transitioning for a general perturbations -...

9
1 TRANSITIONING FROM A GENERAL PERTURBATIONS TO A SPECIAL PERTURBATIONS SPACE OBJECT CATALOG Matthew P. Wilkins 1 Kyle T. Alfriend 2 Shannon L. Coffey 3 Alan M. Segerman 4 1 Graduate Research Assistant, Texas A&M University, College Station, TX 77843-3141, phone: (409) 845-0745, fax: (409)845-6051 email: [email protected] 2 Professor and Head, Dept. of Aerospace Engineering, Texas A&M University, phone: (409) 845-5920, fax: (409) 845-6051, email: [email protected]. 3 Naval Research Laboratory, Washington, DC 20375-5355 4 GRCI at Naval Research Laboratory, Washington, D.C. 20375-5355 Abstract Naval Space Command maintains a catalog of orbital element sets for space objects. Element sets are based on the method of general perturbations which relies on an analytic theory for orbit propagation. A more accurate method for propagating orbits is special perturbations which is based on numerical integration. The improved accuracy of special perturbations has led Naval Space Command to develop and maintain a second, special perturbations catalog, which is distinct from the general perturbations catalog. In the future the special perturbations catalog may become the only catalog maintained by Naval Space Command. In that case, a method must be developed for supporting users with the traditional element sets. This paper describes one method of constructing element sets from special perturbations vectors and the resulting accuracy of these element sets. Introduction Naval Space Command is currently maintaining two catalogs for space objects. The traditional catalog of element sets makes use of general perturbations (GP) propagation software called PPT3 which is based on the analytical theory of Brouwer 1 . Typical prediction accuracy of the general perturbations elements is on the order of 1-5 km over a few days. A new catalog based on special perturbations (SP) which employs numerical integration for orbit propagation is 5-10 time more accurate than GP. Naval Space Command is considering transitioning completely to the special perturbations catalog as their primary catalog. This means the internal mechanism of associating observations with objects, retagging observations and processing uncorrelated targets (UCT) would be centered around the SP catalog. However, NSC will still need to support users with the traditional element sets. Figure 1. illustrates the role that general perturbations plays in the catalog maintenance procedure at Naval Space Command. NSC Fence Unassociated Observations NSC Fence Associated Observations PPT3 Ephemeris Predictor Users SSN Observations GP DC SP DC Unassociated Observations UCT Good Observations Elements State Vectors Association Process Figure 1: Current Catalog Maintenance Procedure at Naval Space Command Since it will be too expensive to maintain all the cataloging machinery for both catalogs it is necessary to have an alternate method of supplying element sets to users. One method would be to derive element sets from SP vectors. This would eliminate the need for keeping a full catalog of element sets, the required element sets could be derived on demand from the SP vectors. If this method is followed then the processing diagram in Fig. 1 would be changed by substituting the SP integrator for the PPT3 Ephemeris Predictor and the GPDC would be linked to the SP State vectors rather than to the Real Observations. The resultant processing diagram is given in Figure 2.

Upload: vonhan

Post on 15-May-2018

245 views

Category:

Documents


2 download

TRANSCRIPT

1

TRANSITIONING FROM A GENERAL PERTURBATIONS TO A SPECIAL PERTURBATIONS SPACE OBJECT CATALOG

Matthew P. Wilkins1

Kyle T. Alfriend2 Shannon L. Coffey3 Alan M. Segerman4

1 Graduate Research Assistant, Texas A&M University, College Station, TX 77843-3141, phone: (409) 845-0745, fax: (409)845-6051 email: [email protected] 2 Professor and Head, Dept. of Aerospace Engineering, Texas A&M University, phone: (409) 845-5920, fax: (409) 845-6051, email: [email protected]. 3 Naval Research Laboratory, Washington, DC 20375-5355 4 GRCI at Naval Research Laboratory, Washington, D.C. 20375-5355

Abstract Naval Space Command maintains a catalog of orbital element sets for space objects. Element sets are based on the method of general perturbations which relies on an analytic theory for orbit propagation. A more accurate method for propagating orbits is special perturbations which is based on numerical integration. The improved accuracy of special perturbations has led Naval Space Command to develop and maintain a second, special perturbations catalog, which is distinct from the general perturbations catalog. In the future the special perturbations catalog may become the only catalog maintained by Naval Space Command. In that case, a method must be developed for supporting users with the traditional element sets. This paper describes one method of constructing element sets from special perturbations vectors and the resulting accuracy of these element sets. Introduction Naval Space Command is currently maintaining two catalogs for space objects. The traditional catalog of element sets makes use of general perturbations (GP) propagation software called PPT3 which is based on the analytical theory of Brouwer1. Typical prediction accuracy of the general perturbations elements is on the order of 1-5 km over a few days. A new catalog based on special perturbations (SP) which employs numerical integration for orbit propagation is 5-10 time more accurate than GP. Naval Space Command is considering transitioning completely to the special perturbations catalog as their primary catalog. This means the internal mechanism of associating observations with objects, retagging observations and processing uncorrelated targets (UCT) would be centered around the SP catalog. However, NSC will

still need to support users with the traditional element sets. Figure 1. illustrates the role that general perturbations plays in the catalog maintenance procedure at Naval Space Command.

