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LSTM-Based Zero-Velocity Detection for Robust Inertial Navigation

Brandon Wagstaff, Jonathan Kelly

arXiv:1807.05275v2cs.ROcs.HC

TL;DR

Fixed-threshold zero-velocity detectors are not robust to changes in gait motion, limiting accurate zero-velocity-aided inertial navigation. The paper replaces the detector with an LSTM that classifies stationary periods from raw IMU data, reducing positioning error across evaluated motions. The detector also operates across users, shoe types, and IMU placements without retraining.

  • Problem

    Fixed-threshold zero-velocity detectors do not perform reliably across gait motions, although accurate midstance detection is needed to limit error accumulation in zero-velocity-aided INS.

    Source: §I · p. 1

  • Method

    An LSTM replaces the traditional detector, producing binary zero-velocity classifications from raw IMU data for fusion with the INS.

    Source: §I · pp. 1–2, 1) Stance Hypothesis Optimal… · p. 3

  • Results

    34.8% average ARMSE reduction compared to the best-performing threshold from a baseline detector across building trials.

    Source: B. Building Trials · p. 7

  • Takeaways & Limitations

    The learned detector generalizes across users, shoe types, and foot IMU placements without retraining.

    Source: §I · p. 2, §VI · p. 8

Abstract

from arXiv · show

We present a method to improve the accuracy of a zero-velocity-aided inertial navigation system (INS) by replacing the standard zero-velocity detector with a long short-term memory (LSTM) neural network. While existing threshold-based zero-velocity detectors are not robust to varying motion types, our learned model accurately detects stationary periods of the inertial measurement unit (IMU) despite changes in the motion of the user. Upon detection, zero-velocity pseudo-measurements are fused with a dead reckoning motion model in an extended Kalman filter (EKF). We demonstrate that our LSTM-based zero-velocity detector, used within a zero-velocity-aided INS, improves zero-velocity detection during human localization tasks. Consequently, localization accuracy is also improved. Our system is evaluated on more than 7.5 km of indoor pedestrian locomotion data, acquired from five different subjects. We show that 3D positioning error is reduced by over 34% compared to existing fixed-threshold zero-velocity detectors for walking, running, and stair climbing motions. Additionally, we demonstrate how our learned zero-velocity detector operates effectively during crawling and ladder climbing. Our system is calibration-free (no careful threshold-tuning is required) and operates consistently with differing users, IMU placements, and shoe types, while being compatible with any generic zero-velocity-aided INS.

I. INTRODUCTION

Foot-mounted IMUs support infrastructure-free localization, but drift makes accurate midstance detection essential to zero-velocity-aided navigation. This work replaces motion-specific or threshold-based detection with an LSTM that learns zero-velocity classifications from raw IMU data.

I. INTRODUCTION

  • Accurate zero-velocity detection matters because foot-mounted INS uses midstance velocity pseudo-measurements to limit dead-reckoning intervals and position-error growth.Without this aid, position error grows cubically with time.Source: §I · p. 1
  • Fixed-threshold detectors can fail when gait type or intensity changes, while a single learned detector avoids requiring motion to be classified into predefined types.The authors argue that discrete classification can limit detection during transitions and undefined motions.Source: §I · p. 1, §II · p. 2
  • The LSTM outputs binary zero-velocity classifications from raw IMU data and operates across users, IMU placements, and shoe types without retraining.The model is trained with ground-truth labels spanning a variety of gait motions.Source: §I · pp. 1–2

II. RELATED WORK

  • Park et al. used separate motion-classification and stationary-detection SVMs, evaluated only for walking and not within a zero-velocity-aided INS.Their method also applies a moving-average filter to SVM output; the LSTM approach instead uses one detector independent of motion type.Source: §II · p. 2
  • Rather than replace the filtering architecture with an end-to-end learned INS such as IONet, the authors learn only the zero-velocity detector and retain the INS.The paper presents zero-velocity detection as an integral part of the architecture.Source: §II · p. 2

III. LSTM-BASED ZERO-VELOCITY DETECTION

The detector is trained on labeled raw IMU measurements, with labels derived from zero-velocity detectors tuned to minimize INS position error. The labeling procedure assumes trials maintain uniform motion type and intensity.

