Two-Dimensional Collision in Parallel Paths

A particular case of “blind approach” is considered: that in which two vehicles travel with different speeds along parallel mean paths in a two-dimensional region. It is shown that the problem of calculating the probability of safe passage can be put in the form of equivalent zero-crossing problems for stationary, nonzero mean random processes, within a relatively long record. A lower bound for the probability of absence of zero-crossings is given in the form of a finite sum and some arguments on convergence are discussed.