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Air traffic management evaluation tool

  • US 7,702,427 B1
  • Filed: 07/30/2004
  • Issued: 04/20/2010
  • Est. Priority Date: 07/30/2004
  • Status: Active Grant
First Claim
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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,
    r(t;

    n
    1;

    app)=r0(n1)+r1(n1)·

    (t−

    t
    1)+r2(n1)·

    (t−

    t
    1)2,
    r(t;

    n
    2;

    app)=r0(n2)+r1(n2)·

    (t−

    t
    1)+r2(n2)·

    (t−

    t
    1)2,
    Δ

    r(t;

    app)=r(t;

    n
    1;

    app)−

    r(t;

    n
    2;

    app)=Δ

    r0+Δ

    r1(t−

    t
    1)+Δ

    r2(t−

    t
    1)2,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)|2 is zero,
    2Δ

    r


    r1+{Δ

    r

    Δ

    r1+2Δ

    r


    Δ

    r2)(t−

    t
    1)+6Δ

    r


    Δ

    r2(t−

    t
    1)2+4Δ

    r


    Δ

    r2(t−

    t
    1)3=0,and by interpreting the vector magnitude |r(t=t(min);

    n1)−

    r(t=t(min);

    n2)| as the minimum distance d(min).

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