AIAA 10-Xxx Orbit Determination Results From Optical Data

American Institute of Aeronautics and Astronautics

Orbit Determination Results From Optical Measurements

David A. Vallado 1 Center for Space Standards and Innovation, Colorado Springs, Colorado, 80920, USA

Vladimir Agapov 2 Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Russia

Operations in geosynchronous orbit are important for many aspects of commerce. Avoiding conjunctions in an ever increasingly crowded geosynchronous environment is therefore becoming more important especially in light of the Iridium 33 / Cosmos 2251 collision. SOCRATES-GEO has combined owner operator numerical ephemerides with Two-Line Element (TLE) set information for over 2 years. Unfortunately, the TLE information is of limited quality, and obtaining high quality ephemerides is often difficult. Previously we explored how we could replace the TLE data for those objects for which we do not get operator data (non-participating SOCRATES-GEO operational satellites or debris). The International Scientific Observing Network (ISON) resource provides high-quality optical observations on numerous GEO satellites. This paper introduces additional orbit determination results of optical data and seeks to understand what observation mix is necessary to meet certain accuracy requirements.

I. Introduction ince May 2004, the Center for Space Standards and Innovation (CSSI) has been providing daily reports of likely conjunctions for the upcoming week for all objects in earth orbit using the full catalog of unclassified NORAD

TLEs available to the public. The program is called Satellite Orbital Conjunction Reports Assessing Threatening Encounters in Space (SOCRATES) [1]. The information is publicly posted at http://www.celestrak.com/SOCRATES/.

SOCRATES-GEO grew from the initial SOCRATES effort and began operations in December 2007 focusing on geosynchronous satellites. The emphasis on GEO is because over 25% of the total known population is comprised of operational satellites, where we can obtain data directly from the operators. These satellites represent an important region because it’s a limited resource, close locations are desired for many satellites, existing space surveillance is not very good, and any debris created from a collision would impact hundreds of additional satellites for many decades. At the time of this writing, we are processing 184 of the satellite owner-operator satellites, with several more in work. This is over 50% of the active geosynchronous satellite population. Each of the owner ephemerides includes all maneuvers, whether planned or already executed. The maneuver information is arguably the most important and unique aspect of using this information.

Further expansion of SOCRATES-GEO occurred on April 12, 2010, when the Space Data Association Ltd. (SDA) selected Analytical Graphics, Inc. (AGI) to develop and operate its Space Data Center (SDC). The system is an automated space situational awareness (SSA) program designed to reduce the risks of on-orbit collisions and radio frequency interference. It is the satellite industry’s first global operator-led network for sharing high-accuracy operational data to improve overall space situational awareness and satellite operations.

The SDA and SOCRATES-GEO efforts look at all objects that pass within 250 km of GEO, combining owner ephemerides and TLE information as available. The reports are similar to the regular SOCRATES reports, but also include the ability to directly use improved data sources (supplemental TLE’s or independent ephemerides), getting standard reports, allowing for restricted access, and customizable user notification.

1 Senior Research Astrodynamicist, Center for Space Standards and Innovation, Colorado Springs, Colorado, 80920, USA. Email: [email protected]. AIAA Associate Fellow. 2 Senior Research Scientist, Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Russia, Email: [email protected].

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Our experience from SDA and SOCRATES-GEO shows us many more things than just the original intent of refining the conjunction processing for GEO satellites. The SDC concept conclusively demonstrates improvements to orbital accuracy, the ability to reduce search volumes for sensors, the reduction of false alarm rates for conjunctions, and even shows how SSA tracking requirement could be reduced (trust but verify).

Unfortunately, the TLE information is of significantly lower quality than the owner ephemerides, but a large improvement in the conjunction processing is still achieved over analysis using TLE information for both objects. With over 50% of the GEO operators already providing data, we have sought ways to replace the TLE data for those objects for which we do not get operator data (non-participating operational satellites, or debris). The International Scientific Observing Network (ISON) is an excellent resource from which we can obtain high quality observations on satellites to support non-operational satellites and debris ephemeris generation.

Vallado and Agapov [2] showed some initial examples of successful integration of ISON observational data to replace TLE information. This paper extends the processing of additional observational data to provide more complete and accurate Space Situational Awareness (SSA) for conjunction operations. Using Analytical Graphics Inc. Orbit Determination Toolkit (ODTK), we process the ISON observational data. Details are provided to demonstrate the filter results of the orbit determination, and to give confidence in the overall processing.

