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Deep Learning for Inertial Positioning: A Survey

Changhao Chen, Xianfei Pan

arXiv:2303.03757v3cs.ROcs.CV

TL;DR

Real-world modeling imperfections, measurement errors, and environmental influences limit classical inertial navigation and contribute to drift. This survey reviews deep-learning approaches to calibration, drift compensation, and sensor fusion, reporting improved positioning accuracy and reliability for learned integration and fusion methods.

  • Problem

    Classical inertial-navigation performance is limited by imperfect modeling, measurement errors, and environmental influences, with inevitable positioning drifts.

    Source: E. Discussion · p. 4

  • Method

    The survey reviews deep-learning approaches to inertial sensor calibration, drift compensation, and multimodal sensor fusion.

    Source: §XI · pp. 13–14

  • Results

    Deep-learning-based IMU integration and sensor fusion methods enable improved positioning accuracy and reliability.

    Source: A. Taxonomy · p. 2

  • Takeaways & Limitations

    The survey identifies challenges and future opportunities for deep-learning-based inertial positioning.

    Source: §XI · p. 14

    Generalization remains difficult to assess because models lack comprehensive long-term evaluation across devices, users, and application scenes.

    Source: 1) Generalization and Self-learning · p. 14

Abstract

from arXiv · show

Inertial sensors are widely utilized in smartphones, drones, robots, and IoT devices, playing a crucial role in enabling ubiquitous and reliable localization. Inertial sensor-based positioning is essential in various applications, including personal navigation, location-based security, and human-device interaction. However, low-cost MEMS inertial sensors' measurements are inevitably corrupted by various error sources, leading to unbounded drifts when integrated doubly in traditional inertial navigation algorithms, subjecting inertial positioning to the problem of error drifts. In recent years, with the rapid increase in sensor data and computational power, deep learning techniques have been developed, sparking significant research into addressing the problem of inertial positioning. Relevant literature in this field spans across mobile computing, robotics, and machine learning. In this article, we provide a comprehensive review of deep learning-based inertial positioning and its applications in tracking pedestrians, drones, vehicles, and robots. We connect efforts from different fields and discuss how deep learning can be applied to address issues such as sensor calibration, positioning error drift reduction, and multi-sensor fusion. This article aims to attract readers from various backgrounds, including researchers and practitioners interested in the potential of deep learning-based techniques to solve inertial positioning problems. Our review demonstrates the exciting possibilities that deep learning brings to the table and provides a roadmap for future research in this field.

I. INTRODUCTION

Low-cost inertial measurements accumulate into unbounded drift, while existing domain-specific and sensor-fusion solutions have application limits. The survey organizes deep-learning approaches across sensor calibration, inertial algorithms and fusion, and applications.

I. INTRODUCTION

  • Low-cost MEMS measurement errors can be amplified during inertial integration, producing unbounded drift and failures within seconds in real-world applications.Errors include bias, temperature-dependent error, sensor noise, and random-walk noise.Source: §I · p. 1
  • Camera or LiDAR fusion can improve pure inertial positioning on drones and robots, but remains application-specific and does not resolve inertial navigation’s fundamental problem.Source: §I · p. 2

A. Taxonomy

  • The survey reviews deep learning for inertial sensor calibration, drift reduction, and fusion with other sensor information.Source: A. Taxonomy · p. 2, §I · p. 2
  • At the sensor level, deep learning models measurement errors and noise to calibrate inertial sensors.Source: A. Taxonomy · p. 2
  • At the algorithm level, learned methods replace or enhance inertial-navigation modules and fuse inertial data with cameras or LiDAR, improving positioning accuracy and reliability.Source: A. Taxonomy · p. 2
  • At the application level, the survey covers pedestrians, vehicles, drones, and robots, including learned motion patterns for PDR and ZUPT.It also discusses existing-work limitations, challenges, and future opportunities.Source: A. Taxonomy · p. 2

B. Comparison with Other Surveys

The survey distinguishes its deep-learning-based inertial-positioning focus from broader machine-learning and older positioning surveys. It then outlines the survey’s organization and reviews classical inertial-navigation mechanisms and measurement errors.

