TRAC based sensing for autonomous rendezvous

The Targeting Reflective Alignment Concept (TRAC) sensor is to be used in an effort to support an Autonomous Rendezvous and Docking (AR&D) flight experiment. The TRAC sensor uses a fixed-focus, fixed-iris CCD camera and a target that is a combination of active and passive components. The system experiment is anticipated to fly in 1994 using two Commercial Experiment Transporters (COMET's). The requirements for the sensor are: bearing error less than or equal to 0.075 deg; bearing error rate less than 0.3 deg/sec; attitude error less than 0.5 deg.; and attitude rate error less than 2.0 deg/sec. The range requirement depends on the range and the range rate of the vehicle. The active component of the target is several 'kilo-bright' LED's that can emit 2500 millicandela with 40 milliwatts of input power. Flashing the lights in a known pattern eliminates background illumination. The system should be able to rendezvous from 300 meters all the way to capture. A question that arose during the presentation: What is the life time of the LED's and their sensitivity to radiation? The LED's should be manufactured to Military Specifications, coated with silicon dioxide, and all other space qualified precautions should be taken. The LED's will not be on all the time so they should easily last the two-year mission

Random projections for linear programming

Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known Johnson-Lindenstrauss lemma states that there are random ma- trices with surprisingly few rows that approximately preserve pairwise Euclidean distances among a set of points. This is commonly used to speed up algorithms based on Euclidean distances. We prove that these matrices also preserve other quantities, such as the distance to a cone. We exploit this result to devise a probabilistic algorithm to solve linear programs approximately. We show that this algorithm can approximately solve very large randomly generated LP instances. We also showcase its application to an error correction coding problem.Comment: 26 pages, 1 figur