The present disclosure relates to an overtaking estimating system for estimation of a minimum overtaking speed of a vehicle. The overtaking estimating system determines in view of a host vehicle a remaining distance of an overtaking lane contiguous to a driving lane of the host vehicle. The system further determines a delta distance between the host vehicle and a preceding vehicle positioned in the host vehicle driving lane. Moreover, the system determines a delta time for the host vehicle to reach the preceding vehicle. The system further determines, based on the delta distance, the delta time and a determined host vehicle speed, a speed of the preceding vehicle. Furthermore, the system determines, based on the remaining distance, the delta distance, the preceding vehicle speed, and an overtaking-affecting parameter, a minimum overtaking speed of the host vehicle for overtaking the preceding vehicle in the remaining distance of the overtaking lane.