We define SSA as the process by which an organization maintains a catalog of all objects in space, to some level of accuracy, and in a timely fashion. Several relevant attributes are discussed in Vallado [3]: complete and robust, timely and efficient, standardized and maintainable, accurate, and importantly, trusted.

The primary question we seek to investigate is what observations and processing are needed to achieve a certain level of accuracy on a particular satellite, now, and at a future time?

II. Background Beginning in about 2001, cooperation of optical observatories began, and by 2005 the International Scientific

Optical Network (ISON) [4] was created. Additional observatories have been added to primarily study scientific and applied problems in space, notably in geosynchronous orbits. A great deal of modernization of equipment and software has taken place, and the Keldysh Institute of Applied Mathematics Russian Academy of Sciences (KIAM RAS) has been a principal scientific and organizational coordinator of ISON. By 2010, 33 telescopes at 23 observatories in 11 countries were operating around the world with over 90 researchers. The current tasks include regular GEO monitoring, new object discovery and tracking, and maintenance of as complete a catalog as possible. ISON is currently tracking 1467 objects in GEO compared to the TLE catalog of 1016 objects, and the observers track between 150 up to 800 individual objects each night. The data are stored at the KIAM Ballistic Center upon collection. The processing and analysis of information on space debris is also developed at the Center.

For the most part, the TLE data are regularly updated and made available electronically via the US Air Force Space Command (AFSPC) Space Track web site. That database is not fully comprehensive, however, because it intentionally omits those satellites deemed vital to US national security—a couple hundred payloads along with the associated rocket bodies and upper stages which delivered them to orbit. Even so, current orbital data is available for 14261 of 15618 (91 percent) cataloged by NORAD. Not all of these missing objects are for restricted objects, though. Some are considered lost since they have not been tracked for the past 30 days or longer. This database does not include those objects too small to be detected or regularly tracked by the US Space Surveillance Network (SSN).

Because the TLE information is of limited quality, we use public data such as GPS almanacs, GLONASS precise ephemerides, and the Intelsat 11-parameter data to supplement the TLE’s. These data sources can all be imported into STK directly, or used to generate TLE’s. We term the latter resulting data as supplemental TLE’s. An advantage is possible through the supplemental TLE’s. Here, we process an external ephemeris (usually from a numerical orbit determination and subsequent propagation), and fit a TLE to this information. Because of the larger observation density, SGP4 is able to better model the orbit, and predictions from the resulting TLE’s can be 10-20 times better than a comparable TLE developed from AFSPC processing of SSN observations [5].

The various options of data to use for conjunction operations are shown in Fig. 1. SOCRATES uses the TLE on TLE approach. SOCRATES-GEO takes advantage of each of the various options depending on what data is available. The status of the second satellite (active or not) influences the choices available for ephemeris information. There are many permutations when combining each of these data sources. The operator ephemeris vs operator ephemeris derived from observations results in the most accurate processing, and the TLE vs TLE is the least accurate.


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Figure 1. Conjunction Processing Options. Various options are available as different data is available for processing. The most accurate data sources are desirable for conjunction operations.

III. Orbit Determination Processing We processed additional observations to replace the TLE information with the Kalman filter in Analytical

Graphic Inc’s Orbit Determination Toolkit (ODTK). Because the filter processes data differently than traditional batch least squares, we show 3 basic reports used to demonstrate confidence in the results.

Optical observations present many challenges for the operator. We briefly review these below. The coordinate frame for optical measurements is generally topocentric, but some centers perform conversions to

other coordinate systems. We also found that not all systems with the same names are the same as well. Initial test cases between organizations are essential to fully understand exactly what data is being transferred. In ODTK, we use the ICRF from the latest IERS conventions [6, 7].

The initial estimate is crucial to processing the data. Often, a TLE is not sufficient to initiate an OD process. We saw this with both satellites examined. The type of data can also affect our ability to arrive at an accurate initial estimate. Radar data generally produces a much more accurate initial estimate, while optical data generally requires additional processing (IOD and LS) to get the initial estimate.

The accuracy we obtain from observational data is a function of many variables including the number, type, and quality of the observations in a pass over a sensor, the location of the data within a pass, the total number of tracks, number of sensors, location of the sensors, the processing technique, etc. To obtain the best accuracy, we trade-off the merits of each of these aspects versus their costs.

