Patent ID: 7702427
Filing Date: 2010-04-20
Classification: G08G

Abstract:
1. A method for estimating a minimum distance of approach of two aircraft that are airborne, the method comprising: providing information on an initial location vector r0(t=t1;n), on an initial velocity vector r1(t=t1;n) and on an initial acceleration vector r2(t=t1;n) at a selected time t=t1, for each of N aircraft, numbered n=1, . . . , N (N≧2) that are airborne; approximating said location vector r(t;n) for aircrafts number n=n1 and n=n2 (n1≠n2) over a selected time interval [t1,t2] by quadratic vector functions of time, respectively, where t1 is a selected time within a selected time interval [T1,T2], each of the location vectors r(t;n1;app) and r(t;n2;app) substantially describes motion on a great circle in a plane, and the vector coefficients r0;n1), r1(n1), r2(n1), r0(n2), r1(n2) and r2(n2) are chosen to optimally match the vector functions r(t;n1;app) and r(t;n2;app) in the selected time interval [T1,T2]; and estimating a minimum distance of approach d(min) for a magnitude |r(t;n1)−r(t;n2)| of a vector difference, by identifying at least one real time t(min) for which a time derivative of the quantity |r(t;n1)−r(t;n2)| and by interpreting the vector magnitude |r(t=t(min);n1)−r(t=t(min);n2)| as the minimum distance d(min).