B. Comparison with Other Surveys

  • Deep-learning-based inertial-positioning surveys are relatively scarce; a broader machine-learning inertial-sensing survey exists, while surveys on pedestrian positioning, indoor positioning, step-length estimation, and pedestrian dead reckoning do not cover recent deep-learning solutions,,,.The authors describe their article as the first survey to discuss deep-learning-based inertial positioning thoroughly and deeply.Source: B. Comparison with Other Surveys · p. 2

C. Survey Organization

  • Sections II–V cover classical mechanisms, calibration, inertial-navigation algorithms, and sensor fusion; Sections VI–IX turn to applications, followed by datasets and comparisons in Section X.Source: C. Survey Organization · pp. 2–3

II. CLASSICAL INERTIAL NAVIGATION MECHANISMS

  • The classical-mechanisms section covers strapdown navigation, PDR, ZUPT, and sensor fusion, with PDR and ZUPT discussed for pedestrian tracking.Source: §II · p. 3

A. Inertial Measurement Model

  • Low-cost MEMS errors include deterministic bias, nonorthogonality, misalignment, scale-factor, and temperature-dependent errors, plus random noise and long-term random-walk noise.The random errors are challenging to model and eliminate; Allan variance models random sensor-error processes for calibration.Source: A. Inertial Measurement Model · p. 3

B. Strapdown Inertial Navigation System

Strapdown inertial navigation updates orientation, velocity, and position from body-frame inertial measurements. Measurement errors can be amplified through integration, producing inertial drift.

B. Strapdown Inertial Navigation System

  • Orientation is updated by inferring a rotation matrix using the Rodrigues formula.The body-to-navigation rotation relates the two frames.Source: B. Strapdown Inertial Navigation System · p. 3
  • Body-frame accelerations are rotated into the navigation frame and corrected for gravity before integration into velocity and position.The IMU measures body-frame linear acceleration and angular rate; the navigation-frame acceleration is then integrated to update velocity and location.Source: B. Strapdown Inertial Navigation System · p. 3
  • Even small measurement errors can be exponentially amplified, causing inertial error drift in low-cost MEMS systems.The article notes that high-precision laser or fiber sensors can keep measurement error small, while current MEMS size and cost limits make compensation necessary.Source: B. Strapdown Inertial Navigation System · p. 3

C. Domain Specific Knowledge

The section surveys domain-specific and learned approaches to reducing inertial positioning drift, including pedestrian methods, sensor fusion, and neural calibration. It also describes their operating boundaries and the need for data-driven models that tolerate measurement errors.

1) Pedestrian Dead Reckoning:

  • PDR detects steps, estimates heading and stride length, then updates location, avoiding acceleration double integration but remaining vulnerable to step and stride errors.Its Weinberg stride formula uses segmented accelerations and user height; dependence on walking periodicity limits PDR to pedestrian navigation,.Source: 1) Pedestrian Dead Reckoning · p. 3

2) Zero-velocity Update:

  • ZUPT uses detected still phases as zero-velocity observations in a Kalman filter to limit open-loop drift, but depends on a truly stationary foot.Incorrect still-phase detection or small motion disturbances can cause drift, and ZUPT is limited to pedestrian tracking.Source: 2) Zero-velocity Update · p. 4

D. Integrating IMU with Other Sensors

  • Fusing IMU data with cameras, LiDAR, UWB, or magnetometers can improve pose accuracy and robustness, but availability, environment dependence, calibration, initialization, and synchronization matter.Visual perception may be unavailable or environment-dependent, affecting inertial positioning's egocentric property.Source: D. Integrating IMU with Other Sensors · p. 4

E. Discussion

  • Domain-specific knowledge such as walking models or scene geometry can constrain inertial drift, while data-driven models can extract such knowledge from large inertial datasets.The discussion frames this as a potential way to improve inertial positioning accuracy and robustness amid imperfect modeling, measurement errors, and environmental influences.Source: E. Discussion · p. 4