III. LSTM-BASED ZERO-VELOCITY DETECTION

  • Training and some testing used a 200 Hz foot-mounted IMU, worn under the laces of subjects’ preferred running shoes.The sensor was mounted near the center of the right foot.Source: §III · p. 2

A. Zero-Velocity Ground Truth Labelling

  • The dataset pairs raw IMU measurements at each timestep with a binary stationary-or-moving label, whose accurate assignment is non-trivial.Motion type, IMU placement, shoe type, and ground surface can affect zero-velocity detection.Source: A. Zero-Velocity Ground Truth Labelling · p. 2
  • Labels are taken from the detector producing minimum position ARMSE, under the assumption that this yields the most accurate available zero-velocity labels for a trial.Each trial’s motion type and intensity were kept as uniform as possible; changing them would make a fixed threshold unsuitable for generating accurate labels.Source: A. Zero-Velocity Ground Truth Labelling · p. 3

1) Stance Hypothesis Optimal Estimation (SHOE) Detector:

The SHOE detector uses a generalized likelihood ratio test to assess whether the IMU is moving. It accepts the stationary hypothesis when the test output falls below a threshold.

1) Stance Hypothesis Optimal Estimation (SHOE) Detector:

  • SHOE uses a generalized likelihood ratio test (GLRT) to indicate how likely the IMU is to be moving.The output is defined over a window of inertial measurements.Source: 1) Stance Hypothesis Optimal… · p. 3
  • When the GLRT output falls below threshold γ, SHOE accepts the stationary hypothesis.Under that hypothesis, measured specific force is due strictly to gravity and angular rotation rate is zero.Source: 1) Stance Hypothesis Optimal… · p. 3
  • The test uses a window of inertial measurements; its prose-defined quantities include the window’s specific-force mean and local gravity magnitude.The passage also identifies measurement variances for specific force and angular rate.Source: 1) Stance Hypothesis Optimal… · p. 3

2) Angular Rate Energy Detector (ARED):

The section describes threshold-based zero-velocity detectors that use angular-rate energy, acceleration variance, or distances between sample sub-windows to identify stationary periods.

2) Angular Rate Energy Detector (ARED):

3) Acceleration-Moving Variance Detector (AMVD):

  • AMVD computes an accelerometer-variance measure over a sample window and assumes stationarity when that measure falls below threshold γv.The threshold γ is the primary tuning parameter with the largest effect on detection.Source: 3) Acceleration-Moving Variance… · p. 3

4) Memory-Based Graph Theoretic Detector (MBGTD):

  • MBGTD measures average Euclidean distances between samples in two sub-windows and assumes zero velocity when the maximum distance across possible splits falls below γm.Source: 4) Memory-Based Graph Theoretic… · p. 3

5) VICON Midstance Detection:

VICON foot tracking supplies timestep-level midstance labels by differentiating position measurements and thresholding the resulting velocities. The labeling study also shows that detector accuracy and optimal thresholds vary across motions, while the learned detector could approach optimized-detector accuracy.

