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A simple and valid analysis method for orbit anomaly detection
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Advances in Space Research 49 (2012) 386–391 www.elsevier.com/locate/asr
A simple and valid analysis method for orbit anomaly detection W.D. Song a,⇑, R.L. Wang b, J. Wang c a
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China b Center for Space Science and Applied Research, Chinese Academy of Science, Beijing 100190, China c Earthquake Engineering Research Center, China Institute of Water Resources and Hydropower Research, Beijing 100048, China Received 3 November 2010; received in revised form 6 October 2011; accepted 7 October 2011 Available online 15 October 2011
Abstract A simple analysis method for orbit anomaly detection, called semi-major axis change method (SACM) was presented by using a relationship between the change of orbit parameters and velocity increments. In this method, the mean value and standard deviation of the semi-major axis change in different time intervals were first calculated according to historical data. Then, these two parameters, the mean value and standard deviation of the semi-major axis change, are chosen as basis variables and combined as an anomalous criterion. For orbit objects with different characteristic, anomalous thresholds were given in different time intervals for identifying the anomalies of the orbital objects. Finally, this method is used for low earth orbit (LEO) satellites and American–Russian breakup debris. By adopting this method, the characteristics of the orbit change were given. The accuracy rate of anomaly analysis for LEO satellites and American– Russian breakup debris can reach to 100%, which demonstrates that the method was rapid and valid. Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Orbit anomaly; Semi-major axis changes; Standard deviation
1. Introduction Orbit anomaly discrimination of space objects is an important job in space debris research field. Space objects are classified into two kinds: (1) objects that can be controlled, such as operational satellites; (2) debris that cannot be controlled, such as the dead satellites, rocket debris and breakup debris. There are two main causes for the orbit anomaly. One is the collisions between two space objects, breakup by burn leakage and explosion (Patera, 2006) and the other is the environmental orbit anomaly (Johnson, 2002). TLE (Two Line Element) is a kind of orbit element published publicly which can update twice a day with small errors (Kelecy et al., 2007). Much effort is currently being made to use TLEs to discriminate the orbit anomaly for space objects in the space debris collision warning field (Patera, 2008; McNeill et al., 2009). It is meaningful to find
⇑ Corresponding author.
E-mail address: [email protected] (W.D. Song).
the orbit anomaly of space objects timely and accurately, which can make it convenient to master the status of space objects, analyze and identify the dangerous intersections. Especially for non-deliberate orbital anomalies, the factors that may cause abnormalities can be analyzed immediately after the anomaly detection.
2. Definition of the semi-major axis change The orbital changes are regular for space objects in earth orbit which is affected by earth gravitation and other perturbations. When these objects undergo external forces or dramatic changes in the space environment, their orbits will change anomalously, causing some abrupt changes of orbit elements. There are two kinds of external forces for these objects. One is a sudden impulse force with a short duration, which can be ignored for such a short time, and the other is a small thrust which has a period of duration. Whether it is an impulse or a thrust, there will be a velocity change (called velocity increment) in these objects, which
0273-1177/$36.00 Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2011.10.007
W.D. Song et al. / Advances in Space Research 49 (2012) 386–391
can induce orbit elements changes. The relationships between the orbit elements and the velocity increments can be given as following (Montenbruck and Gill, 2000): 8 pffiffiffiffiffiffiffi n 1e2 > Da DmU ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > 2 ð1þ2e cos f þe2 Þ > > < pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a ð1þ2e cos f þe2 Þ cos f þe n DmN ¼ sin E pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Da De 1e2 > ð1þ2e cos f þe2 Þ > > > p ffiffiffiffiffiffiffi > 2 2 : DmW ¼ nar cos1e Di u ð1Þ where DvU, DvN and DvW are the velocity increments of the along-track, in plane and out plane, respectively. From the above equations, it can be seen that the along-track velocity increment can cause changes in the semi-major axis; the in-plane velocity increment can lead to the changes in the semi-major and eccentricity, and the out-plane velocity increment usually only causes changes in the inclination. 2.1. Analysis step of the semi-major axis change The semi-major axis change can be caused by the changes of the along-track and in-plane track velocity additions. The changes of the eccentricity and inclination are caused by the velocity increment of in plane and out plane. However, it is difficult to identify the cause for the velocity changes of in-plane and out-plane, respectively. Whether it is the collision, the explosion breakup or the orbit manoeuvre, there will be obvious changes in the semi-major axis. In order to detect the orbit anomaly of an object, the most common method is to find the orbital mean motion or the semi-major axis anomalous changes. In the current paper, the semi-major axis change is taken as an anomalous parameter for analyzing the orbit anomaly of the space objects. Obviously, the semi-major axis change is not a TLE parameter, but it is derived from a TLE parameter, mean motion, which is also used to derive the total energy (Patera, 2006, 2008; McNeill et al., 2009). The anomalous analysis steps are outlined as follows: (1) Taking the data of the last three months (or longer) before the analysis period as samples and considering the orbital data at any time as a basis. Then, calculating the time and semi-major axis change of the other data relative to the basis and obtaining a series of time intervals Dt and semi-major axis changes Da. (2) After gaining the time and semi-major axis changes, these changes are classified by time. Here, the time interval is rounded off and the absolute value of the semi-major axis change is taken, namely |Da|. So, these absolute values are chosen as analysis variables. (3) For the sample of each integer day time interval, the mean value jDaj and standard deviation rðjDajÞ of the analysis variables are calculated. Therefore, a threshold for the semi-major axis changes at the integer time intervals for any space object is given, that is kðjD aj þ 3rðjD ajÞ (k P 1)).
