1. Introduction

The penetration of connected vehicles (CV) and large‑scale GNSS/IMU telemetry makes trajectory data a cornerstone for mobility analytics, safety applications, eco‑driving, and infrastructure monitoring. Yet, such data often suffer from low sampling rates, GNSS outages, asynchronous IMU/GNSS timestamps, and vendor‑specific compression artifacts.

This paper proposes a unified and reproducible framework to evaluate and improve trajectory quality in connected vehicle datasets. We focus on compressed acquisition, physics‑aware reconstruction, and quality scoring, building bridges between three domains:

• inertial simulation (RS3),
• road‑network‑aware reconstruction (Huang et al., 2023),
• sparse/compressive sampling in CV datasets (CompressiveCV*).

The contribution is threefold:

1. A problem formulation linking sampling, compression, and spatial‑temporal consistency.
2. A reconstruction framework combining compressive sensing (CS), inertial constraints, and topological priors.
3. A standard‑compliant quality assessment pipeline integrated in Telemachus 0.2.

2. Related Work

2.1 GNSS/IMU fusion and trajectory estimation

Placeholder for citations and discussion (e.g., Kalman, invariant filtering, GNSS outages, IMU drift, SmartphoneIMUSpeed2025, DVSE).

2.2 Compressive sensing for mobility datasets

Placeholder for CompressiveCVData2018, CompressiveCVRecovery2018, sparse dictionaries, sampling theory.

2.3 Network‑constrained trajectory reconstruction

Summary of Huang2023-TransitTrajectoryReconstruction: passenger‑vehicle trajectories, hybrid GNSS/opportunistic sensing, graph‑based inference.

2.4 Data quality frameworks

Telemachus 0.2, event consistency, timestamp coherence, signal completeness.

3. Problem Formulation

Define the observed trajectory ( \mathbf{y}(t) ), true trajectory ( \mathbf{x}(t) ), sampling operator ( \Phi ), and reconstruction operator ( \Psi ).

Include placeholders:

• Equation (1): sampling model
• Equation (2): noise decomposition
• Equation (3): regularization (sparsity + inertial + topology)

Introduce the notion of trajectory quality ( Q(\mathbf{x},\hat{\mathbf{x}}) ).

4. Proposed Framework

4.0 Compressive Pipeline Architecture (Reformulated)

The full end‑to‑end chain for connected‑vehicle compressive processing can be expressed as:

1. Compressive acquisition — subsampling (uniform, random, burst), rate reduction, opportunistic GNSS/IMU availability.
2. Inertial reconstruction — sparse dictionaries, IMU constraints, temporal smoothness priors.
3. Network‑aware refinement — Huang2023 graph continuity, topology enforcement.
4. Event extraction — braking/acceleration/turn events derived from reconstructed signals.
5. Quality scoring — Telemachus‑compliant metrics integrating spatial, temporal and event consistency.

4.1 Overview

Pipeline diagram placeholder: RS3 simulation → Subsampling → CS reconstruction → Network‑aware refinement → Quality scoring → Telemachus export.

4.2 RS3 synthetic trajectories

Description placeholder: 10 Hz, realistic IMU noise, ground‑truth curvature, speed profiles.

4.3 Compressive acquisition

Define subsampling strategies (uniform, random, burst‑based).
Placeholder for Algorithm 1: Compressive Acquisition Strategy.

4.4 Reconstruction core

Sparse recovery using dictionaries + inertial constraints.
Network‑aware refinement following Huang et al. (graph continuity).
Placeholder for Algorithm 2: CS‑Network Reconstruction.

4.5 Integration with Telemachus

Describe pivot schema 0.2, GNSS/IMU alignment, metadata fields (telemetry_quality, sensor_alignment, sampling_strategy).

Représentation compressive dans Telemachus 0.2 (Ajout)

Telemachus 0.2 expose désormais des champs normalisés permettant de transporter les métadonnées compressives :

• sampling_strategy : uniform / random / burst
• compression_ratio : rapport d’échantillonnage effectif
• reconstruction_confidence : indice de fiabilité post‑CS
• event_consistency : cohérence des événements reconstruits

Ces attributs permettent d’aligner sources, pipelines compressifs et évaluations qualité dans un même format pivot.

5. Experimental Setup

5.1 Datasets

• RS3 synthetic dataset (placeholder).
• Telemachus‑Datasets real trajectories.

5.2 Baselines

• Linear interpolation
• Kalman smoothing
• Huang‑style graph‑based reconstruction
• Deep inertial models (DVSE)

5.3 Metrics

• RMSE positionnel

• vitesse cumulative drift

• geometric fidelity (curvature error, radius deviation)

• topology adherence score

• coût énergétique smartphone (proxy basé sur la fréquence d’échantillonnage)

• coût data (volume transmis / compression_ratio)

• ratio qualité/coût (métrique composite normalisée Telemachus)

5.4 Experimental protocol

Parameters, sampling rates, noise models — placeholders.

6. Results (Placeholders)

6.1 Quantitative tables

Placeholder for Table 1, Table 2.

6.2 Reconstruction visuals

Placeholder for Figures 1–4: maps, speed profiles, error envelopes.

6.3 Sensitivity analysis

Placeholder text about robustness to subsampling factors 2×–10×.

7. Discussion

Critical analysis placeholder: trade‑offs, generalization limits, network effects, IMU bias sensitivity.

8. Conclusion and Future Work

Summarize benefits of compressive acquisition, integration with Telemachus, roadmap for full paper:

• full experiments,
• ablation studies,
• network‑scale evaluations,
• release of public RS3 dataset + code.

References

Placeholders retained for the main references:

• SmartphoneIMUSpeed2025
• Huang2023-TransitTrajectoryReconstruction
• CompressiveCVData2018
• CompressiveCVRecovery2018