Sensor observations will not always be available when needed. Maintenance, downtime, and tasking priority can affect the quantity of observations, and personnel actions can even influence quality and, in some cases, prevent the observations themselves from reaching the user. Unfortunately, we can’t reliably predict these effects. One solution is trying to gather as many types of data as possible, so we’ll have a backup whenever normal procedures fail. This is particularly challenging for space surveillance operations.

Closely related is the amount of data available for a satellite. Continuous data does not exist for most satellites (except for satellites with GPS receivers). If we observe only a small arc of a satellite’s orbit, it’s much more difficult to determine an accurate answer. This difficulty can lead to mismodeling of the orbit. Too little data can also result in our inability to estimate additional state (solve-for) parameters. Vallado and Carter [8] show we need more data if we want to solve for sensor biases in addition to the position and velocity vectors. This is especially true for eccentric, deep space, and drag perturbed orbits. Remember the solve-for parameters “soak up” any mismodeling in the force models, so we want to have sufficient data to accurately determine the effect of perturbations, and not just the dynamic mismodeling.

In general, more distinct tracking data should give better accuracy (Central Limit Theorem). However, this assumes that the biases are identified and removed, and that the relative accuracy (weighting) of each observation is known and used in the estimation process. If the orbit solution quality degrades with additional data, the model and


the calibration are probably the cause. Additionally, suppose a sensor reports only two or three data points. Obviously most modern sensors (radars in particular) receive much more data—often hundreds or thousands of points per pass. One approach to obtain more data could be to task more sensors to observe the satellite and report additional sparse sets of observations. Although that would give us a slight improvement, we could incorrectly conclude that sparse data from many sites permits highly accurate orbit determination. This is simply false because there is a trade-off between many variables. Quite often, denser data (even from single sites) can actually improve the quality of the orbits and reduce the overall sensor tasking when combined with accurate biases and proper numerical processing. Fonte [9] showed that dense, real-world observations from a single station could produce orbits accurate to less than 10 m for a 12-hour prediction on a satellite at about 800 km altitude. Sparse data (less than five observations per pass) even from multiple sensors can actually increase this error to over 400 m for the same satellite [10]. This suggests that dense observations (perhaps on the order of 50-100 per pass) can produce precise orbits (10 m to 100 m for many satellites).

The location of the measurements in a pass also affect the OD result. When the satellite is very low to the horizon, a small vertical (elevation) error can result in a large uncertainty about where the satellite is in its orbit—the along-track component. As the satellite travels over the site, a small horizontal (azimuth) error will become a large plane change or a cross-track error. This effect is magnified because the satellite is usually closest to the site at its maximum elevation, or culmination. If we combine these results, we get an error ellipsoid about the satellite. In general, along-track errors are greatest because of a lack of precise timing information and the uncertain nature of the local satellite environment (the non-conservative forces such as drag and solar radiation pressure tend to retard the satellite’s motion). Cross-track errors are usually smaller, typically resulting from a sensor’s misalignment. Radial errors are usually the smallest.

Multiple satellite processing can also produce better results. When multiple sensors track an individual satellite at the same time, or when there are other combinations of sensors and satellites that overlap. The results can be significantly better as the time-varying biases may be more accurately determined.

A more practical concern is the format of the observational data. Most formats are densely packed files with little to no documentation. ISON can produce a .geosc format that is read directly by ODTK. Unfortunately, this format truncates the precision of the measurements, as most formats do. Although simple scripts can be written to convert the data to a useable form for input into ODTK, it may be better to adopt a new format that is a simple ASCII/XML form that permits various data types, precision, and includes enough information to specify what fields are being transmitted.

The system taking the observations must properly accomplish observations correlation and maneuvering, contend with co-located of satellites, process through continual E-W and N-S maneuvering, and minimize the number of lost satellites – usually about 10% of the catalog at any given time, or nearly 1400 objects! There is an important distinction in surveillance (searching to see what objects are visible) vs tracking (observing a known object at a certain time and location).

Small objects are very difficult to observe from the ground (think about 10 cm). Observability problems are particularly difficult for geostationary satellites as they have little relative motion with respect to ground sensors. The radial component is particularly difficult to observe. Sensors are usually limited, and coverage (gap) problems exist in some locations. Weather outages can easily hinder optical operations.

The Initial Orbit Determination (IOD) problem is often degenerate due to the lack of range information. Observations require proper selection of number per pass, where they are located in a pass, total observations available, the quality, how good the calibration values are, and others.

Finally, the perturbing forces present challenges. The third body and solar radiation pressure effects are reasonably well modeled, but not extensively understood. Recent discussion [11] has suggested that coulomb forces may even be partly responsible for some of the observed orbital behaviors.