III. LEARNING TO CALIBRATE INERTIAL SENSOR

  • A direct neural calibration approach maps raw inertial measurements to calibrated measurements, learning and correcting errors from labeled data.The quality of the training dataset significantly affects model performance.Source: §III · p. 4
  • A ConvNet trained on low-precision IMU inputs and high-precision IMU references removed some sensor error, but was not validated in real navigation.Obtaining high-precision IMU reference data can be costly.Source: §III · pp. 4–5
  • Orientation-based calibration learns gyroscope outputs through orientation estimation; OriNet reported approximately 80% improvement in orientation performance on a public drone dataset.Calib-Net uses a dilation ConvNet to compensate gyro noise, reduces orientation error versus raw IMU integration, and improved localization when incorporated into VIO, outperforming representative VIOs such as VINS-mono,.Source: §III · p. 5, Figure 4 · p. 5
  • Calibration models can automatically learn error models without human intervention, but sensor or user changes can shift data distributions and reduce performance.Further analysis is needed to determine which noise types learning-based calibration can effectively remove.Source: §III · p. 5

IV. LEARNING TO CORRECT IMU INTEGRATION

Deep learning corrects IMU integration by learning motion quantities or incorporating them into navigation filters. The survey groups these methods into displacement learning, acceleration correction, and velocity-aided filtering, while also describing orientation-estimation approaches.

Learning displacement

  • IONet learns 2D polar-vector displacements from segmented IMU windows, while TLIO learns 3D displacements and covariances from gravity-aligned inertial data.IONet reports error within 3 meters 90% of the time in a two-minute pedestrian-walking scenario; it requires high-precision pose labels and degrades on data unlike its training set.Source: §IV · pp. 6–7
  • In 3–7-minute human-motion scenarios, TLIO keeps localization error within 3 meters 90% of the time by feeding learned displacements and covariances into an extended Kalman filter.The filter estimates orientation, velocity, location, and IMU bias.Source: §IV · p. 7

Velocity-based acceleration correction

  • RIDI predicts velocity vectors to correct linear accelerations before double integration; RoNIN uses a heading-agnostic frame and velocity losses, while NILoc maps velocity histories to global location.RIDI uses human walking speed as a prior; NILoc may lack a unique motion-pattern fingerprint in open, symmetrical, or repetitive areas.Source: §IV · p. 7

Velocity-aided filtering

  • A separate category treats learned speed or walking velocity as a Kalman-filter observation to constrain inertial-positioning drift, with one method also predicting filter noise.This is described as similar to ZUPT, but it uses full speeds rather than zero velocity.Source: §IV · pp. 7–8

Orientation estimation

  • IDOL first learns orientation, rotates inertial data into an appropriate frame, and then learns position; another approach estimates orientation from magnetic data and combines it with learned odometry.These approaches address the dependence of several inertial-odometry methods on device orientation.Source: §IV · p. 8

V. LEARNING BASED IMU INTEGRATED POSITIONING

Robots, vehicles, and VR/AR devices commonly carry multiple navigation sensors, motivating multimodal learning to map sensor data to pose.

Motivation

  • Robots, vehicles, and VR/AR devices may carry GNSS, cameras, IMUs, and LIDAR sensors.The survey frames these platforms as settings for multimodal navigation.Source: §V · p. 8
  • Multimodal learning is proposed as a way to fuse information from multiple sensors.The passage motivates models that combine sensor modalities rather than treating each sensor separately.Source: §V · p. 8
  • The proposed learning goal is a mapping from multimodal sensor data to pose.The passage describes designing learning models for this mapping.Source: §V · p. 8

A. Learning Based Visual-Inertial Positioning

Deep-learning approaches fuse visual and inertial data for pose estimation, while related IMU/GNSS methods use neural models to support filtering and navigation during signal outages.

A. Learning Based Visual-Inertial Positioning

  • VINet combines image features from a ConvNet with IMU-sequence features from an LSTM to map inputs to a 6-dimensional pose, but remains less accurate than state-of-the-art VIO methods despite greater noise robustness than traditional VIO.It is trained on KITTI and EuroC datasets.Source: A. Learning Based Visual-Inertial… · pp. 8–9
  • On KITTI, selective soft- or hard-feature fusion improves deep VIO performance by 5%–10% over direct feature concatenation.The reported useful visual and inertial features vary with motion: inertial features contribute more to rotation rate, while visual features are used more to increase linear velocity.Source: A. Learning Based Visual-Inertial… · p. 9
  • Self-supervised VIO uses multi-view geometry, including novel-view synthesis, rather than pose labels; reported work finds that adding inertial data improves pose accuracy, particularly rotation estimation.The methods described derive pose transformations from IMU sequences or integrate inertial and visual features through attention.Source: A. Learning Based Visual-Inertial… · p. 9

