Patent ID: 7383153

Claim:
A method for determining maximum conjunction probability of rectangular-shaped objects, comprising: getting primary and secondary object dimensions ht, wd, lt where lt≧wd≧ht; computing a combined object radius OBJ as OBJ=r 1 +r 2 where one-half of a diagonal for a rectangular solid encompassing the primary object is denoted as r 1 , where r 1 = ( lt I ) 2 + ( wd 1 ) 2 + ( ht 1 ) 2 2 and a greatest half-width (r 1p ) perpendicular to r 1 is r 1 ⁢ p = It 1 · 1 - ( It 1 2 · r 1 ) 2 one-half of a diagonal for a rectangular solid encompassing the secondary object is denoted as r 2 , where r 2 = ( It 2 ) 2 + ( wd 2 ) 2 + ( ht 2 ) 2 2 and a half-width (r 2p ) perpendicular to r 2 is r 2 ⁢ p = It 2 · 1 - ( It 2 2 · r 2 ) 2 ; computing a width factor (w) as w = min ⁡ ( r 1 ⁢ p + r 2 , r 1 + r 2 ⁢ p ) OBJ ; projecting relative positions of the primary and secondary objects onto an encounter plane to compute a miss distance (dist); obtaining a combined covariance aspect ratio (AR); and computing a maximum conjunction probability (P max ) as P max = OBJ 2 2 · π · AR · ( σ y ) 2 · ∫ - w w ⁢ ∫ - 1 - y 2 1 - y 2 ⁢ exp ⁡ [ ( - 1 2 ) · [ ( dist + x · OBJ AR · σ y ) 2 + ( y · OBJ σ y ) 2 ] ] ⁢ ⅆ x ⁢ ⅆ y where x and y are variables of integration in the encounter plane such that x lies along a major axis of the combined object radius OBJ, y lies along a minor axis of the combined object radius OBJ, and σ y is a covariance standard deviation along the minor axis in the encounter plane.