1. A cross-traffic alert system for a host vehicle, comprising: an automotive proximity sensing detector mountable to a host vehicle and configured for tracking a relative position of a target object to the host vehicle over a first plurality of time points, where at any given time point, a trajectory of target object and a heading of the host vehicle intersect at a cross-path angle; and a processor for receiving the digital signals and processing the digital signals to calculate the cross-path angle by solving an optimization problem which minimizes variance, across the first plurality time points, of a perpendicular path distance at each time point between a trajectory of target object and a common reference position (across the first plurality of time points) for the host vehicle.