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Estimating Acceleration and Lane-Changing Dynamics Based on NGSIM Trajectory Data
Christian Thiemann, Martin Treiber, Arne Kesting
TL;DR
NGSIM positions contain noise that makes direct velocity and acceleration extraction unreliable. The paper develops boundary-aware smoothing, uses the recovered dynamics for traffic and lane-change analyses, and finds systematic detector underestimation alongside a target-lane velocity advantage before lane changes.
Problem
Positional noise amplified by numerical differentiation limits direct use of NGSIM data for velocity- and acceleration-dependent traffic analyses.
Method
The paper applies a symmetric exponential moving-average smoothing method with boundary handling, then uses smoothed trajectories for detector, traffic-distribution, and lane-change analyses.
Results
Stationary-detector estimates underestimate critical times-to-collision, while discretionary lane changes show a noisy, significant velocity advantage in the target lane that decreases immediately before changing.
Takeaways & Limitations
Smoothed NGSIM dynamics support quantitative analysis of traffic quantities and lane-changing behavior that cannot reliably use the raw positional derivatives.
Takeaways & Limitations
The lane-change-duration definition measures only the interval during which a vehicle occupies two lanes and therefore provides a lower bound; 5–6 s may be more realistic when preparation and post-processing are included.
Abstract
from arXiv · showhide
The NGSIM trajectory data sets provide longitudinal and lateral positional information for all vehicles in certain spatiotemporal regions. Velocity and acceleration information cannot be extracted directly since the noise in the NGSIM positional information is greatly increased by the necessary numerical differentiations. We propose a smoothing algorithm for positions, velocities and accelerations that can also be applied near the boundaries. The smoothing time interval is estimated based on velocity time series and the variance of the processed acceleration time series. The velocity information obtained in this way is then applied to calculate the density function of the two-dimensional distribution of velocity and inverse distance, and the density of the distribution corresponding to the ``microscopic'' fundamental diagram. Furthermore, it is used to calculate the distributions of time gaps and times-to-collision, conditioned to several ranges of velocities and velocity differences. By simulating virtual stationary detectors we show that the probability for critical values of the times-to-collision is greatly underestimated when estimated from single-vehicle data of stationary detectors. Finally, we investigate the lane-changing process and formulate a quantitative criterion for the duration of lane changes that is based on the trajectory density in normalized coordinates. Remarkably, there is a very noisy but significant velocity advantage in favor of the targeted lane that decreases immediately before the change due to anticipatory accelerations.
Introduction
NGSIM offers unusually extensive vehicle trajectories, but positional noise makes direct velocity and acceleration analysis unreliable. The paper introduces smoothing and applies the recovered dynamics to microscopic traffic measures, detector comparisons, and lane-change analysis.
- Data basis: NGSIM recorded thousands of vehicles across multiple datasets, creating a valuable basis for validating and calibrating microscopic traffic models.The Prototype Dataset captured 4733 vehicles, while a later recording captured 5648 vehicles at the same location.
- Research gap: Direct use of NGSIM positions is unsuitable for velocity- and acceleration-dependent analyses because numerical differentiation greatly amplifies positional noise.This limitation affects applications such as car-following and lane-changing model testing and fuel-consumption estimation.
- Approach: The paper proposes smoothing that enables NGSIM trajectories to support analyses using velocity and acceleration information.The approach is designed to address the noise introduced when dynamics are derived from positions.
- Applications: Smoothed velocities support distributions of velocity, inverse distance, time gaps, and times-to-collision, including the microscopic fundamental diagram.These quantities are evaluated across velocity and velocity-difference conditions.
- Applications: The study also compares virtual stationary-detector measurements with trajectory-derived values and proposes a quantitative lane-change-duration method.The introduction frames these as applications of the smoothed trajectory data.
Extracting the Velocity and Acceleration Information
The paper filters noisy NGSIM trajectories before differentiation-based analysis, selecting an operation order and dataset-adaptive smoothing widths. Boundary-aware smoothing is important because short trajectories make edge effects consequential for velocity, acceleration, and lane-change estimates.
- Data artefacts: Two thirds of Prototype accelerations exceed ±3 m/s2, and sample trajectories show implausible switches between hard acceleration and deceleration several times per second.Later I-80 and US-101 datasets are more realistic, but approximately 10% of accelerations still exceed ±3 m/s2.
- Smoothing method: The analysis applies a symmetric exponential moving average filter to trajectories before further data processing.The filter is intended to correct artefacts in the supplied position, velocity, and acceleration information.
