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Millimeter Wave Localization with Imperfect Training Data using Shallow Neural Networks

Anish Shastri, Joan Palacios, Paolo Casari

arXiv:2112.05008v2cs.NIcs.LG

TL;DR

Indoor mmWave localization faces complexity in geometry-based refinement and substantial training-data and computation burdens for learned approaches. This paper proposes shallow neural networks trained with imperfect location estimates, and reports comparable or better localization performance than JADE in the evaluated conditions.

  • Problem

    Geometry-based localization can require increasingly complex refinement, while deep-learning approaches may need large training datasets and substantial computation.

    Source: §I · p. 1, C. Summary · p. 2

  • Method

    Shallow neural networks use angular measurements to localize devices and can be trained with imperfect locations computed by angle-based localization algorithms.

    Source: §I · pp. 1–2

  • Results

    With σ=5°, JADE-trained NNs yielded 88% sub-meter errors and a 0.47 m median error, versus 92% and 0.45 m with perfect labels.

    Source: C. Training the NNs with estimated… · p. 5

  • Takeaways & Limitations

    The shallow, device-centric design is presented as suitable for constrained platforms and scalable distributed localization.

    Source: §I · pp. 1–2

Abstract

from arXiv · show

Millimeter wave (mmWave) localization algorithms exploit the quasi-optical propagation of mmWave signals, which yields sparse angular spectra at the receiver. Geometric approaches to angle-based localization typically require to know the map of the environment and the location of the access points. Thus, several works have resorted to automated learning in order to infer a device's location from the properties of the received mmWave signals. However, collecting training data for such models is a significant burden. In this work, we propose a shallow neural network model to localize mmWave devices indoors. This model requires significantly fewer weights than those proposed in the literature. Therefore, it is amenable for implementation in resource-constrained hardware, and needs fewer training samples to converge. We also propose to relieve training data collection efforts by retrieving (inherently imperfect) location estimates from geometry-based mmWave localization algorithms. Even in this case, our results show that the proposed neural networks perform as good as or better than state-of-the-art algorithms.

I. INTRODUCTION

The paper addresses complexity in iterative geometric localization and the data and computation burden of deep learning by proposing shallow, device-centric neural networks trained with imperfect location estimates. It reports sub-meter accuracy in up to 90% of cases across indoor rooms with typical access-point deployments.

I. INTRODUCTION

  • Prior geometry-based schemes can require increasingly complex iterative refinement, while deep neural networks may demand large datasets and substantial computation.Source: §I · p. 1
  • Shallow neural networks are trained using error-prone locations from an angle-based algorithm instead of explicitly collected, well-labeled and calibrated data.Despite imperfect labels, the models achieve accuracy comparable to models trained with perfect data.Source: §I · pp. 1–2
  • Sub-meter accuracy is achieved in up to 90% of cases across rooms of different shapes with a typical number of access points.The evaluation compares the proposed approach with a state-of-the-art scheme in two indoor deployments.Source: §I · p. 2
  • The device-centric approach lets devices estimate their own locations and cooperate to collect training data before operating independently.The paper describes devices uploading training data to a server and receiving a trained model.Source: §I · pp. 1–2
  • The proposed model estimates device coordinates using angle-of-arrival measurements for multipath components in receiver-side angular spectra.Source: §I · p. 2

II. RELATED WORK

The related-work section surveys indoor localization approaches based on mmWave technology and divides them into classical and machine-learning-based schemes.

II. RELATED WORK

  • The survey organizes indoor mmWave localization approaches into classical and machine-learning-based schemes.Source: §II · p. 2

A. Classical mmWave localization systems

The related work covers classical mmWave localization techniques and machine-learning approaches, including their input signals and environmental requirements.

A. Classical mmWave localization systems

  • Triangulation and ADoA-based methods may require device orientation, environmental knowledge, and access-point deployment information; CIR-based AoA and time-of-flight localization also requires environment knowledge.Source: A. Classical mmWave localization systems · p. 2
  • A map-assisted method estimates user location, while another approach uses beam training and ADoAs to localize devices and anchors and map environmental boundaries.The latter was evaluated on 60 GHz hardware, though not on COTS devices.Source: A. Classical mmWave localization systems · p. 2

B. Machine learning-based mmWave localization systems

  • Machine-learning approaches use SNR, RSSI, beam indices, spatial beam SNR, or beam-covariance images for localization, position and orientation classification, or coordinate estimation.The cited approaches include fingerprinting and ResNet-inspired models for LoS and NLoS scenarios.Source: B. Machine learning-based mmWave… · p. 2

C. Summary

The paper contrasts its approach with geometric and deep-learning methods that can require iterative computation, extensive training data, or substantial resources. It proposes a shallow regression network that learns device location from ADoA measurements and can use imperfect location labels.

C. Summary

  • Prior methods may require environment and device-orientation knowledge, increasingly complex iterative refinement, or substantial training data and computation.Source: C. Summary · p. 2
  • The proposed shallow networks use location estimates from a localization algorithm as training labels, then switch to the neural network despite errors in those labels.Source: C. Summary · p. 2

III. PROPOSED LOCALIZATION SCHEME

  • Figure 1 illustrates virtual anchors and first-order reflections as part of the proposed localization scheme.Source: Figure 1 · p. 3

A. Main Idea

  • A shallow regression network learns the relationship between collected ADoA measurements and device locations, and is described as more robust to error-prone training labels.The approach is intended to reduce training-data collection effort and the complexity of accurate geometric localization as measurements accumulate.Source: A. Main Idea · p. 3

B. Input features

The model uses angular information from visible access points and virtual anchors to estimate a client's location. It feeds orientation-invariant ADoA features into a small neural network that regresses the two location coordinates.