Several satellites were examined. Because the data came from simple routine ISON tracking of the GEO population, we selected various epoch times to consider the processing. This required additional steps for Initial orbit Determination. Generally, we initialized from a TLE, ran a short Least Squares to refine the estimate, and then processed the observations. For satellites for which there were no TLE information, we simply used an angles-only IOD technique for initialization. Some work was done to align the sensor statistics so that the Filter Smoother Consistency test looked reasonable, further indicating the proper setup in the filter-smoother. We look at each satellite independently, but we do not consider multiple satellite processing in this paper, nor dedicated tracking for an individual object. Previous work has shown the benefit of processing multiple satellites simultaneously. While the existing ISON tracking density is greater than most standard operations at AFSPC, we are certain that additional accuracy can be achieved by slightly increased tracking. Future work will examine the applicability of increased dedicated tracking.


IV. Intelsat F3 (NORAD 4376) Testing This satellite is interesting because it is a large satellite (~90 m2) and although it has been non-functional for

many years, the latest AFSPC TLE data is from 1971! ISON regularly tracks this object. Aside from the obvious conjunction implications, the ability of external sensor networks to provide observations where holes in coverage may exist is of great interest. Our ISON data included measurements from 01 Jan 2008 21:47:42.200 UTCG to 14 Apr 2010 15:39:15.830 UTCG.

Satellite:Sat4376Tracker Names: KRAO_PH-1, Mayaki, KRAO_AT64, Kitab_A_ORI, Andrush_Z600, Zvenigorod50cm 10012, Mondy_AZT14, 10059, Uss_25, Blagov, Uss_B_ORITrackerIDs: 10533, 10016, 10031, 10069, 10901, 10517, 10012, 10003, 10059 10066, 10077, 10067

Time of First Data Point:1 Jan 2008 21:47:42.200 UTCG

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Figure 2. Measurement Times – Satellite 4376. The observations are shown by each sensor number (vertical axis).

We can also look at the frequency of the observations from each pass.

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Figure 3. Observation Numbers – Satellite 4376. The number of observations for each pass are shown. The time span covers over 2 years so the frequency may appear more dense than it actually is.

The data spans several years and was not tasked specifically with the intention of obtaining a certain accuracy level to support conjunction operations. Rather, the data is simply routine measurements to enable future tracking. Knowing that “some” additional observations are needed to support any increase in accuracy for numerical processing, we chose several periods containing slightly more observations


A. Data from 20 Apr 2009 19:30:25.5899999 Using the first three observations, the Gooding angle-only technique provides an initial estimate of the solution.

Orbital elements were as follows: a km e i ° Ω ° ω ° u ° 43068.754043 0.02043901 10.346662 320.734690 146.086260 185.820887 Inserting a Least Squares (LS) solution for the data from 20-25 April (76 obs), we refine the solution to a km e i ° Ω ° ω ° u ° 42158.187976 0.00026464 10.235637 320.898468 320.026116 185.666411 We now process the data from 20-29 April because we don’t want to end the filter where there is limited data as

it will give erroneous signatures in the Filter Smoother Consistency (FSC) test. This is warranted because in actual operations, the solution would end precisely on the last observation taken.

The filter residual ratios (residuals divided by the noise) provide a normalized look at the results.

Tracker: ISON1.Mayaki, ISON1.KRAO_PH-1, ISON1.KRAO_AT64Satellite: Sat4376Meas. Type: Right Ascension, Declination

Time of First Data Point:20 Apr 2009 19:32:56.110 UTCG

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3-Sigma -3-Sigma Figure 4. Filter Residual Ratios – Satellite 4376. The residual ratios are within bounds.

Note that the observations are not extremely dense, but are well processed in the simulation. The smoother is then run we look at the position uncertainty.

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Figure 5. Smoother Position Uncertainty – Satellite 4376. The position uncertainty shows a few km uncertainty.

Note that there is about a 5-6 km approximate uncertainty – a significant improvement from TLE data where differences are routinely many 10’s of km.


Satellite(s): Sat4376 Target: Filter Reference: Smoother


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Figure 6. Filter Smoother Position Consistency Test – Satellite 4376. The position consistency test looks normal, except for the final times when there are no observations.

The FSC test looks reasonable. The last spike in the data occurs because we have data at the end of the processing, but then a large gap with no data for several days. We’ll see additional cases of this in this paper.