NSCFence Unassociated

Observations NSCFence Associated

ObservationsPPT3EphemerisPredictor

Users

SSN Observations

GP DC SP DC

UnassociatedObservations

UCT

Good Observations

Elements StateVectors

AssociationProcess

Figure 1: Current Catalog Maintenance Procedure at Naval Space Command Since it will be too expensive to maintain all the cataloging machinery for both catalogs it is necessary to have an alternate method of supplying element sets to users. One method would be to derive element sets from SP vectors. This would eliminate the need for keeping a full catalog of element sets, the required element sets could be derived on demand from the SP vectors. If this method is followed then the processing diagram in Fig. 1 would be changed by substituting the SP integrator for the PPT3 Ephemeris Predictor and the GPDC would be linked to the SP State vectors rather than to the Real Observations. The resultant processing diagram is given in Figure 2.

NSCFence Unassociated

Observations NSCFence Associated

ObservationsSP

Integrator

Users

SSN Observations

GP DC SP DC

UnassociatedObservations

UCT

Good Observations

Elements StateVectors

AssociationProcess

Figure 2: Proposed Cataloging Procedure with SP as the Primary Propagator The technique of constructing element sets from SP vectors is not a difficult one in principal or in practice. What is more important is the quality of the resultant element set. This paper presents some accuracy results from one method we implemented. Procedure The procedure we pursued was as follows. First we produced an element set for a particular satellite from real SSN data using PPT3. Then we constructed an SP vector from the same data. The SP vector was used to generate a set of look ahead pseudo data. The pseudo data was generated in earth fixed, earth centered xyz coordinate frame. This pseudo data was used to construct a second element set. The first and second element sets were then compared to truth reference ephemeris with the result that the element sets

constructed from pseudo data were always better than the element sets constructed from real data. In the case of low earth satellites the improvement was 2-3 time better. For higher satellites the improvement was 5-10 times better. Constructing element sets from pseudo data is not a new concept. It is the standard method used by Naval Space Command to construct SGP4 element sets from PPT3 element sets for transfer to AF Space Command. The satellites we worked with were a subset of the satellites that are tracked with Satellite Laser Ranging (SLR). The SLR observations for these satellites are processed into vectors with the vectors integrated to produce an extremely accurate ephemeris called a Precision Orbit Ephemeris (POE). The resulting POE is accurate to a few meters. This set of satellites provides an excellent testbed for measuring the improvement of the method described in this paper. A similar procedure has been used previously to validate the implementation of PPT2 in the Draper R&D GTDS2. In that work, orbits were constructed from pseudo data generated by the Draper Semianalytical Satellite Theory (DSST). Comparisons were also made between element sets constructed from the SLR POE and pseudo DSST data constructed from orbits fit to the SLR POE. This produced accuracy on the order of 390 meters. In the present paper, we are not processing SLR data, rather we are working with the much noisier SSN data. Element Set Comparisons The set of satellites we worked with are given by their SSN numbers in Table 1. The graphs that follow show the improvements for each of these satellites.

SSN # Name Perigee Ht. Kilometers 7646 Starlette 806 22824 Stella 794 25398 Westpac 807 16908 Ajisai 1479 22076 Topex 1340 8820 Lageos 1 5833 22195 Lageos 2 5626 19751 Etalon 1 19093 20026 Etalon 2 19096

Table 1: Satellites Used for Comparisons

The first five graphs given in Fig. 3 -- Fig 7 are for SLR satellites that are near to the earth. The common error in the GP ephemeris as derived from an element set based on real data was about 1.5 km., whereas the error for the GP ephemeris as derived from an element set based on the pseudo data was on the order of about 800 meters for these five satellites. Also on each graph is the curve for the error in the SP ephemeris. The SP ephemeris is also the pseudo data. Of particular interest was the greater improvement derived from higher satellites. In particular for the satellites in Fig. 8 - Fig 11. The improvement in accuracy provided by the pseudo data went from errors as great as several kilometers to only about 500 meters. Interpretation of the Results

