Predictive Avoidance for Ground-Based Laser Illumination

Abstract

Predictive avoidance determines discrete windows of time for safe laser illumination from a ground-based laser platform. That is, the analysis identi es time periods during which the laser will not inadvertently illuminate a satellite. The geometry of the problem is utilized to lter satellites that cannot possibly be illuminated by a speci c laser platform. Further, several nongeometric lters are introduced to lter remaining satellites by removing those which cannot be illuminated by the platform in a speci ed period. Both sets of lters improve the ef ciency of the analysis by reducing the number of state propagations necessary. A method for determining the times of possible accidental illumination using cubic polynomial approximation is also presented. Finally, a test case is run that considers the entire catalog of objects publicly available from the U.S. Space Command. The complete analysis, which considers the entire catalog as potential victims for one target satellite pass, yields veri ed results in less than 3.5 s on a laptop personal computer running at 266 MHz. Nomenclature c(s ) = cubic spline el low = minimum topocentric elevation angle at the laser platform f (t) = function that indicates whether potential victim is in safety cone i PV = inclination of the potential victim p = semilatus rectum r = distance from center of the Earth to edge of the engagement envelope r a = geocentric apogee distance r p = geocentric perigee distance r pl = geocentric position vector of the laser platform r pv/ s = position vector of potential victim relative to the laser platform r sat = position vector for satellite r t / s = position vector of target relative to the laser platform t min = actual time of minimum f (t ) t new = estimate of time of function f (t ) minimum based on c(s ) t start = time at beginning of illumination t stop = time at end of illumination (t 1 , t 2 ) = time interval input for cubic spline v pv/ s = velocity vector of potential victim relative to the laser platform v sat = velocity vector for satellite v t / s = velocity vector of target relative to the laser platform a = separation angle between potential victim and target b = safety cone half-angle c i = order i coef cient D u = maximum geocentric angle between laser platform and potential victim such that it enters the engagement envelope at apogee D u best = geocentric angle between laser platform and orbital plane of potential victim D u max = geocentric angle between laser platform and the edge of the engagement envelope g = angle opposite D u in apogee lter

Probability of a Laser Illuminating a Space Object

“…5 The angularkeep-outregionsof the geometric method may unnecessarilyreduce the solid angle available for laser operation.Rather than preventing inadvertentillumination, the current work develops a method to calculate the probability of a laser beam illuminating a space object. Once the probability is known, the tradeoff can be made between risk of illumination vs the cost of operational delays.…”