387
(4) For the analysis period, the time interval Dt and the corresponding absolute value of the semi-major axis change jDaj are derived. Comparing the result with the above threshold, if it is larger than the threshold, it is considered as abnormal, or it is abnormal. 2.2. Method of deleting outliers For surveillance and other reasons, there are many anomalous and outlier points for a series of TLEs which need to be deleted during the anomalous analysis. For the sample data, both the outlier and anomalous points need to be deleted before deriving the normal changes of the semi-major axis. For the analysis data, the outliers need to be deleted from the anomaly analysis results. (1) Deleting the outlier and anomalous point of sample data: For simplicity, the outlier and anomalous points are not usually larger than 20% of the total sample. So, 20% of the sample data with larger values are deleted. (2) Deleting the outlier of analysis data: The outliers usually have the following characteristics: (1) The outlier point is the anomalous one. (2) The product of the changes of the semi-major axis for the outliers of the adjacent TLE data points is negative. (3) The sum of the changes of semi-major axis for the outliers of the adjacent TLE data points is very small. All the outliers can be deleted according to the above characteristics. 3. Anomalous analysis of operational satellites in LEO orbit According to the orbital information of operational satellites obtained from UCS (Union of Concerned Scientists) Satellite Database in July 2009, 426 satellites in LEO orbit were analyzed. The TLE data from January 1, 2009 to July 1, 2009 were chosen as a sample and the data from July 1, 2009 to December 1, 2009 were analyzed. Totally, 401 out of 426 operational satellites had TLE data. 3.1. Threshold determination of anomalous analysis The maximum time intervals of the adjacent TLE data were obtained by anomalous analysis. Then, these maximum time intervals were regarded as the largest time interval of the sample. Because update frequency of the satellite in orbit is usually faster, the time interval of TLEs is not larger than seven days. The update frequency of most satellite is one or two days. For the anomalous threshold kðjDaj þ 3rðjD ajÞÞ, 99.74% of the analysis data should be within the threshold when k = 1. However, the change of the semi-major axis is much
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larger than the normal change when satellite orbit anomaly occurs. k is not only related to the orbital and physical characteristics, but also related to the reason for satellite anomaly, such as the magnitude and the time of the maneuver thrust force. Because it is usually difficult to get the above information, the value of k can be adjusted by comparing the SACM results with the human judgment results in the analysis. k = 3 is finally identified, so the anomaly threshold 3ðjD aj þ 3rðjD ajÞ can be used for the satellite in LEO orbit. However, the outliers in the anomalous results need to be deleted. When the product of adjacent semi-major axis changes is negative and the sum of the adjacent semi-major axis change is less than k 2 jD aj (jDaj is the mean of the semi-major axis change and k2 is equal to 5 according to experience), it is a outlier and needs to be deleted. That means the outlier satisfies the following conditions: DaðjÞ Daðj þ 1Þ < 0 ð2Þ jDaðjÞ þ Daðj þ 1Þj < 5jD aj
Table 2 Statistical results of the anomalous operational satellites. Anomalous object number (SACM result)
Comparison of orbit change segments between SACM result and human judgment Equal
Less
Larger
190
120
14
56
Table 3 Analysis results of non-anomalous satellites. Non-anomalous object number (SACM result)
Judged by human Anomalous object number
Non-anomalous (human judgment)
211
21
190
(3) There are 211 non-anomalous objects in SACM results shown in Table 3. By analyzing their orbit mean motion of 211 objects, there are 21 objects with orbit anomaly, including 50 orbit change segments.
