Physics-guided AI turns sparse GPS and camera data into citywide traffic volumes

Demonstrated on Manhattan in New York City, the approach delivers measurable improvements in accuracy over estimates based on floating car data alone, and it produces calibrated traffic volumes with uncertainty estimates in an environment where most road segments are never directly observed.

Floating Car Data, or FCD, derived from GPS-equipped probe vehicles, mobile devices, and fleet services, has been increasingly adopted by cities and transportation agencies to monitor traffic conditions. Its appeal lies in broad spatial coverage and high temporal resolution. Yet the data capture only a partial picture of urban traffic. Probe-vehicle penetration rates vary significantly across locations, time periods, and travel modes, so the resulting representation of traffic states is biased and incomplete, particularly on low-volume arterial roads. Surveillance cameras, by contrast, provide high-fidelity traffic information, but only at a limited set of locations, and their high installation and maintenance costs restrict widespread deployment in dense urban environments.

The scale of the undersampling problem in Manhattan is striking. The study network consists of 2,394 directed road segments with lengths ranging from 50 to 2,000 meters, and traffic volumes are on the order of one million vehicle trips per day. On average, probe trajectories from the commercial INRIX dataset account for less than five percent of true traffic volume, and arterial road segments are represented by only a handful of measurements. Penetration rates can exceed fifteen percent in commercial districts with intense taxi and ride-hailing activity, such as Midtown, while residential areas dominated by private vehicles, like the Upper East Side, may fall below five percent. Penetration also shifts systematically with time of day and day of week, as commuters, taxis, delivery fleets, and recreational travelers participate differently in location-based services.

To counter this, the researchers analyzed a history of vehicle trajectories over three consecutive months, from September through November 2025, covering 1,031,206 vehicle trips within the Manhattan study area. Assuming approximately stationary traffic conditions within a season, they aggregated trajectories into representative one-month datasets built from time-of-week bins, raising the effective penetration rate to as high as twenty percent. Both single-month and aggregated datasets were discretized into fifteen-minute intervals. Ground-truth reference measurements came from nine municipal traffic cameras, six covering both directions of traffic and three covering one direction, processed with a computer vision pipeline using the YOLO26 object detection model optimized for low-resolution 352 by 240 pixel footage.

The framework’s first stage rests on physics. Traffic dynamics are governed by conservation laws and capacity constraints, formalized in the Cell Transmission Model, a discrete time and space conservation-law model with an established fundamental diagram and explicit supply-demand constraints. Rather than fitting model parameters directly to biased probe counts, which would largely fit the sampling bias rather than the traffic dynamics, the team extracted CTM-consistent kinematic features from the aggregated trajectories. A triangular fundamental diagram maps observed speeds to pseudo-density, demand, and supply, from which the model computes physically admissible traffic transitions. Calibration factors for quantities such as free-flow speed and congestion wave speed are comparatively identifiable under these assumptions.

Those physics-derived features feed a Graph Neural Network that learns the spatiotemporal evolution of traffic states across the road network. Spatially, the network performs message passing over road segments to capture inter-segment dependencies and spillover effects; temporally, transformer-style self-attention layers represent recurrent and nonstationary patterns, while cyclical hour-of-day and day-of-week encodings plus regime indicators inject daily and weekly periodicity beyond the input window. The model outputs a probabilistic forecast of count increments for each segment, trained end-to-end with data-fit losses alongside soft regularizers enforcing network-level vehicle conservation and segment capacity limits. Signal timing, absent from the FCD, is absorbed implicitly through mesoscopic space-time averaging and through the learned deviations from the CTM baseline, which capture signal delay, turning friction, queue spillback, and intersection interactions.

The second stage calibrates these predictions against camera observations using a progressive data assimilation scheme based on the Ensemble Square-Root Kalman Filter. A positive, time-varying calibration factor maps GNN predictions to camera counts, estimated in log-space and decomposed into baseline, hour-of-day, day-of-week, and traffic-regime components. Ten camera-observed road segments were used to estimate the calibration field, while five were held out exclusively for validation. Crucially, a topology-informed, flow-weighted transition matrix propagates the learned corrections to camera-unobserved locations, with influence decaying along flow-connected paths, so that segments with no flow-reachable connection receive no direct update and instead revert conservatively toward a network-wide prior.

The results show the framework aligning predictions into close agreement with camera observations despite severe undersampling. Across all validation segments, calibrated predictions achieved positive coefficients of determination, indicating predictive superiority over a mean-baseline model. Arterial segments showed low errors and strong correlation with ground truth, while freeway segments, carrying roughly 900 vehicles per fifteen minutes compared with about 150 on arterials, showed larger absolute errors that partly reflect their higher volume ranges, though scale-invariant metrics remained positive. Averaged over all camera observations, the overall coefficient of determination rose from 0.524 with month-specific FCD to 0.801 with three-month aggregation, with the largest gains concentrated on arterial roads, precisely where per-bin sample sizes are lowest.

Ablation and benchmark comparisons reinforced the design rationale. Removing the CTM-derived features degraded performance, and their advantage grew as FCD penetration was progressively subsampled downward, supporting the argument that physics-derived structure matters most in the low-penetration regime the framework targets. Benchmarked against state-of-the-art architectures including STGCN, a DCRNN-style graph-convolution GRU, and AGCRN, each given identical FCD inputs and a static hour-of-week calibration factor, the baselines reproduced diurnal structure but overestimated volume magnitudes, yielding negative or near-zero coefficients of determination on held-out segments. The proposed framework, with a compact backbone of roughly 35,000 parameters and an EnSRF calibration stage taking under a minute for a full one-week validation window, attained substantially positive coefficients of determination, and a flow-weighted propagation kernel outperformed alternative adaptive approaches prone to overfitting under sparse supervision.

The practical significance extends beyond Manhattan. The framework operates entirely on data sources most cities already own, commercial FCD and existing traffic cameras, requires no new sensor deployment, and accommodates varying sensor availability while producing road-level volumes suitable for operational monitoring and evaluation of transportation policies. Because transportation agencies increasingly procure commercial FCD as their primary network-wide data source, decisions on signal control, curb management, and policy evaluation currently rest on volumes that may be severely understated; a principled bias-correction mechanism addresses that gap directly. The authors note limitations and future directions, including extending the framework to account for holidays, severe weather, incidents, and construction, refining intersection and signal effects, evaluating transferability across multiple urban networks, and adapting the method to online estimation when streaming probe data offer sufficient coverage.

Subject of Research: Traffic volume estimation from floating car data and sparse traffic cameras using a physics-informed graph neural network with Kalman filter calibration

Article Title: Harnessing floating car data, traffic camera observations, and network flow analysis for traffic volume estimation

Article References: Kosikova, A., Turkcan, M. K., Darrat, A., & Smyth, A. (2026). Harnessing floating car data, traffic camera observations, and network flow analysis for traffic volume estimation. Discover Civil Engineering, 3(1), Article 257. https://doi.org/10.1007/s44290-026-00657-x

Image Credits: AI Generated

DOI: 10.1007/s44290-026-00657-x

Keywords: floating car data, traffic volume estimation, graph neural network, Cell Transmission Model, Ensemble Square-Root Kalman Filter, traffic cameras, Manhattan, data assimilation, probe vehicle penetration rate, flow-weighted transition matrix, uncertainty quantification, urban traffic monitoring