4

We provide here an interpretation of why the element sets based on pseudo data are significantly better than element sets based on real data. First of all, the pseudo data extracted from SP ephemeris was extremely close the actual future orbit of the object. Because it is data in the future it enables the resulting GP ephemeris to do a good job of following this future motion of the object. This is information that is not provided to an element set constructed from real data in the past. The second advantage that elements constructed from pseudo data enjoy is that the pseudo data is noise free. The GP fits have a much better chance of following the orbit than when they are fit to noisy data. Finally the data is extremely dense with no data gaps. The SP system is able to fit through the data gaps of the real data and still produce an extremely good orbit. From this good orbit the GP system can better construct an orbit that follows the SP ephemeris than it could do from data that is not as uniformly distributed. One may be motivated to ask the question of why the GP element sets cannot better fit the SP ephemeris. The most noticeable situations occur for the low earth objects. The reason is that the GP processor is based on

an analytic theory which only includes zonal harmonics through J5 and has a few enhancements for resonant tesseral terms. Thus the element sets will not be able to reproduce the motion of a satellite due to the short periodic terms in the earth's potential field. Just for the fun of it, we tested this hypothesis by fitting pseudo data with PPT3 and with the special perturbations system where the geopotential model was reduced to only J5 zonal harmonics. We provide in Fig. 12 the results of one such test case. In this case, it is almost impossible to determine the difference between the SP/J5 ephemeris and the PPT3 ephemeris. Continuing with our interpretation of the results, we can conclude that for higher satellites that are not perturbed as much by the earth's gravitation, we should see that the PPT3 orbits based on pseudo data are much better than for the lower satellites. This is indeed the case. As seen in the graphs for the higher altitude satellites, in particular, Lageos 1 and 2, and Etalon 1 and 2, the element sets based on pseudo data come much closer to approximating the SP orbits than for the lower altitude satellites.

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3

Days

Meters

SP (Real) PPT (NSC) PPT (Pseudo)

Figure 3: Starlette (7646) Position Difference, p=104.1, e=0.021, I=49.8

5

0

500

1000

1500

2000

2500

0 1 2 3Days

Meters

SP (Real) PPT (NSC) PPT (Pseudo)

Figure 4: Stella (22824) Position Difference (p=100.9, e=0.001, I=98.4)

6

0

500

1000

1500

2000

2500

0 1 2 3Days

Meters

SP (Real) PPT (NSC) PPT (Pseudo)

Figure 5: Westpac (25398) Position Difference (p=101.1, e=0.001, I=98.7)

0

200

400

600

800

1000

1200

0 1 2 3Days

Meters

SP (Real) PPT (NSC) PPT (Pseudo)

Figure 6: Ajisai (16908) Position Difference (p=115.6, e=0.001, I=50)

7

0

500

1000

1500

2000

0 1 2 3Days

Meters

SP (Real) PPT (NSC) PPT (Pseudo)

Figure 7: Topex (22076) Position Difference (p=112.5, e=0.001, I=66.1)

0

500

1000

1500

2000

2500

0 1 2 3

Days

Meters

SP (Real) PPT (NSC) PPT (Pseudo)

Figure 8: Lageos 1 (8820) Position Difference (p=225.5, e=0.004, I=109.8)

8

0100200300400500600700800

0 1 2 3Days

Meters

SP (Real) PPT (NSC) PPT (Pseudo)

Figure 9: Lageos 2 (22195) Position Difference (p=222.5, e=0.014, I=52.6)

0500

10001500200025003000350040004500

0 1 2 3Days

Meters

SP (Real) PPT (NSC) PPT (Pseudo)

Figure 10: Etalon 1 (19751) Position Difference (p=675.5, e=0.001, I=65.9)

9

0

1000

2000

3000

4000

5000

6000

0 1 2 3Days

Meters

SP (Real) PPT (NSC) PPT (Pseudo)

Figure 11: Etalon 2 (20026) Position Difference (p=675.5, e=0.001, I=64.8)

Ajisai (16908) Position Difference

0

100

200

300

400

500

600

700

0 1 2 3Days

SP (J5) PPT (Pseudo) p=115, e=0.01, I=50, Perigee=1479

Figure 12: Comparison between PPT3 and SP/J5 Model

10

Application to Irredium Satellites There has been much discussion in the last year about deorbiting the Irredium satellites. If this occurs then they would be brought down through the orbits of numerous other satellites and space debris. Deorbiting such a large number of satellites, 66, would present concerns about possible collisions with existing active satellites. The common method of determining close conjunctions is with the use of COMBO programs that make use of GP element sets. The higher accuracy element sets proposed in this paper would enhance the accuracy of the conjunction assessment that would have to be done for deorbiting these satellites. Conclusion With the advent of the special perturbations catalog, an unexpected benefit may very well be realized. By basing the standard element sets on SP vectors a significant improvement in accuracy on the order of 2-3 time the current error may result. These results are still preliminary in that we have only analyzed results for SLR satellites. These satellites are extremely well tracked, are circular and experience little drag. Continued research is being planned to determine the benefit realized by more common space objects. Acknowledgements The authors wish to express their gratitude to Naval Space Command for providing the funding for this research. Special thanks to Mr. Keith Akins for his diligence in making the computer runs that produced the data and the plots presented in this paper. References 1Brouwer, D., "Solution of the problem of artificial satellite theory without drag, "Astronomical Journal, Vol. 64, PP. 378-397. 2 Cefola, P.J., Fonte, D.J., and Shah, N., "The Inclusion of the Naval Space Command Satellite Theory PPT2 in the R&D GTDS orbit Determination System," paper 96-3606, AIAA/AAS Astrodynamics Specialist Conference, San Didgo, CA July, 1996.