B. Data from 21 Jul 2009 23:39:39.0500 The IOD provides the following initial estimate of the orbital elements. a km e i ° Ω ° ω ° u ° 39644.896537 0.04644448 10.108916 319.909300 174.721648 354.965378 Running the LS, the orbital elements are refined. a km e i ° Ω ° ω ° u ° 42150.669446 0.00018126 10.118728 320.494189 297.835103 352.760075 The residual ratios show more evenly spaced observations throughout the interval.

Tracker: TrackingSystem1.KRAO_PH-1, TrackingSystem1.Mayaki, TrackingSystem1.Kitab_A_ORI TrackingSystem1.Andrush_Z600Satellite: Sat4376aMeas. Type: Right Ascension, Declination

Time of First Data Point:21 Jul 2009 23:39:39.050 UTCG

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TrackingSystem1.Andrush_Z600 Right Ascension Meas Residuals TrackingSystem1.Andrush_Z600 Declination Meas Residuals

3-Sigma -3-Sigma Figure 7. Filter Residual Ratios – Satellite 4376. The residual ratios are within bounds. Notice the reasonably regular spacing of the observations.

The smoother position uncertainty is again about 6 km. The FSC looks reasonable, although some additional work could be done to remove or reduce the couple of exceptions noted in the test.


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Figure 8. Smoother Position Uncertainty and Filter Smoother Position Consistency Test – Satellite 4376. The position uncertainty shows a few km uncertainty and the consistency test is normal.

From these few test, we conclude that the IOD when averaged (number of observations taken sequentially or in permutation) can get close, but the solution time may far from the desired epoch. The IOD seemed to work better taking obs separated in time (a few minutes) and then forming an initial estimate from there.

A Least Squares process was almost always needed right after the IOD because the solutions are just not close enough. Sometimes, a smaller fit span worked, but usually the results were better with 4-5 days of data (50-100 observations with no thinning). This worked well with the filter-smoother.

The best processing occurred with about 10-15 observations per day, and on subsequent days for 3-4 days. When running the filter smoother, it’s desirable to end after a good set of observations, otherwise the FSC test

can exhibit unusual behavior, and obscure the results from the portion where the data is being processed. Overall, the results show the satellite is being tracked to an accuracy of a few km.

V. Transtage (NORAD 33509) Testing A GEO debris object (33509), this one had about 5084 observations from data from 19 Sep 2006 22:11:01.090

UTCG to 25 Apr 2010 15:50:15.170 UTCG. As in the previous case, note the long time period observations were available. Also note the date of the first TLE in Feb 2009 – an important consideration when determining the full extent of the catalog.

Satellite:Sat33509cTracker Names: 10531, Mondy_AZT14, 10041, KRAO_AT64, 10191, Mondy_33IK, Mayaki Simeiz, Gissar_AZT8, 10010, 10508, Uss_B_ORI, Uss_25TrackerIDs: 10531, 10003, 10041, 10031, 10191, 10103, 10016, 10019, 10044 10010, 10508, 10067, 10066

Time of First Data Point:19 Sep 2006 22:11:01.090 UTCG

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Looking at when the observations occur on a pass basis,


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We examine multiple test dates as before.

C. Data from 11 Oct 2007 00:40:22.01000 The IOD taken from observations spread through the first pass provides the following orbital elements. a km e i ° Ω ° ω ° u ° 41397.147065 0.00553558 10.145965 332.263304 241.509575 26.297631 The LS option refines this to the following. a km e i ° Ω ° ω ° u ° 41680.170365 0.00401170 10.130341 332.272258 308.934156 25.984515 The residual ratios look reasonable,

Tracker: ISON1.10191, ISON1.Mayaki, ISON1.Simeiz, ISON1.10041, ISON1.Gissar_AZT8Satellite: Sat33509aMeas. Type: Right Ascension, Declination

Time of First Data Point:11 Oct 2007 00:40:22.010 UTCG

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3-Sigma -3-Sigma Figure 11. Filter Residual Ratios – Satellite 33509. The residual ratios are within bounds. Notice the sparse observations at the start and some possibly bad right-ascension measurements at the end.

And the position uncertainty and FSC look as we have seen before.


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Figure 12. Smoother Position Uncertainty and Filter Smoother Position Consistency Test – Satellite 33509. The position uncertainty shows a few km uncertainty and the consistency test is normal.

The FSC almost passes, but the lack of data produces some minor departures.