5) VICON Midstance Detection:

  • VICON position data are numerically differentiated into foot velocities, then thresholded from 0.02 to 0.4 m/s to generate timestep-level zero-velocity labels.Markers were attached to the shoe-mounted IMU, with position recorded at every IMU timestep.Source: 5) VICON Midstance Detection · p. 3

B. Data Collection

  • The VICON dataset comprised 60 trials and approximately 1,025 m of motion from one subject in a roughly 5 × 5 m capture area.Trials included walking, running, crawling, step climbing, and shuffling, typically along circular trajectories.Source: B. Data Collection · p. 3
  • The optimized SHOE detector was most accurate overall, followed by VICON-based detection and then ARED.The table’s “Num. Trials” counts trials in which a detector achieved the lowest ARMSE.Source: B. Data Collection · p. 3, Table I · p. 4
  • The optimized thresholds spanned different values across motion types or intensities, while a single threshold would not attain the optimized detectors’ dynamic-motion accuracies.VICON labeling was treated as optimal for non-walking motions including shuffling, crawling, and step climbing.Source: B. Data Collection · p. 4
  • The LSTM trained on optimized-detector midstance labels could in theory approach their accuracy, and the authors report coming close in Section V-A.The added detector was critical to producing training labels that generalized to non-walking motions.Source: B. Data Collection · p. 4

C. LSTM Network Architecture

The detector uses an LSTM to classify IMU sequences as moving or stationary. Its confidence-filtered outputs remove false positives, which otherwise can cause irreversible error accumulation.

C. LSTM Network Architecture

  • Among the evaluated feedforward and recurrent network structures, the authors found that an LSTM achieved the highest accuracy for this task.They omit a full architecture comparison.Source: C. LSTM Network Architecture · p. 4
  • The recurrent hidden output combines the current input with the previous hidden state and passes the result through an activation function.The associated weight matrices are updated during training.Source: C. LSTM Network Architecture · p. 4
  • LSTMs propagate an internal state updated by input, forget, and output gates, enabling information to persist across timesteps.The internal state provides a direct connection across distant timesteps, supporting backpropagation over long sequences and learning long-range dependencies.Source: C. LSTM Network Architecture · p. 4
  • The detector has six LSTM layers with 80 units each, followed by a fully connected layer producing two softmax confidence outputs for motion and stationary states.The IMU is assumed stationary only when confidence exceeds 0.85, a threshold empirically selected to minimize false-positive error.Source: C. LSTM Network Architecture · p. 4
  • Confidence filtering removes false-positive stationary detections, which can otherwise cause irreversible error accumulation during movement.Figure 2 identifies removed false positives at 35.1 and 36.6 seconds.Source: C. LSTM Network Architecture · p. 4, Figure 2 · p. 4

D. Training

Training uses raw six-channel IMU sequences labeled by the midstance state at each sequence’s final timestep. Rotations, scaling, and jittering augment the training samples, and the reported test accuracy is 97.0%.

D. Training

  • The dataset was split into 51 training trials totaling approximately 840 m and nine test trials totaling approximately 182 m.The test set was used during hyperparameter tuning.Source: D. Training · pp. 4–5
  • Training used 100-timestep, six-channel raw IMU sequences, each labeled by the midstance state at its final timestep, for 420,000 samples overall.Each sequence represents 0.5 seconds of data sampled at 200 Hz.Source: D. Training · pp. 4–5
  • Training augmentation applied random rotations, scaling from 0.92 to 1.02, and zero-mean Gaussian noise with σ = 0.075 to improve invariance to placement, orientation, shoe, and gait factors.The model was trained for 300 epochs with Adam and cross-entropy loss.Source: D. Training · p. 5
  • Training used gradient clipping below magnitude one to avoid exploding gradients, a learning rate of 5 × 10^-3, weight decay of 1 × 10^-5, and minibatches of 800.The learning rate was halved every 30 epochs.Source: D. Training · p. 5
  • The LSTM achieved 97.2% training accuracy and 97.0% test accuracy; hyperparameters were tuned by maximizing test-set accuracy.Results on a validation set are presented in Section V.Source: D. Training · p. 5

IV. SYSTEM OVERVIEW

The system propagates an IMU pose estimate with an error-state extended Kalman filter and fuses detected zero-velocity events as measurements. The implementation stays minimal to make comparisons of zero-velocity detectors clearer.

