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Highway Traffic State Estimation with Mixed Connected and Conventional Vehicles

Nikolaos Bekiaris-Liberis, Claudio Roncoli, Markos Papageorgiou

arXiv:1504.06879v1math.OC

TL;DR

Reliable real-time traffic-state estimates are needed for highway control, while roadside detectors are costly and connected vehicles can provide mobile measurements. The paper estimates connected-vehicle share with a conservation-based Kalman-filter approach; simulations show successful estimation across traffic conditions and robustness to filter tuning. Under the stated assumptions, that share supports estimates of total density and flow in selected segments.

  • Problem

    Highway control needs reliable real-time traffic-state estimates, while roadside detectors entail considerable purchase, installation, and maintenance costs.

    Source: §I · p. 1

  • Method

    A linear time-varying conservation-law model and Kalman filter estimate connected-vehicle percentage using connected-vehicle information and total-flow measurements.

    Source: §I · p. 2, §IV · pp. 6–7

  • Results

    Simulations show successful connected-vehicle percentage estimation in congested and free-flow conditions, fast convergence from remote initial values, and robustness to the Kalman-filter tuning parameter Q.

    Source: C. Evaluation of the Performance of… · p. 5

  • Takeaways & Limitations

    Under the stated assumptions, estimating connected-vehicle percentage supports total density and flow estimation in arbitrarily selected highway segments.

    Source: §I · p. 2

    The approach relies on connected-vehicle flow and density measurements; an alternative using only reported average speeds remains ongoing research.

    Source: §IV · p. 7

Abstract

from arXiv · show

A macroscopic model-based approach for estimation of the traffic state, specifically of the (total) density and flow of vehicles, is developed for the case of "mixed" traffic, i.e., traffic comprising both ordinary and connected vehicles. The development relies on the following realistic assumptions: (i) The density and flow of connected vehicles are known at the (local or central) traffic monitoring and control unit on the basis of their regularly reported positions, and (ii) the average speed of conventional vehicles is roughly equal to the average speed of connected vehicles. Thus, complete traffic state estimation (for arbitrarily selected segments in the network) may be achieved by merely estimating the percentage of connected vehicles with respect to the total number of vehicles. A model is derived, which describes the dynamics of the percentage of connected vehicles, utilizing only well-known conservation law equations that describe the dynamics of the density of connected vehicles and of the total density of all vehicles. Based on this model, which is a linear time-varying system, an estimation algorithm for the percentage of connected vehicles is developed employing a Kalman filter. The estimation methodology is validated through simulations using a second-order macroscopic traffic flow model as ground truth for the traffic state. The approach calls for a minimum of spot sensor-based total flow measurements {according to a variety of possible location configurations.

I. INTRODUCTION

The paper reframes highway traffic-state estimation in mixed traffic as estimating the connected-vehicle share, given connected-vehicle data and an assumption of similar average speeds. It develops a conservation-law model and Kalman-filter estimator for that share, with simulation validation.

I. INTRODUCTION

  • Prior work had addressed traffic modeling and control with vehicle automation and communication systems, motivating further methods for modeling, estimation, and control.The introduction cites examples using both microscopic and macroscopic approaches.Source: §I · p. 1
  • Connected vehicles can act as mobile sensors, potentially reducing the number and cost of roadside spot sensors needed for traffic monitoring.The paper targets mixed traffic across connected-vehicle penetration rates.Source: §I · p. 1
  • Estimating connected-vehicle percentage can provide total density and flow for arbitrarily selected highway segments, given connected-vehicle measurements and roughly equal average speeds.A minimum of conventional traffic-volume measurements, for example at highway entries and exits, is also required.Source: §I · pp. 1–2
  • A linear time-varying conservation-law model and Kalman filter estimate the connected-vehicle percentage, with the design demonstrated against a second-order macroscopic traffic model.The model uses conservation equations for connected-vehicle density and total density, without requiring speed modeling such as a fundamental diagram.Source: §I · p. 2

II. MODEL DERIVATION FOR THE PERCENTAGE OF CONNECTED VEHICLES

The section derives a segment-level model for connected-vehicle percentage from conservation dynamics for total and connected-vehicle densities. Its formulation relies on connected-vehicle reports, average-speed equivalence, and selected conventional total-flow measurements.

