The Use of Short-Arc Angle and Angle Rate Data for Deep-Space Initial Orbit Determination and Track Association

Transcription

1 The Use of Short-Arc Angle and Angle Rate Data for Deep-Space Initial Orbit Determination and Track Association Dr. Moriba Jah (AFRL) Mr. Kyle DeMars (UT-Austin) Dr. Paul Schumacher Jr. (AFRL)

2 Background/Motivation High-value assets near GEO within a population of sparsely observed or never-seen-before objects Insufficient resources for uninterrupted/persistent tracking of each object Need for automated, near real-time, and robust methods of initial orbit determination to support catalog development and follow-on maintenance

3 Methodology for Angles Only Photon counting device provides dense angles measurements for an apparent number of objects Topocentric Right Ascension and Declination at 500 Hz Measured angles are smoothed over a specified time (e.g. 20 seconds) One pair of angles is used in conjunction with several hypotheses to initiate the process Hypothesize object distances (range magnitude since angles provide range direction) Hypothesize object velocity vector magnitude and direction Multiple Hypothesis Filter is initialized based on ad hoc discretized region in 4-dimensional parameter space N-objects and M-hypotheses per object yields NxM initially equallyweighted individual Unscented Kalman Filters running simultaneously

4 Methodology for Angles and Rates Photon counting device provides dense angles measurements for an apparent number of objects Topocentric Right Ascension and Declination at 500 Hz Measured angles are smoothed over a specified time (e.g. 20 seconds) and angle rates are appropriately derived One pair of angles and associated rates are used to form the 2- dimensional admissible region of range and range-rate for each apparent object The admissible region is constrained on maximum and minimum range as well as energy (via a semi-major axis constraint) The constrained admissible region is discretized into regions of hypotheses to be tested Multiple Hypothesis Filter is initialized based on discretized and constrained 2-dimensional admissible region N-objects and M-hypotheses per object yields NxM initially equally-weighted individual Unscented Kalman Filters running simultaneously

5 Methodology

6 Admissible Region

7 Admissible Region

8 Sigma-Point (Unscented) Estimation

9 Methodology

10 Methodology

11 Methodology

12 Simulated Scenario Estimated Parameters A Priori Uncertainty (1 ) Remarks Position (O) 1000 kilometers Each hypothesis initialized with uncertainty based upon admissible region discretization and/or other factors Velocity (O) 1000 meters/sec Each hypothesis initialized with uncertainty based upon admissible region discretization and/or other factors Data Parameters Data Weights (1 ) Remarks Right Asc./Declination 0.4 arcseconds Data noise assumed to be at 20 sec sampling rate Right Asc./Declination Rate 0.07 arcseconds/sec Data noise assumed to be at 20 sec sampling rate

13 True RSO Epoch State Vectors

14 True Topocentric Angular RSO Positions

15 Simulation Results: Angles-Only

16 Simulation Results: Angles and Angle- Rate

17 Conclusions/Summary A method has been implemented which exploits the concept of the range/range-rate admissible region to initialize a set of hypotheses for autonomous and near real-time multiple-object initial orbit determination from short-arc optical measurements While the state errors are rather large after 10 minutes of observations (~ 0.7% of the full orbit arc), the method results in an encouraging discrimination of multiple objects having different orbits and yields state vectors with associated covariances (~ 40 arcminutes in FOV) suitable to hand-off to follow-on sensors. Previous work has shown that if the tracks are updated several hours later with an equivalent short-arc, the trajectory is sufficiently determined to yield successful track correlation on the subsequent evening. Angle rate data provided an improvement in state error reduction, but more importantly, allowed for better constraint of initial orbit hypotheses via the admissible region

18 Future Work Assess how many data of what accuracy / precision are required to obtain approximately Gaussian state pdfs Compare the current method with non-gaussian pdf approaches Adaptive Gaussian Mixtures Investigate the utility of information-theoretic approaches to determining what observations should be collected in a pass in order to successfully and unambiguously correlate to subsequent passes

19 Interactive Multiple Model Probabilistic Data Association Filter

20 Interactive Multiple Model Probabilistic Data Association Filter