Sergey A. Sukhanov (Vympel Corporation), Sergey Yu. Kamensky (Vympel Corporation), Zakhary N. Khutorovsky (Vympel Corporation), Nickolay N. Sbytov (Vympel Corporation), Kyle T. Alfriend (Texas A&M University)
Keywords: Astrodynamics
Abstract:
Efficient solution of the problem of warning of collisions between important spacecraft and other orbiting satellites requires expanding of the catalog of tracked satellites (currently comprising about 15,000 satellites) by an order of magnitude or more. This is a very difficult scientific and technical task. One of the major aspects is the creation of software tools capable of automatic maintenance of such a great catalog in real time. The amount of radar or optical measurements to be processed can reach millions, which is more than order of magnitude greater than the currently existing measurement fluxes.
It is known that the increase of the number of measurements by the order of magnitude results in at least two orders of magnitude increase of computational effort required by the procedures used for correlation of measurements with the catalog. This results in significant problems with processing the measurements in real time. The preliminary “compression” of measurement data acquired during one penetration of the radar’s field of view will essentially (by the order of magnitude and more) reduce the requirements to the computers’ capacity. The compression will happen in case all the single measurements (marks) acquired during one penetration will be replaced by the orbit generated using these measurements. Here we mean that a single radar measurement is the result of measuring radar parameters (range, azimuth, elevation angle and maybe range rate) by one pulse.
Traditionally for orbit determination by one penetration two types of techniques have been used – recurrent and joint processing. The recurrent procedures, convenient for the real time processing are usually based on generalized Kalman filter. The less convenient joint processing techniques are based on different modifications of least squares or least modules techniques. This work suggests and investigates a very simple algorithm combining the features of these two approaches and that is highly efficient for the considered task.
When the errors of single measurements are time correlated and also for all the cases when the statistical characteristics of the errors of single measurements are not known completely, the traditional techniques do not provide the guarantee estimate of the accuracy of acquired estimates. Now this limitation becomes important since the accurate evaluation of collision risk requires coincidence between the real and calculated values of the errors of orbit determination. Now we need the “guarantee” techniques of orbit determination, which along with the estimates of orbital parameters generate the guaranteed intervals or the errors for each of them. In addition, since the traditional techniques are efficient (for linear problem, non – correlated errors of measurements) the guarantee approach should not be less efficient than these methods.
The work formulates the general algorithm based on guarantee approach. It is characterized by significantly greater amount of calculations compared to traditional procedures. However, this san not be treated as a limitation since in the system maintaining the catalog and predicting collision hazard this algorithm is used much more rarely than the traditional technique. The work also presents a simple and elegant modification of the general guarantee approach procedure that has certain geometrical sense. The comparative analysis of this simplified algorithm with the least squares method is given as well.
Mathematical simulation is used for investigation of comparative characteristics of different procedures. This is done under the assumption that the radar measures the local spherical coordinates of the satellite within the zone limited in range (not more than 3000-7000 km) and elevation angle (not more than 40°-60°) with errors of single measurements about tens of meters for the range and several angular minutes for angular coordinates.
Date of Conference: September 1-4. 2009
Track: Astrodynamics