D. Data from 25 Nov 2008 18:20:30.67999 The IOD gives the initial orbital elements. a km e i ° Ω ° ω ° u ° 43500.368062 0.20864731 9.471354 322.488278 352.914587 82.671129 Running the LS for 2 days, we find refined orbital elements. a km e i ° Ω ° ω ° u ° 41677.347848 0.00566450 9.697247 330.150307 328.094569 75.127335

Tracker: ISON1.10010, ISON1.Mayaki, ISON1.Gissar_AZT8Satellite: Sat33509bMeas. Type: Right Ascension, Declination

Time of First Data Point:25 Nov 2008 18:20:36.080 UTCG

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ISON1.Gissar_AZT8 Right Ascension Meas Residuals ISON1.Gissar_AZT8 Declination Meas Residuals

3-Sigma -3-Sigma Figure 13. Filter Residual Ratios – Satellite 33509. The residual ratios are within bounds, but with very sparse observations.

Good results, but notice the long intervals without data. Because we have some noise or dispersion in the final observations, we will expect some variation in the FSC.


Process: SmootherSatellite(s): Sat33509b


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Figure 14. Smoother Position Uncertainty and FSC Test – Satellite 33509. The position uncertainty looks normal and the FSC tests passes all cases.

E. Data from 8 Apr 2010 22:24:56.660 We wanted to try a case where we have TLE data. The difficult part for this case was forming the initial orbit

estimate. The TLE gave a position and velocity of position km velocity km/s -41580.309965 3984.964410 -3046.549922 -0.24579227 -3.03677513 -0.43390938 at 8 Apr 2010

22:24:56.660 UTCG This did not work well enough for the filter to run directly. So we used angles-only IOD. The results were

difficult because of the data and some minor observability problems, but a case was selected where the orbital elements were

a km e i ° Ω ° ω ° u ° 1 7 22 42,085.5483 0.00302084 9.177917 327.743399 231.412560 212.202475 1 8 Apr 2010 22:27:55.22 This gave significantly better residual ratios and was good enough to initiate a short LS stage. The LS produced a km e i ° Ω ° ω ° u ° 41676.152013 0.00599440 9.137256 327.735612 349.700826 212.310789

Tracker: ISON1.Mayaki, ISON1.10531, ISON1.KRAO_AT64, ISON1.Mondy_AZT14Satellite: Sat33509cMeas. Type: Right Ascension, Declination


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ISON1.KRAO_AT64 Right Ascension Meas Residuals ISON1.KRAO_AT64 Declination Meas Residuals

ISON1.Mondy_AZT14 Right Ascension Meas Residuals ISON1.Mondy_AZT14 Declination Meas Residuals

3-Sigma -3-Sigma Figure 15. Filter Residual Ratios – Satellite 33509. The residual ratios are within bounds, but with very sparse observations at the end.

The position uncertainty and FSC tests look normal. The differences at the end of the FSC test are a result of very sparse observations at the end of the interval.


Process: SmootherSatellite(s): Sat33509c


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Figure 16. Smoother Position Uncertainty and FSC Test – Satellite 33509. The position uncertainty looks normal and the FSC tests passes almost all cases. The points at the end are a result of very sparse observations right at the end of the observation interval.

Comparing to TLE’s from the same period (Fig. 17), notice the extreme difference at the beginning of the interval – 70-90 km, although the ODTK position uncertainty was only 10-12 km. The TLE’s improve relative to the ODTK orbit after that time.

Figure 17. Smoother Ephemeris vs TLE Spliced Ephemeris – Satellite 33509. The comparison of the smoother results and the TLE information show significant differences during the first several weeks, but more normal differences during the remainder of the interval.

VI. Intelsat 804 (NORAD 25110) Testing This satellite had about 704 observations from 10 Mar 2010 18:46:13.500 UTCG to 13 May 2010 21:42:49.210

UTCG.


Satellite:Intelsat804Tracker Names: Andrush_Z600, KRAO_RST221, KRAO_PH-1, Kitab_A_ORI2TrackerIDs: 10901, 10541, 10533, 10059

Time of First Data Point:10 Mar 2010 18:46:13.500 UTCG

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Looking at when the observations occur on a pass basis, we see fewer observations than before, but somewhat steady numbers of observations.

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Figure 19. Observation Numbers – Satellite 25110. The number of observations for each pass are shown. The time span covers a little more than 2 months.

We examine a single test date.

