A computer program product for providing Signal Phase and Timing (SPaT) messages for influencing operation of a vehicle, wherein the SPAT messages include timing parameters for a minimum-end-time, likely-time, and maximum-end-time for a next signal switch of at least one signal group of a traffic light system affecting the vehicle, and wherein the computer product is tangibly embodied in a non-transitory memory and includes instructions, which, when executed by at least one processor of a computer cause the computer to:
- receive signal state data from a controller controlling one or more signal groups (S1 to S4) of a traffic light system, wherein the signal state data of a particular signal group (S*) comprises a current signal state (SD*) of the respective signal group (S*), and
- information about a time interval (Te*) which has elapsed since a last state switch of the respective signal group (S*);
- generate a feature vector (FV) for the one more signal groups (S1 to S4), the feature vector comprising for each of the one or more signal groups at least:
- a first value indicating the elapsed time (T*p) since a latest switch of the respective signal group (S*) to a pass-state (1), and a second value indicating the elapsed time (T*s) since a latest switch of the respective signal group (S*) to a stop-state (0);
- predict, by at least one quantile regression neural network with a particular current feature vector (T*p, T*s) as test input, for at least one of the one or more signal groups (S1 to S4), as one or more outputs (O1), a low conditional quantile (Ql) representing the minimum-end-time (ETmin), a medium conditional quantile (Qm) representing the likely-time (Tl) and a high conditional quantile (Qh) representing the maximum-end-time (ETmax) for the at least one of the one or more signal groups (S1 to S4), wherein the at least one quantile regression neural network has been trained with stochastic gradient descent, on past feature vectors of at least a subset of the one or more signal groups of the traffic light system and respective low, medium and high conditional quantile outputs, using a loss function being a sum of individual loss functions over the at least one of the one or more signal groups (S1 to S4), and a corresponding one or more conditional quantiles, wherein the individual loss functions are hinge loss functions (HL);
- composing a SPAT message including the predicted minimum-end-time (ETmin), likely-time (Tl), and maximum-end-time (ETmax) of the at least one of the one or more signal groups (S1 to S4);
- provide the SPaT message to a receiving device associated with the vehicle, and
- if the time interval between an actual point in time (t−1) and the current predicted likely-time (Tl-1) is below a predefined filter time interval (FTI)
- a current maximum-end-time prediction (Etmax-1) which predicts a later point in time than a previous filtered maximum-end-time prediction (Etmax-2) is filtered out,
- a current minimum-end-time prediction (Etmin-1) which predicts an earlier point in time than the previous filtered minimum-end-time prediction (Etmin-3) is filtered out,
- else,
- only filtering out the current minimum-end-time prediction (Etmin-2) which predicts an earlier point in time than the previous filtered minimum-end-time prediction (Etmin-3).