B. Learning based IMU/GNSS Integrated Positioning

  • Neural models support GNSS/INS navigation by compensating inertial drifts, correcting filtering errors, or refining filter parameters and noise covariances.The surveyed approaches include GNSS-outage methods using denoised inertial data or learned observation vectors within Kalman-filter frameworks.Source: B. Learning based IMU/GNSS Integrated… · pp. 9–10
  • During GPS outages, the LSTM-based SL-SRCKF learns observation vectors and filter parameters, with stronger error-prediction ability than other neural networks across various outage conditions.It is introduced as a self-learning square-root cubature Kalman filter.Source: B. Learning based IMU/GNSS Integrated… · p. 10

C. Learning to Fuse IMU with Other Sensors

The survey reviews learning-based fusion of IMU with modalities beyond visual-inertial and GNSS navigation, then turns to deep learning for pedestrian dead reckoning and its stride and heading estimates.

C. Learning to Fuse IMU with Other Sensors

  • Deep learning-based LiDAR-, thermal-, and radar-inertial odometry uses selective fusion or IMU-derived transformations, and the surveyed methods report improved pose accuracy and robustness from including IMU data.DeepTIO and MilliEgo use attention-based feature reweighting; an unsupervised LiDAR-inertial method uses IMU-derived motion for novel-view synthesis.Source: C. Learning to Fuse IMU with Other… · p. 10

VI. LEARNING TO CORRECT PEDESTRIAN INERTIAL POSITIONING

  • For pedestrian navigation, deep learning is applied to PDR and ZUPT, while PDR drift is linked to inaccurate stride and heading estimates.The survey identifies step detection, dynamic step-length estimation, and walking-heading estimation as targets for learning.Source: §VI · p. 10, A. Learning to Correct Pedestrian Dead… · p. 10

A. Learning to Correct Pedestrian Dead Reckoning

  • SmartStep reports 99% step-detection accuracy across motion modes, while StepNet reports a 2.1%–3.2% error rate against traditional static step-length estimation.Data-driven step detection does not require fixed IMU placement, specific motion modes, pre-calibration, or threshold setting; domain adaptation is also used for stride estimation across device-attachment modes.Source: A. Learning to Correct Pedestrian Dead… · p. 10
  • Learned heading methods address unconstrained device orientation and device-to-pedestrian misalignment; one reports a median heading error of 10° on unseen data.PDRNet replaces step-length and heading modules with neural networks, and its experiments find joint learning outperforms separate regression.Source: A. Learning to Correct Pedestrian Dead… · p. 10

B. Learning to Correct Zero-Velocity Update

The section reviews learned zero-velocity detection for pedestrian navigation and learned inertial positioning and sensor fusion across vehicles, drones, and robots. It also describes fusion approaches for vehicle, robotic, and pedestrian applications.

B. Learning to Correct Zero-Velocity Update

  • Mixed human motions make reliable threshold selection difficult, while learned classifiers identify the zero-velocity phase used to decide when ZUPT updates system states.An example six-layer LSTM takes IMU sequences, typically 100 consecutive data points, and outputs a probability of stillness or motion at the current timestep.Source: B. Learning to Correct Zero-Velocity… · pp. 10–11
  • Over 34% localization error reduction versus fixed threshold-based ZVDs was reported for an LSTM-based method, which was also more robust across walking, running, and stair climbing.The approach classifies whether the user is still or moving from sequences of IMU data; a ConvNet-based adaptive ZUPT is also described.Source: B. Learning to Correct Zero-Velocity… · p. 11

VII. LEARNING TO CORRECT INERTIAL POSITIONING ON VEHICLES, UAV AND ROBOTIC PLATFORMS

  • Across vehicle, drone, and robotic platforms, studies learn motion or error information for positioning, including drone displacement prediction, car speed and zero-velocity detection, and lightweight or high-frequency robot odometry.AbolDeepIO showed competitive performance against VINS-mono; TinyOdom reduced model size by 31 to 134 times and had 2.5–12 m localization error within 60 seconds; one legged robot navigated a mine for 20 minutes at 400 Hz.Source: §VII · p. 11
  • Deep learning-based inertial positioning is presented as promising across pedestrians, vehicles, drones, and robots, with model efficiency considered for resource-constrained deployment.The section describes learned models as mitigating error drift and improving positioning accuracy.Source: §VII · p. 11