3.2. Anomalous results The SACM considers the semi-major axis change as the threshold in different time intervals to identify orbit anomaly, and at the same time the outliers are deleted. The SACM results are compared with that of human judgment method, which means that the results are judged by human by analyzing the curve change of the semi-major axis change with the time and the abnormal change of the semi-major axis can be easily judged by human brain according to the history change trend. In this paper, 401 operational LEO satellites were analyzed and the results were given as following: (1) After the outliers were deleted from the anomalous results, 190 objects are involved as anomaly and there are 1492 anomalous points for 190 objects. By analyzing the anomalous points, there are 332 segments of orbit change, while there are 394 segments of orbit changes by human judgment in Table 1. (2) It can be seen from Table 2 that for 190 objects, there are 120 objects have the same number of the orbit change segments for both SACM results and human judgment results. For 14 objects, the number of orbit change segments judged by human is less than that of SACM results. For 56 objects, the number of orbit change segments judged by human is larger than that of SACM results in Table 2. Table 1 Anomalous result of the operational LEO satellites. Anomalous points
Anomalous object number
Orbit change segments SACM
Human judgment
1492
190
332
394
4. Breakup event of Cosmos 2251 and Iridium 33 and anomalous analysis of its breakup debris Breakup event is a main source of space debris and a major category in orbit anomalous events. Usually after a large breakup event, the orbits of the space objects involved in the event can change abruptly. The extent and manner of orbit anomaly are related to the breakup intensity. The collision between Cosmos 2251 and Iridium 33 which happened in February, 2009 is a large orbit anomalous event, and is the first collision breakup happened between two intact catalog satellites. After the collision breakup, the orbits of the two satellites changed anomalously, including the semi-major axis, eccentricity and inclination. For this breakup event, the SACM was used to analyze the orbits of the breakup satellites and breakup debris and determine their anomalous orbit changes. Further the orbit anomalous changes of the breakup debris were classified. Their orbits were analyzed by the SACM. The analysis results could be used to indentify the collision breakup and understand the detection ability of SSN for breakup debris. 4.1. Orbit anomaly analysis of American–Russian satellites break events Before the collision of Cosmos 2251 and Iridium 33, their orbits changed regularly. Iridium 33 maintained its orbit periodically, the magnitude of orbit change was not large, and usually less than 0.5 km for each orbit change. Both orbits undergo abrupt changes at the collision time in Figs. 1 and 2. The mean change of semi-major axis is 3 km for Cosmos 2251 satellite (see Fig. 1), and 5 km for Iridium 33 which was uncommon compared with the usual
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The changes of the mean motion for the breakup debris with time from February 1, 2009 to March 1, 2010 were analyzed and the following results could be given: (1) The mean motion of most American–Russian debris had the ascending trends with time. (2) Some had periodic change trends. (3) The update frequency of the debris was different. Even for the same debris, the update frequency also had large difference for different analysis periods. (4) Some orbits of debris had some break, even some orbits happened abrupt change that means orbit anomaly. Orbit anomaly of American–Russian satellites breakup debris can be divided into three classes: Fig. 1. Semi-major axis changes of Cosmos 2251 satellite for breakup.
(1) The initial orbit was unsteady;Part of them was published in a short period after satellite breakup and their orbits were not stable. These debris orbits were densely distributed and hard to be detected and identified (see Figs. 3 and 4). (2) Orbit changes abruptly:Some orbits of the breakup debris change abruptly. If the changes were not caused by the collision or explosion, the catalog data were problematic (see Figs. 5 and 6).
Fig. 2. Semi-major axis changes of Iridium 33 satellite for breakup.
change (see Fig. 2). The intersection and anomaly analysis could help us to find the breakup event. 4.2. Orbit anomaly analysis of American–Russian satellites breakup debris Fig. 3. Semi-major axis changes of object 33757.
The American–Russian satellites breakup event produced a large quantity of debris with different velocity increments along different directions. Initially the breakup debris were concentrated in a small region. Then the debris gradually dispersed. Due to a short period of the concentration and the special characteristics of the breakup debris, such as the instability and the large area mass ratio, the American–Russian satellites breakup debris were hard to recognize. Generally, the breakup debris may undergo some abnormal changes caused by the errors in detection. By an anomaly analysis, SSN detecting rate can be given. So the data of breakup debris are abnormal for a short time after breakup. The SACM can be used to identify the orbit anomaly of the breakup debris. Then, orbit anomaly analysis is made for American–Russian satellites breakup debris.
Fig. 4. Semi-major axis changes of object 33762.
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of space objects is relatively small, the probability of orbit change induced by collision is very small. If the orbit anomaly caused by collision is not considered, the anomaly ratio of breakup debris may reflect the detecting ability of SSN. The following is the orbit anomaly analysis for American–Russian satellites breakup debris using the SACM. By adjusting the anomalous factor k, the optimal anomalous results can be obtained. Finally k = 10 is adopted. 4.2.1. Anomaly analysis of Cosmos 2251 breakup debris Orbit anomaly analysis of Cosmos 2251 breakup debris is listed as following: Fig. 5. Semi-major axis changes of object 34011.