F. Data from 2 May 2010 21:12:57.67000 The IOD taken from observations spread through the first pass provides the following orbital elements. a km e i ° Ω ° ω ° u ° 40241.194775 0.03626625 4.986219 69.765782 316.235531 138.256341 The LS option refines this to the following. a km e i ° Ω ° ω ° u ° 42189.707273 0.00060735 4.934275 69.098916 271.820152 138.914699 The residual ratios look reasonable,


Tracker: TrackingSystem1.KRAO_PH-1, TrackingSystem1.KRAO_RST221Satellite: Satellite1Meas. Type: Right Ascension, Declination

Time of First Data Point:2 May 2010 21:14:12.420 UTCG

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-3-Sigma Figure 20. Filter Residual Ratios – Satellite 25110. The residual ratios are within bounds. Notice the sparse observations at the start and some possibly bad right-ascension measurements at the end.


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UpperBound LowerBound Figure 21. Smoother Position Uncertainty and Filter Smoother Position Consistency Test – Satellite 25110. The position uncertainty shows a few km uncertainty and the consistency test is normal.

The FSC almost passes, but the lack of data produces one minor departure. We compare the ISON processed results to the spliced together TLE information. Notice the significantly larger differences from the TLE ephemeris.


Figure 22. Smoother Ephemeris vs TLE Spliced Ephemeris – Satellite 25110. The comparison of the smoother results and the TLE information show large differences during the entire interval.

VII. Intelsat 904 (NORAD 27380) Testing This one had about 1966 observations from 02 Aug 2008 19:38:49.300 to 09 Nov 2008 23:11:33.930 UTCG.

Satellite:Sat904Tracker Names: KRAO_PH-1, Kitab_A_ORI, Tiraspol, KRAO_RST221TrackerIDs: 10533, 10069, 10064, 10541

Time of First Data Point:2 Aug 2008 19:38:49.300 UTCG

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Figure 24. Observation Numbers – Satellite 27380. The number of observations for each pass are shown. The time span covers a couple of years.

We examine a single test date.

G. Data from 1 Aug 2008 00:30:22.68300 The IOD taken from observations spread through the first pass provides the following orbital elements. a km e i ° Ω ° ω ° u ° 40241.194775 0.03626625 4.986219 69.765782 316.235531 138.256341 The LS option refines this to the following. a km e i ° Ω ° ω ° u ° 42189.707273 0.00060735 4.934275 69.098916 271.820152 138.914699 The residual ratios look reasonable,

Tracker: ISON.KRAO_PH-1, ISON.Kitab_A_ORI, ISON.Tiraspol, ISON.KRAO_RST221Satellite: Sat904wmanvMeas. Type: Right Ascension, Declination


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ISON.KRAO_RST221 Right Ascension Meas Residuals ISON.KRAO_RST221 Declination Meas Residuals

3-Sigma -3-Sigma Figure 25. Filter Residual Ratios – Satellite 27380. The residual ratios are within bounds. There are two maneuvers in this span of data, indicated by the vertical lines.



Process: SmootherSatellite(s): Sat904wmanv


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UpperBound LowerBound Figure 26. Smoother Position Uncertainty and Filter Smoother Position Consistency Test – Satellite 27380. The position uncertainty shows a few km uncertainty and the consistency test has a few departures.

The FSC almost passes, but the lack of data produces some departures. We compare the ISON processed results to the spliced together TLE information. Notice the significantly larger differences from the TLE ephemeris.

Figure 27. Smoother Ephemeris vs TLE Spliced Ephemeris – Satellite 27380. The comparison of the smoother results and the TLE information show significant differences during the entire interval.

VIII. Molnyia (NORAD 20813) Testing Finally, we tried processing observations on a decaying Molnyia satellite (20813). The measurement times were

as follows:


Satellite:Sat20813Tracker Names: 10003, 10031, 10533, 10069, 100, 10517, 10064TrackerIDs: 10003, 10031, 10533, 10069, 100, 10517, 10064


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This was an interesting case because we had observations during the re-entry period as well as TLE information. Figure 30 shows the apogee/perigee heights as established with the TLE information.

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The first step was to initiate a value from the TLE. Using the TLE on 23 Apr 2009 16:57:36.157, the classical

orbital elements were a km e i ° Ω ° ω ° u ° 26367.634926 0.75196286 62.396585 71.136500 269.424123 114.741765 Running a simple LS refined these values. a km e i ° Ω ° ω ° u ° 26349.383813 0.75194485 62.339482 71.137448 269.429376 117.201172

Tracker: ISON.10003, ISON.10031, ISON.10533Satellite: Sat20813Meas. Type: Right Ascension, Declination


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3-Sigma -3-Sigma Figure 31. Filter Residual Ratios – Satellite 20813. The residual ratios are within bounds, but there were some observations at the end that seemed a little out of bounds.