VIII. LEARNING SENSOR FUSION FOR IMU INTEGRATED POSITIONING APPLICATIONS

  • For vehicle navigation, deep learning models IMU/GNSS error drifts or learns filtering parameters; for visual-inertial systems, learned features address fragility from occlusion, image degradation, and illumination changes.Self-supervised visual-inertial approaches use multi-view geometry between consecutive images without high-precision pose labels.Source: §VIII · pp. 11–12
  • Pedestrian fusion approaches compress visual-inertial models for efficiency and combine IMUs with thermal or mmWave radar for pose estimation in degraded-visibility settings.The cited examples use generative frameworks to extract features from thermal images or noisy mmWave radar point clouds, including smoke-filled environments.Source: §VIII · p. 12

IX. LEARNING BASED HUMAN MOTION ANALYSIS AND ACTIVITY RECOGNITION

This section distinguishes human motion analysis and activity recognition from inertial positioning, then introduces public datasets used in inertial-positioning research. It describes datasets for vehicles, drones and robots, and pedestrians.

IX. LEARNING BASED HUMAN MOTION ANALYSIS AND ACTIVITY RECOGNITION

A. Human Motion Analysis

  • Human motion analysis reconstructs pose or motion rather than localizing users, using body-worn IMUs for tasks including gait, gesture, and full-body pose estimation.Examples include recurrent models reconstructing or estimating pose from six IMUs and a neural kinematics estimator paired with a physics-aware motion optimizer.Source: A. Human Motion Analysis · p. 12

B. Human Activity recognition (HAR)

  • Human activity recognition uses inertial data to classify activities, with one ConvNet-based model reporting 97% accuracy versus 96% for SVM-based models.Other described approaches include LSTM class probabilities and a framework combining automatically extracted and hand-crafted features for real-time recognition on low-end devices.Source: B. Human Activity recognition (HAR) · p. 12

X. DATASETS AND EVALUATION METRICS

  • The survey presents five public datasets and evaluation metrics, and compares representative methods on two widely used pedestrian datasets.The section identifies KITTI, EuRoC MAV, OxIOD, RONIN, and SIMD as datasets used in inertial-positioning research.Source: §X · p. 12

A. The Inertial Positioning Datasets

  • KITTI provides car-driving images, LiDAR, IMU, and GPS/IMU ground truth; EuRoC MAV provides synchronized stereo-video and IMU data across 11 flight trajectories with motion-capture and laser-tracker ground truth.KITTI inertial data are recorded at 100 Hz, while EuRoC images are recorded at 20 FPS and IMU measurements at 200 Hz.Source: A. The Inertial Positioning Datasets · pp. 12–13
  • OxIOD, RONIN, and SIMD capture pedestrian motion with varied device placements and scenarios, ranging from 158 OxIOD sequences to more than 4,500 SIMD trajectories.RONIN includes 100 subjects with unrestricted phone orientation and placement; SIMD includes more than 150 volunteers across four cities and over 700 km of walking trajectories.Source: A. The Inertial Positioning Datasets · p. 13

B. Evaluation Metrics and Results

The section compares traditional and learning-based pedestrian inertial positioning on OxIOD and RONIN using trajectory-error metrics. It also concludes that deep learning offers promising approaches to calibration, drift compensation, and multimodal fusion.

