural networks.The model was evaluated across multiple users, devices, environments, and trolley tracking.Source: Conclusion and Future Work · p. 8
  • Across extensive experiments, IONet outperformed traditional step-based PDR and SINS mechanisms.The reported evaluation included multiple users and devices, large-scale indoor localization, and trolley tracking.Source: Conclusion and Future Work · p. 8

Future Work

  • The current model is trained and tested separately for different attachments, leaving joint training and improved cross-attachment robustness as open challenges.Performance also degrades under high sensor bias and can be influenced by challenging motions and distinct walking habits.Source: Conclusion and Future Work · p. 8
  • Future work aims to learn transferable features without limitations from measurement units, users, and environments across mobile devices and robots.This extends the approach beyond its current domain-specific training and testing conditions.Source: Conclusion and Future Work · p. 8

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