Systems and methods for estimating traffic signal information

1. A method of estimating traffic signal information and adjusting an operation of an on-board system of a vehicle, the method comprising:

obtaining positioning system data from each of a plurality of vehicles, wherein said positioning system data for each of the plurality of vehicles comprises position and velocity of a vehicle as functions of time;

for an intersection having a traffic signal, estimating an average acceleration of the vehicles when leaving the intersection;

for each of a subset of the vehicles, estimating a start time at which the respective vehicle leaves the intersection based on the positioning system data for the respective vehicle and the average acceleration;

wherein the subset of vehicle is determined by:

selecting vehicles whose positioning system data include data points within a distance interval surrounding the intersection, wherein at least a first one of the data points is before the intersection and at least a second one of the data points is after the intersection,

removing vehicles from the subset whose velocity is lower, at a point either before the intersection or after the intersection, than a threshold;

estimating a cycle time of the traffic signal by:

for each pair of consecutive vehicles in the subset, calculating a difference between the start times of the vehicles, and

solving an optimization problem based on the differences and the cycle time; and

adjusting the operation of the on-board system of the vehicle based, at least in part, on an estimated start of a future green phase of the traffic signal.

2. The method according to claim 1 , further comprising:

fitting a Gaussian mixture model to a histogram of a remainder of a division of the difference and the cycle time; and

estimating a signal offset caused by a schedule change of the traffic signal based on clusters within the Gaussian mixture model.

3. The method according to claim 1 , wherein the average acceleration is estimated based on the positioning system data for the vehicles and a location of a stop bar behind which the vehicles stop at the intersection.

4. The method according to claim 3 , wherein estimating the average acceleration comprises using a least-square estimation based on data points of velocity versus traveled distance corresponding to the vehicles and by removing outliers of said data points.

5. The method according to claim 1 , wherein estimating the average acceleration comprises using a least-square estimation based on data points of velocity versus traveled distance corresponding to the vehicles and by removing outliers of said data points.

6. The method according to claim 1 , wherein the subset of the vehicles is further determined by:

for each of the remaining vehicles after said removing, estimating an intersection delay based on the positioning system data for the respective vehicle; and

removing vehicles whose estimated intersection delay is negative or zero.

7. The method according to claim 1 , wherein each data set is obtained from at least one of a cellular telephone or a navigation device within the vehicle.

8. The method according to claim 1 , wherein an update frequency of the positioning system data is not greater than twice per minute.

9. A method of estimating traffic signal information and adjusting an operation of an on-board system of a vehicle, the method comprising:

obtaining positioning system data from each of a plurality of vehicles, wherein said positioning system data for each of the plurality of vehicles comprises position and velocity of a vehicle as functions of time;

for an intersection having a traffic signal, estimating an average acceleration of the vehicles when leaving the intersection;

for each of a subset of the vehicles, estimating a start time at which the respective vehicle leaves the intersection based on the positioning system data for the respective vehicle and the average acceleration;

estimating a cycle time of the traffic signal by:

for each pair of consecutive vehicles in the subset, calculating a difference between the start times of the vehicles, and

solving an optimization problem based on the differences and the cycle time;

adjusting the operation of the on-board system of the vehicle based, at least in part, on an estimated start of a future green phase of the traffic signal;

fitting a Gaussian mixture model to a histogram of a remainder of a division of the difference and the cycle time; and

estimating a signal offset caused by a schedule change of the traffic signal based on clusters within the Gaussian mixture model.

10. The method according to claim 9 , wherein the average acceleration is estimated based on the positioning system data for the vehicles and a location of a stop bar behind which the vehicles stop at the intersection.

11. The method according to claim 9 , wherein estimating the average acceleration comprises using a least-square estimation based on data points of velocity versus traveled distance corresponding to the vehicles and by removing outliers of said data points.

12. The method according to claim 9 , wherein the subset of the vehicles is determined by:

selecting vehicles whose positioning system data include data points within a distance interval surrounding the intersection, wherein at least a first one of the data points is before the intersection and at least a second one of the data points is after the intersection;

removing vehicles whose velocity is lower, at a point either before the intersection or after the intersection, than a threshold;

for each of the remaining vehicles, estimating an intersection delay based on the positioning system data for the respective vehicle; and

removing vehicles whose estimated intersection delay is negative or zero.

13. The method according to claim 9 , wherein each data set is obtained from at least one of a cellular telephone or a navigation device within the vehicle.

14. The method according to claim 9 , wherein an update frequency of the positioning system data is not greater than twice per minute.