B. Evaluation Metrics and Results

  • ATE is the average RMSE between actual and predicted locations over the full trajectory, while RTE is the average RMSE within a specified time interval.Lower ATE and RTE indicate better performance; the comparison uses both metrics on OxIOD and RONIN.Source: B. Evaluation Metrics and Results · p. 13
  • IONet outperforms PDR on RONIN, while PDR performs well on simpler, smoother OxIOD trajectories; RoNIN outperforms IONet and PDR significantly, and TinyOdom is comparable to RoNIN on OxIOD but lags on RONIN.RoNIN assumes correct orientation and uses a heading-agnostic, gravity-aligned frame; the comparison is summarized in Table V.Source: Table V · p. 13, B. Evaluation Metrics and Results · p. 13

XI. CONCLUSIONS AND DISCUSSIONS

  • The survey concludes that deep learning has produced promising approaches for inertial sensor calibration, drift compensation, and multimodal sensor fusion.It also discusses existing challenges and future opportunities in the field.Source: §XI · pp. 13–14

A. Benefits

The section describes learned function approximation, parameter estimation, and adaptation as benefits of deep learning for inertial positioning. It also identifies generalization and explainability as challenges for real-world use.

1) Learn to approximate complex and varying function:

  • Deep networks can approximate complex, varying factors in inertial positioning, calibrate measurement noise, and estimate velocity or displacement without IMU integration.The section also describes learned step-length estimation as an alternative to empirical equations in PDR.Source: A. Benefits · p. 14, 1) Learn to approximate complex and… · p. 14

2) Learn to estimate parameters:

  • Data-driven models can estimate Kalman-filter parameters and classify zero-velocity phases, reducing reliance on manually set parameters and update decisions.The section also describes reinforcement learning for discovering calibration-algorithm parameters.Source: 2) Learn to estimate parameters · p. 14

3) Learn to self-adapt in new domains:

  • Transfer learning and self-supervised learning are presented as ways to adapt inertial models to new domains, including changed sensor attachments and training without high-precision pose labels.The cited visual-inertial approaches use novel-view synthesis as a self-supervision signal.Source: 3) Learn to self-adapt in new domains · p. 14

1) Generalization and Self-learning:

  • Performance may degrade when test domains differ from training domains, and the surveyed models lack comprehensive evaluation over long-term operation and varied devices, users, and scenes.The authors say these gaps make real performance in open environments difficult to determine.Source: 1) Generalization and Self-learning · p. 14

2) Black-box and Explainability:

  • Deep networks are criticized as black boxes, and learned positioning quantities lack the concrete mathematical models available in traditional inertial navigation.The authors call for estimating uncertainty and investigating the governing mathematical or physical models behind learned methods.Source: 2) Black-box and Explainability · p. 14

3) Efficiency and Real-World Deployment:

Real-world deployment of deep inertial positioning faces constraints in model efficiency, data and benchmarks, and reliability. The review outlines research directions spanning physical constraints, new learning methods, sensor fusion, and robustness.

3) Efficiency and Real-World Deployment:

  • Deep positioning models carry substantial computation and memory burdens, making lightweight, efficient models important for low-end devices and real-world deployment.The review also identifies latency, safety, and reliability as design considerations.Source: 3) Efficiency and Real-World Deployment · p. 15

4) Data Collection and Benchmark:

  • A lack of a widely adopted inertial-positioning benchmark, alongside costly data collection and difficult ground-truth labeling, hinders fair comparisons.Training data should span users, platforms, motion dynamics, and sensors to support generalization.Source: 4) Data Collection and Benchmark · p. 15

5) Failure Cases and Physical Constraints:

  • DNNs may produce large, abrupt errors without physical constraints, so failure cases matter in safety-conscious real-world applications.The review suggests imposing physical constraints or combining learning with physical models.Source: 5) Failure Cases and Physical… · p. 15

6) New Deep Learning Methods:

  • Future work may explore transformers, diffusion models, and generative models, alongside transfer, reinforcement, contrastive, unsupervised, and meta-learning.The review also points to neural rendering and voice synthesis as sources of insight.Source: 6) New Deep Learning Methods · p. 15

7) Deep Sensor Fusion:

  • Deep sensor fusion must address diverse data formats, temporal synchronization, calibration, real-time processing, dynamic environments, and limited labeled data.Deep learning can learn fusion strategies, synchronization, and calibration from data while adapting across applications.Source: 7) Deep Sensor Fusion · p. 15

8) Robustness and Reliability:

  • Extreme conditions can challenge model adaptation in safety-critical settings; proposed reliability measures include diverse training data, adversarial testing, monitoring, adaptive algorithms, and certification.The review discusses autonomous vehicles as an example of a safety-critical domain.Source: 8) Robustness and Reliability · p. 15
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