- Boundary handling: Boundary-aware windows reduce smoothing widths near trajectory ends, preserving symmetric windows when data are limited.The smoothing width is expressed in real time and converted to dataset-specific datapoint units through Δ = T/dt.
- Method comparison: The proposed filter is more accurate but slower than a larger-step alternative equivalent to moving-average filtering for velocities and compounded moving averages for accelerations.The comparison is explicitly presented as a speed-versus-quality trade-off.
- Boundary handling: Smoothing positions before differentiation is discouraged because changing offsets near boundaries bias velocity and can create acceleration jumps.Large position-smoothing widths can also smear trajectories and increase estimated lane-change durations.
- Smoothing method: Differentiating first and then smoothing all three variables better reproduces artificial benchmark trajectories than smoothing positions before differentiation.The paper therefore selects the second operation order, while noting that boundary regions prevent the methods from being equivalent everywhere.
- Parameter selection: A smoothing width of about 4 s is suggested for acceleration because noise-induced acceleration variance drops rapidly before the remaining variance becomes nearly constant.The estimate is based on acceleration-variance behavior for vivid trajectories across smoothing widths.
- Parameter selection: Noise amplification by differentiation motivates weaker smoothing for positions and velocities than for acceleration.The selected widths are Tx = 0.5 s, Tv = 1 s, and Ta = 4 s.
Results
Virtual-detector comparisons show which spatial and temporal traffic quantities can be recovered from trajectory data and where stationary measurements become unreliable. The analysis also characterizes stopped-traffic headways, time gaps, inverse TTC, and lane-changing dynamics.
- Measurement comparison: Virtual loop detectors represent stationary measurements, while space-parallel lines represent momentary measurements in trajectory data.This framework compares temporal and spatial quantities at corresponding intersections in the space-time plot.
- Microscopic fundamental diagram: 8.3 m for cars and 9.7 m for trucks: mean stopped-vehicle headways are right-skewed and cannot be obtained from stationary detector data.The distribution mode is approximately 7 m for cars and 8 m for trucks, with a smaller second peak at 14 m.
- Time gap distribution: Time-gap distributions are largely indifferent to measurement method, although stationary measurements shift spatial gaps to larger values in jammed traffic.Spatial-gap distributions agree well in free and bound traffic.
- Time gap distribution: 2.6 s, 1.9 s, and 2.0 s: mean time gaps in jammed, bound, and free traffic, respectively.The time-gap mode shifts from approximately 1.5 s in jammed traffic to 1 s in free traffic; larger velocity differences correspond to larger time gaps.
- Time-to-collision: 0.8% of datapoints: critical positive TTC values below 5 s in free traffic are underestimated by stationary measurements by about a factor of 2.The inverse TTC distribution is especially sensitive to spatial-gap errors, particularly when gaps are small.
- Lane changes: 5–6 s: trajectory-density modes provide a rough lane-change duration estimate, while the occupancy-based definition supplies only a lower bound.The lower-bound definition measures the interval during which a vehicle occupies two lanes; preparation and post-processing make 5–6 s realistic.
- Lane changes: Approximately 1 m/s: the destination-lane leader gains a mean velocity advantage before lane changes.The advantage rises before the maneuver, indicating anticipatory actions by drivers.
Discussion and Future Research
The filtered NGSIM trajectories support empirical analyses of traffic interactions, detector-estimation errors, and lane-changing behavior. The discussion highlights both practical applications and the need for more sophisticated filtering.
- Future research: Determining filter parameters is inherently difficult because excessive smoothing can suppress acceleration information, motivating more sophisticated, possibly nonlinear filters.The discussion frames this as an area requiring further research.
- Detector-based estimation: Critical times-to-collision are underestimated by a factor of 2 and more when inferred from single-vehicle data at stationary detectors.Virtual stationary detectors were used to quantify errors in estimating spatial quantities from temporal data, with relevance to safety-related applications.
- Lane-changing applications: A noisy but significant velocity difference favors the target lane before discretionary lane changes, implicating velocity differences alongside gaps in lane-changing decisions.The authors also identify accelerations as a possible factor considered in lane-changing models.
- Lane-changing applications: NGSIM trajectory data enable empirical investigation of strategic and tactical actions that prepare for or facilitate lane changes.This includes actions by lane-changing drivers and cooperative actions by other drivers, such as zip-like merging.
- Modeling applications: Velocity and acceleration data support empirical tests and parameter calibration for car-following and lane-changing models.Acceleration data can also examine how the local traffic environment influences longitudinal driving behavior.
- Modeling applications: Velocity and acceleration information can be combined with characteristic maps to estimate fuel consumption and pollutant emissions in real traffic situations.The paper identifies this as an application of the processed trajectory data under congestion.