B. Input features

  • Sparse angular spectra distinguish line-of-sight and first-order reflected paths; the approach neglects paths with more than one reflection and treats access points and virtual anchors as anchors.Virtual anchors appear as mirror images of physical access points across reflective surfaces.Source: B. Input features · p. 3
  • Using ADoAs relative to a reference MPC yields Na−1 input features and makes location estimation invariant to client orientation.The inputs are formed from AoA measurements collected at the client from different anchors.Source: B. Input features · p. 3

C. Neural network architecture

  • The network takes Na−1 inputs, uses two hidden layers, and outputs two neurons for the client's 2D coordinates.The second hidden layer contains half as many neurons as the first.Source: C. Neural network architecture · p. 3
  • The network learns a nonlinear mapping from ADoA inputs to coordinates; its small size keeps computation to a few matrix multiplications and vector sums.It uses ReLU activations, Adam optimization, and an MSE loss.Source: C. Neural network architecture · pp. 3–4

D. Hyperparameter tuning

The network is optimized by tuning hidden-layer size, dropout, and learning rate to minimize its loss function.

D. Hyperparameter tuning

A. Simulation environment and setup

The simulations evaluate the scheme in rectangular and reverse L-shaped indoor rooms, with noisy AoA measurements and separate training and test trajectories.

A. Simulation environment and setup

  • The rectangular test room measures 15×10 m2 and uses three APs, each mapped to four VAs corresponding to different walls.Source: A. Simulation environment and setup · p. 4
  • The reverse L-shaped room has a 6×10 m2 bottom-left section and an 8×18 m2 right section, covered by three APs.Source: A. Simulation environment and setup · p. 4
  • Fig. 3 depicts the two room shapes and the locations of APs and VAs.Source: Figure 3 · p. 4
  • AoA measurements include zero-mean Gaussian error with standard deviation σ ∈ {5°, 7°, 10°}, reflecting imperfect beam training and non-pencil-shaped beams.Training uses ray-traced AoAs at 30 points along simulated trajectories; a separate test set has 30 trajectories and 900 locations uniformly distributed across each room.Source: A. Simulation environment and setup · p. 4

B. Performance evaluation

In the rectangular room, the neural network and JADE show lower error dispersion than TV and geometric ADoA, while the network matches or exceeds JADE accuracy with constant post-training complexity. In the reverse L-shaped room, both methods reconstruct trajectories accurately, with the network estimates closer to ground truth.

B. Performance evaluation

  • In the rectangular-room comparison, NN and JADE show small dispersion, while TV and ADoA yield larger errors that increase as AoA-error standard deviation σ rises from 5° to 10°.Fig. 4 compares cases with 3 or 4 APs at σ = 5° and 10°.Source: B. Performance evaluation · p. 4, Figure 4 · p. 5
  • The neural network matches or exceeds JADE accuracy while its post-training complexity remains constant, unlike JADE's measurement- and AP-dependent complexity.With four APs, all algorithms have better estimation errors, smaller maximum errors, and less dispersion than with three APs.Source: B. Performance evaluation · p. 5
  • In the reverse L-shaped room, both methods reconstruct the trajectory accurately, with neural-network estimates closer to ground truth than JADE's.The evaluation uses σ = 5°; remaining outliers for both methods are attributed to erroneous AoA values.Source: B. Performance evaluation · p. 5

C. Training the NNs with estimated user locations

Neural networks trained on imperfect JADE location estimates perform comparably to JADE at σ = 5° and better at σ = 10°. With σ = 5°, their sub-meter accuracy is close to that of networks trained with perfect labels.

C. Training the NNs with estimated user locations

  • The imperfect training labels are location estimates from JADE, and the L-shaped-room evaluation uses networks with (18, 13, 7, 2) neurons in each stage.For σ = 5°, the selected hyperparameters are p = 0 and r = 0.006; for σ = 10°, p = 0.05 and r = 0.0004.Source: C. Training the NNs with estimated… · p. 5
  • With σ = 5°, imperfect JADE labels yield sub-meter errors in 88% of cases and a median error of 0.47 m, versus 92% and 0.45 m with perfect labels.Source: C. Training the NNs with estimated… · p. 5
  • Networks trained with JADE estimates perform as well as JADE at σ = 5° and better at σ = 10°.The comparison is shown as location-error CDFs for the L-shaped room, with networks trained using perfect and error-prone data.Source: C. Training the NNs with estimated… · p. 5, Figure 6 · p. 5

D. Impact of number of training samples

As training sets grow, localization errors and their dispersion decrease even with JADE-derived labels; with large datasets, those labels yield nearly true-location accuracy. The conclusion reports sub-meter accuracy in ≈90% of scenarios despite large AoA errors, with no significant degradation from imperfect labels.

D. Impact of number of training samples

V. CONCLUSIONS AND FUTURE WORK

  • The conclusion reports sub-meter accuracy in ≈90% of scenarios with large AoA errors, while imperfect labels do not significantly degrade accuracy.Source: §V · p. 6
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