IV. SYSTEM OVERVIEW

  • The error-state Kalman filter tracks IMU position, velocity, and quaternion orientation in nominal and linearized error states.A nonlinear model propagates the nominal state by integrating accelerations and angular velocities from the IMU.Source: §IV · p. 5
  • The motion model updates position, velocity, and orientation using IMU accelerations and angular velocities over the sampling period, accounting for gravity and quaternion rotation.The nominal state accumulates error, which is estimated separately in the linearized error state.Source: §IV · p. 5
  • A detected zero-velocity event makes velocity error observable, and its approximately zero velocity is fused through the standard EKF measurement update.Zero-velocity measurements can correct errors in all filter states except yaw.Source: §IV · p. 5
  • The system omits optional barometer, magnetometer, map-aided, and multi-IMU improvements so comparisons of learned and existing detectors use a baseline system.The authors emphasize zero-velocity detection rather than these additional localization improvements.Source: §IV · p. 5

V. INERTIAL LOCALIZATION EXPERIMENTS

A single fixed-parameter LSTM model was evaluated in VICON trials against threshold-based detectors. It reduced INS position error without operation-time threshold tuning and approached the optimized-threshold detectors.

V. INERTIAL LOCALIZATION EXPERIMENTS

  • One fixed-parameter model was selected for the highest VICON test-set detection accuracy to evaluate generalization to new data.The experiments included the VICON tracking-area dataset and a separate building dataset.Source: §V · p. 5

A. VICON Laboratory Trials

  • The LSTM closely approximated the optimized-threshold ground truth and outperformed fixed-threshold SHOE and ARED across VICON motion trials.Figure 3 plots error against threshold; the optimized threshold is per trial, whereas fixed thresholds produced larger errors.Source: A. VICON Laboratory Trials · pp. 5–6, Figure 3
  • 60.1% and 51.6%: the LSTM reduced error on the VICON training and test sets, respectively, while approaching optimized-detector accuracy.The test-set reduction indicates generalization beyond the training data.Source: A. VICON Laboratory Trials · p. 6

B. Building Trials

Building trials assessed localization using surveyed floor markers and a 200 Hz VectorNav VN-100 IMU. The LSTM detector reduced average position error relative to fixed-threshold baselines, including across walking, running, and combined motions.

B. Building Trials

  • The approximately 220 m hallway trajectory used surveyed floor markers as position ground truth, with a VectorNav VN-100 IMU operating at 200 Hz.Subjects pressed a trigger when stepping on marker origins so the timestamped IMU poses could be compared with marker positions.Source: B. Building Trials · p. 6
  • Trials included walking, running, and combined walk/run motions, with stairs and a ramp in a supplementary room; the building dataset exceeded 6.6 km.Running error was evaluated at four markers, while walking and combined walk/run error used all eight markers.Source: B. Building Trials · pp. 6–7
  • 34.8%: the LSTM reduced average ARMSE compared with the best-performing fixed-threshold baseline detector across building trials.The baselines used thresholds optimized on the VICON dataset; the comparison covers all collected trials.Source: B. Building Trials · p. 7, Table III · p. 7

C. Evaluation for Varying Motion Type

The LSTM detector remained effective during stair climbing, ladder climbing, and crawling, where SHOE and ARED failed. The conclusion reports generalization across gait types, users, shoes, IMU types, and foot placements.

C. Evaluation for Varying Motion Type

  • The LSTM produced accurate trajectories during stair climbing, ladder climbing, and crawling, while SHOE and ARED failed.The authors attribute the threshold-based detectors’ false positives to small foot rotation rates and angular-velocity dependence.Source: C. Evaluation for Varying Motion Type · p. 8

VI. CONCLUSION & FUTURE WORK

  • The conclusion reports generalization across gait types, users, shoe types, IMU types, and foot placements.The authors identify IMU arrays as a direction for future work to improve the single-IMU detector.Source: §VI · p. 8

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