The Variable Lag smoother shows the clear problems associated with the close perigee, but is able to process through the data.

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Figure 32. VLS Smoother Position Uncertainty and FSC Test – Satellite 20813. The position uncertainty exhibits some large variations, and the FSC tests passes almost all cases. The points at the end are a result of very sparse observations right at the end of the observation interval.

Comparing the VLS ephemeris to the TLE spliced ephemeris,


Figure 33. VLS Smoother Ephemeris vs TLE-Spliced Ephemeris – Satellite 20813. The RIC differences show large discrepancies at some points where the observations are thin, but relatively consistent performance throughout the interval.

Note that although the VLS processed through the data, the uncertainty was very high. The general “noise” of the TLE information is in the 30-40 km range, but the VLS ephemeris is significantly different in the two intervals with little data. Obviously, additional data during this time is warranted, but again, the available data for this case was only routine tracking information.

IX. Summary and Conclusions We have examined the option of processing additional observations for satellites under consideration in

conjunction screening to improve the quality of the existing TLE information. In particular, we examined geosynchronous satellites and the use of optical angles-only data from ISON. Different epoch values were chosen for several satellites. Some had reasonably evenly spaced data, others had more data at the start or the end, and others had very sparse data. In all cases, the position uncertainty (once reasonably acceptable FSC test results had been obtained) was in the few km range – a significant improvement over the TLE information. We stress that these results are for non-dedicated tracking, and simply the result of tasking to maintain the GEO catalog.

We feel confident in the outcomes of the results to proceed to the next phase which will be to evaluate what can be done with additional targeted tracking. This work is underway and will be the subject of future papers. The improved accuracy ultimately reduces the number of unnecessary avoidance maneuvers by better modeling the predicted conjunction.

References 1. Kelso, T. S., and S. Alfano. 2005. “Satellite Orbital Conjunction Reports Assessing Threatening Encounters in Space

(SOCRATES).” Paper AAS 05-124 presented at the AAS/AIAA Space Flight Mechanics Conference. Copper Mountain, CO. 2. Vallado, David A., T.S. Kelso, Vladimir Agapov, and Igor Molotov. 2009. Orbit Determination Issues and Results to

incorporate Optical Measurements in Conjunction Operations. Paper presented at the 5th European Conference on Space Debris. Darmstadt, Germany.

3. Vallado, David A. 2007 Fundamentals of Astrodynamics and Applications. Third edition. Springer/Microcosm, Hawthorne, CA.

4. Molotov I., Agapov V. et al. 2008. International scientific optical network for space debris research, Advances in Space Research, Volume 41, Issue 7, 1022-1028.

5. Kelso, T. S.. 2007. Validation of SGP4 and IS-GPS-200D Against GPS Precision Ephemerides, Paper AAS 07-127 presented at the AAS/AIAA Space Flight Mechanics Conference. Sedona, AZ.

6. Souchay, Jean, and Martine Feissel-Vernier. 2006. IERS Technical Note #34—The International Celestial Reference System and Frame. IERS ICRS Centre, Paris.

7. Fey, A. L. and D. Gordon, C. S. Jacobs. 2009. IERS Technical Note #35— The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry. U.S. Naval Observatory

8. Vallado, David A. and Scott S. Carter. 1997. Accurate Orbit Determination from Short-arc Dense Observational Data. Paper AAS 97-704 presented at the AAS/AIAA Astrodynamics Specialist Conference. Sun Valley, ID.

9. Fonte, Daniel J. Jr. 1993. Implementing a 50 x 50 Gravity Field Model in an Orbit Determination System. M.S. Thesis, CSDL-T-1169.


10. Phillips Laboratory. 1995. 1995 Success Stories. Kirtland Air Force Base, NM: Phillips Laboratory History Office. 11. Agapov, Vladimir, and Moriba Jah. 2010. Personal discussions. 12. Vallado, David A. 2010. Evaluating Gooding Angles-only Orbit Determination of Space Based Space Surveillance

measurements. Paper USR 10-S4.5 presented at the US/Russian Workshop. Maui, HI.

Documents

AIAA 10-Xxx Orbit Determination Results From Optical Data