An intersection assistance system includes at least one vehicle sensor and a gap estimator. The vehicle sensor is configured to obtain vehicle information on vehicles approaching the intersection along a main roadway. The gap estimator is configured to estimate gap information relating to a gap between the vehicles based on the vehicle information. The gap information includes a length of the gap, a location of the gap, and a velocity of the gap. In a method of obtaining information for use in assisting a driver of an entering vehicle to safely enter an intersection, vehicle information is obtained on vehicles traveling toward the intersection on a main roadway. Next, gap information is estimated relating to a gap between the vehicles based on the vehicle information. The gap information includes a length of the gap, a location of the gap, and a velocity of the gap.