Abstract

This concept paper proposes a roadmap for integrating road curvature estimation models into open mobility data standards such as Telemachus.
Building upon recent curvature-aware simulation results (P008, P009) and validated by field data from a 3-way GPS/OSM/IGN comparison, the goal is to define consistent metadata, validation metrics, and interoperability rules for the representation of road curvature in datasets and APIs.

1. Motivation

Curvature estimation underpins safety, energy optimization, and digital mapping.
However, current open standards (e.g., OSM, SENSORIS) lack consistent definitions for curvature, radius, or grade uncertainty.
Telemachus provides a unique opportunity to formalize these as semantic fields linked to real and simulated telemetry.

2. Methodological Basis

The integration relies on three building blocks:

• Empirical curvature models from literature (ACME 2016, IFAC 2023, RoadRisk 2020);
• Simulation contracts from RS3 curvature pipelines (P009);
• Validation metadata through curvature_radius, curvature_sign, and curvature_confidence fields in Telemachus schema.

3. Proposed Standardization

We propose to introduce a Road Geometry Extension in Telemachus v1.1:

• geometry_curvature_radius (m)
• geometry_curvature_sign (+1 left / −1 right)
• geometry_grade_angle (°)
• geometry_confidence (0–1)
• source_geometry (enum: [simulated, sensor, map])

These fields will enable standard interoperability across simulation, telemetry, and map fusion systems.

4. Implementation Path

1. Prototype schema in telemachus-spec/rfcs/RFC-0015-RoadGeometry.md;
2. Validate with RS3 simulated datasets;
3. Field dataset now available: 14 trips (67 km) with 3-way curvature comparison (GPS / OSM / IGN BD TOPO), providing empirical ground truth for schema validation (see Section 6);
4. Publish open dataset (Telemachus Curvature Benchmark v1.0);
5. Draft a white paper (IEEE IV 2026 / ITS World Congress).

5. Expected Impact

• Harmonized representation of curvature across sensors and maps.
• Reusable open datasets for risk, energy, and comfort analysis.
• Enhanced reproducibility and safety research collaboration.

6. Field Validation — First 3-Way Curvature Comparison

The need for standardized curvature fields was empirically demonstrated through the first 3-way comparison of curvature estimates from three independent sources on the same road network:

Dataset: 14 trips (67 km) recorded by a commercial telematics device in an urban/periurban environment (France, 2025). GPS traces at 1 Hz were matched against OSM (via OSRM) and IGN BD TOPO (19.8M road segments, full France coverage).

Results (representative trip, 14.8 km):

Key observations for standardization:

1. Source matters more than method: The same 3-point radius algorithm produces median curvatures ranging from 97 m (IGN) to 259 m (OSM) — a 2.6× factor — depending solely on the source geometry. Any standard MUST include a source_geometry field.

2. GPS curvature is noisy but informative: The 1 Hz GPS overestimates curvature (125 m vs 97 m IGN ground truth) due to positioning noise, but correctly identifies the distribution of tight, medium, and gentle curves. A confidence or noise_model field would quantify this.

3. IGN outperforms OSM for curvature: The IGN BD TOPO (median 97 m) is 2.6× more accurate than OSM (259 m) for curvature estimation, consistent with findings from a prior Normandy comparison. The proposed geometry_curvature_radius field in Telemachus v1.1 should indicate the reference source.

4. Multi-source fusion is viable: The three sources are complementary — OSM for broad coverage, IGN for geometric precision, GPS for real driving lines. The Telemachus standard should support curvature arrays with per-point source provenance.

These results strengthen the case for the RFC-0015 curvature extension proposed in Section 3, and provide the first empirical validation of the need for source-aware curvature metadata.

References

• Drosescu A. et al. (2016) Road Curvature Measurement Using IMU/GPS.
• IFAC World Congress (2023), Visual–Inertial Road Curvature Estimation.
• Road Geometry Risk Estimation Model (2020).
• Telemachus Specification (2025), Open Mobility Data Standard.
• RoadSimulator3 (2025), Curvature Simulation Framework.