II. MODEL DERIVATION FOR THE PERCENTAGE OF CONNECTED VEHICLES

  • The model uses discrete conservation dynamics for total and connected-vehicle densities to derive the dynamics of connected-vehicle percentage under an equal-average-speed assumption.The highway is divided into N discrete segments; the model's variables are indexed by segment and time.Source: §II · p. 2
  • The percentage at the highway exit is the system output, obtained using the measured total exit flow.The section describes the inverse of the connected-vehicle percentage and its output role.Source: §II · pp. 2–3
  • Connected-vehicle segment densities and flows, as well as their ramp flows, are obtained from regularly received vehicle messages.The equal-average-speed assumption is used in the model formulation.Source: §II · p. 3
  • The formulation assumes conventional detectors measure total flows at the highway entry and exit and at on-ramps and off-ramps.The entry flow and ramp flows act as system inputs; the section identifies the exit flow as a measurement.Source: §II · pp. 2–3
  • Alternative mainstream total-flow measurements can replace some ramp measurements without affecting observability.Additional mainstream measurements may also be treated as outputs to potentially increase filter responsiveness; this is under investigation.Source: §II · p. 3
  • Under certain conditions, the later extension removes the requirement to measure total off-ramp flows.Source: §II · p. 3

A. Observability of the System

The system is observable under the stated positivity and boundedness conditions, provided a measurement is taken at the highway’s last segment. The observability argument uses the structure of its observability matrix.

A. Observability of the System

  • The observability analysis treats the system as linear time-varying, with its matrices and input calculated from available quantities.The measurement may differ from the actual quantity because of measurement noise.Source: A. Observability of the System · p. 3
  • Positive, bounded connected-vehicle densities make the observability matrix invertible, so the system is observable after N steps.The matrix is anti-lower triangular, and its anti-diagonal entries are positive under these conditions.Source: A. Observability of the System · p. 3
  • Measuring the connected-vehicle percentage or flow at the last segment is necessary for percentage observability.A sensor placed before the last segment leaves columns of the observability matrix zero.Source: A. Observability of the System · p. 3

B. Kalman Filter

The Kalman filter estimates connected-vehicle percentages from the model and noisy measurements. Those estimates, together with available connected-vehicle data, yield total-flow and density estimates for each segment.

B. Kalman Filter

  • The filter uses a noisy measurement and tuning parameters Q and R; in the ideal noise model, these represent process- and measurement-noise covariances.The paper notes that tuning may be needed because the system equations are relatively complex.Source: B. Kalman Filter · p. 4
  • The estimator’s initial conditions are specified by μ and H, representing the initial state mean and autocovariance in the ideal Gaussian case.This interpretation applies when the initial state is Gaussian.Source: B. Kalman Filter · p. 4
  • The Kalman filter estimates inverse connected-vehicle percentages, which are combined with available connected-vehicle data to estimate total flow and density at every segment.The resulting total-state estimates are indicated at the filter output.Source: B. Kalman Filter · p. 4

C. Evaluation of the Performance of the Estimator Based on a METANET Model as Ground Truth

A preliminary simulation uses second-order METANET as ground truth to assess the estimator. The filter estimates connected-vehicle percentages in both tested traffic conditions and is reported to be robust to its Q tuning parameter.

C. Evaluation of the Performance of the Estimator Based on a METANET Model as Ground Truth

  • Second-order METANET, whose average vehicle speed has its own dynamics, supplies ground truth for this preliminary assessment.The simulation uses the total- and connected-vehicle density and flow equations.Source: C. Evaluation of the Performance of… · p. 4
  • The simulation distinguishes measurement noise on entry, exit, and ramp flows from process noise affecting the speed and flow equations.The noise statistics are summarized in Table II.Source: C. Evaluation of the Performance of… · p. 4, Table II · p. 4
  • In both tested traffic conditions, the filter successfully estimates connected-vehicle percentages, with very fast convergence from remote initial values.The resulting total-density estimates are also shown for the evaluated segments.Source: C. Evaluation of the Performance of… · p. 5
  • With R fixed at 100 over T = 1080, the relative performance index indicates robustness to the Kalman filter's Q tuning parameter.The index is evaluated as Q varies.Source: C. Evaluation of the Performance of… · p. 5

D. The Case of Unmeasured Total Flow at Off-Ramps

For unmeasured total flow at off-ramps, the approach derives an alternative model for estimating connected-vehicle percentages from assumed off-ramp flow relations. The resulting system is observable under stated conditions and is applied in a METANET-based simulation.

D. The Case of Unmeasured Total Flow at Off-Ramps

IV. CONCLUSIONS

The conclusions present connected-vehicle percentage estimation with a Kalman filter and report its effectiveness in simulation against a second-order macroscopic model. They also describe the off-ramp extension and identify further estimation and validation work.

IV. CONCLUSIONS

  • The authors report effective connected-vehicle percentage estimation in simulation using a second-order macroscopic traffic model as ground truth.The approach estimates total traffic state through the percentage of connected vehicles.Source: §IV · pp. 6–7
  • The paper discusses applying the methodology when total off-ramp flow is unmeasured.The conclusions frame this as a possibility rather than a separately reported validation result.Source: §IV · p. 7
  • An alternative total-density estimator using only connected-vehicle average speeds remains ongoing research.It is intended to relax the need to measure connected-vehicle flows and densities; the two estimation approaches are also under comparison.Source: §IV · p. 7
  • Future work includes fixed-sensor placement, microscopic-simulation validation, and handling unmeasured on-ramp flow using additional mainstream measurements.Source: §IV · p. 7
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