An extensive analysis and calibration of the Modular Aggregation Algorithm across three categories of for GNSS trajectories data sources

This technical report aims to complement the conference paper (https://doi.org/10.1145/3678717.3691325) by providing additional experiments or further details that could not be included in the paper.

💡 Research Summary

This technical report expands on the conference paper “An extensive analysis and calibration of the Modular Aggregation Algorithm across three categories of GNSS trajectories data sources” by providing a comprehensive description of the Modular and Iterative Aggregation Algorithm (MIAA), its calibration procedures, and extensive experimental validation on three distinct types of GNSS trajectory data: synthetic, multi‑sensor, and crowdsourced.

The authors begin by motivating the work within the context of increasing outdoor recreation and the need to quantify human pressure on ecosystems. GNSS tracks collected from various platforms (e.g., Visorando, Wikiloc) are identified as valuable but heterogeneous sources of spatio‑temporal information. The challenge lies in integrating these data despite differences in sensor quality, canopy cover, sampling density, and possible missing segments.

The report first details the data sets used. Synthetic trajectories are generated by modeling GNSS errors as a second‑order stationary process with three components: a long‑wavelength coordinate‑system error, an intermediate‑wavelength autocorrelated observation error, and a white‑noise component. Covariance functions are built from Gaussian and exponential kernels, and Cholesky decomposition is employed to produce realistic correlated noise. Multi‑sensor data were collected in a controlled field campaign involving five sensor types (smartphone, wrist‑watch, Garmin, Keymaze, professional Ublox) under three canopy conditions (open, moderate, dense). A topometric survey provided a high‑precision ground‑truth reference sampled at ~7 m intervals with sub‑centimetre accuracy. Crowdsourced data were downloaded from two public repositories, focusing on three spatial‑constraint scenarios: ridge (terrain‑constrained), switchback trail (infrastructure‑constrained), and heterogeneous‑shape routes.

MIAA is presented as a modular pipeline consisting of four components: (1) master‑trajectory selection, (2) trajectory‑to‑master matching, (3) representative‑point selection for each matched segment, and (4) aggregation of the representative points. The master is chosen using heuristics that combine trajectory length, average quality scores, and sensor diversity. Matching can be performed with Dynamic Time Warping (DTW) under L∞ or L2 norms, or with the discrete Fréchet distance; the algorithm builds a bipartite graph and solves a maximum‑weight matching to obtain homologous segments. Representative points are derived by analysing the covariance matrix of the matched positions; the direction of minimal variance (principal component with smallest eigenvalue) is selected, and sensor‑specific noise models are incorporated as weights. Aggregation replaces a simple arithmetic mean with a robust M‑estimator (e.g., Huber loss) to mitigate the influence of outliers.

Calibration follows a four‑step protocol: (i) generate a reference track, (ii) simulate N trajectories with the error model, (iii) run MIAA, and (iv) evaluate error against ground truth using two metrics—average positional error (mean absolute distance) and shape deviation (Fréchet distance). Experiments varying N from 5 to 50 show rapid convergence: for N ≥ 10, mean positional error falls below 0.8 m and shape deviation below 1.2 m. DTW‑L2 generally yields lower shape deviation on highly curved sections, while DTW‑L∞ provides more stable matching under abrupt direction changes.

In the multi‑sensor study, 150 trajectories were collected. After calibrating each sensor’s noise characteristics, MIAA achieved an average positional error of 1.1 m and shape deviation of 1.5 m even for the least accurate wrist‑watch data, demonstrating the algorithm’s robustness to heterogeneous noise levels.

Crowdsourced experiments on the French Alps data set confirm the algorithm’s applicability to uncontrolled data. Across the three spatial‑constraint scenarios, MIAA produced aggregated tracks with average positional error ≈ 0.9 m and shape deviation ≈ 1.3 m, outperforming naïve averaging by roughly 30 %. The ridge scenario, which includes steep elevation changes, benefited from the DTW‑L∞ matching option, reducing mismatches caused by large vertical gradients.

The report also discusses termination criteria: the algorithm stops when the average change in aggregated points over three consecutive iterations falls below 0.5 m or after a maximum of 20 iterations. In practice, convergence is reached within 10–15 iterations for all tested data sets.

Limitations are acknowledged. Extreme data loss (e.g., > 60 % of trajectories missing large segments) can prevent convergence, and the selection of heuristic thresholds still requires expert insight. Future work includes real‑time streaming integration, extension to full 3‑D trajectories with elevation modeling, and tighter coupling with GIS knowledge graphs for automated metadata propagation.

Overall, the report demonstrates that MIAA, by explicitly modelling GNSS error correlation, offering flexible matching strategies, and employing robust aggregation, provides a significant improvement over traditional averaging methods for constructing reliable reference paths from heterogeneous GNSS trajectory collections.