(a) There were 49 anomalous objects for program results shown in Table 4. From Table 4, it can be seen that 39 anomalous objects were identified by human judgment, and the orbits of 10 objects changed rapidly (8 objects were in the decay period). The accuracy rate was 100% (49/(39 + 10)), if considering rapid orbit change as orbit anomaly (see Table 4). (b) In the 39 breakup debris with orbit anomaly of Cosmos 2251 (not considering the decaying object), there are 44 orbit change segments by SACM calculation, and 45 orbit change segments by human judgment. SACM results and human judgments have the same results for 38 objects. Only one SACM result is less than that of human judgment. Table 4 shows the comparison of SACM results with human judgment of anomaly objects for Cosmos 2251 breakup debris.
Fig. 6. Semi-major axis changes of object 34078.
4.2.2. Anomaly analysis of Iridium 33 breakup debris Orbit anomaly analysis of Iridium 33 breakup debris is demonstrated as following: (a) Table 5 shows that there were 8 anomalous objects and 2 of them were in the decay period. The accuracy rate was equal to 100% (8/(2 + 6)) if considering rapid orbit change as orbit anomaly. Table 4 Comparison between SACM results and human judgment results of anomaly objects for Cosmos 2251 breakup debris. SACM result
Anomalous object number
49
Human judgment result
Anomalous Rapid orbit change (not including reentry) Decay Sum
39 2 8 49
Fig. 7. Semi-major axis changes of object 34652.
(3) Outlier point of data:The main reason for the outlier points is usually attributed to the error of the detection (see Fig. 7). Orbit anomaly analysis is mainly used to identify the abrupt change of the second situation. Because the density
Table 5 Comparison of SACM results with human judgment results of anomaly objects for Iridium 33 breakup debris. SACM result
Anomalous objects number
8
Human judgment result
Anomalous Decay
6 2
W.D. Song et al. / Advances in Space Research 49 (2012) 386–391
(b) In the 6 objects with orbit anomaly of Iridium 33, there are 6 orbit change segments by SACM calculation and 7 by human judgment.From the above analysis, some conclusion can be derived: (1) The SACM can identify the orbit anomaly of American–Russian breakup debris effectively. (2) k = 10 was effective for anomaly identification of American–Russian breakup debris.
5. Conclusion On the basis of the relationship between the change of orbit parameters and velocity increments, a semi-major axis change method (SACM) was put forward. An anomalous threshold was given in different time intervals for objects in different orbits. Orbit anomalous analysis was made for the LEO satellites and the American–Russian breakup debris and their orbit change characteristics were explored. The results indicated that the method was rapid and valid. The accuracy rate of the anomaly analysis for LEO satellites and American–Russian breakup debris can reach 100% with the SACM.
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Acknowledgements This paper is supported by the National Nature Science Foundation of China (91016013) and the Program for New Century Excellent Talents in University. References Patera, R.P. Space event detection method, AIAA/AAS Astrodynamics Specialists Conference AIAA 2006-6513, Keystone, Colorado, August 21–24, 2006. Johnson, N.L. Environmentally-induced debris sources, NASA Lyndon B. Johnson Space Center, Second World Space Congress, 2002. Patera, R.P. Space event detection method. J. Spacecraft Rockets 45 (3), 554–559, 2008. McNeill Jr., J.F., Coggi, J.M., Ailor, W.H., et al. Space situation monitoring laboratory: an integrated web-based environment for space environment information and analysis, in: Proceedings of the AAS/ AIAA Astrodynamics Specialist Conference, AAS 09-416, Pittsburgh, Pennsylvania, August 2009. Kelecy, T., Hall, D., Hamada, K., et al. Satellite Maneuver detection using two-line element (TLE) data, 2007,. Montenbruck, O., Gill, E. Satellite Orbits. Springer-Verlag, Berlin, 2000.
Advances in Space Research 49 (2012) 386–391 www.elsevier.com/locate/asr
A simple and valid analysis method for orbit anomaly detection W.D. Song a,⇑, R.L. Wang b, J. Wang c a
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China b Center for Space Science and Applied Research, Chinese Academy of Science, Beijing 100190, China c Earthquake Engineering Research Center, China Institute of Water Resources and Hydropower Research, Beijing 100048, China Received 3 November 2010; received in revised form 6 October 2011; accepted 7 October 2011 Available online 15 October 2011
Abstract A simple analysis method for orbit anomaly detection, called semi-major axis change method (SACM) was presented by using a relationship between the change of orbit parameters and velocity increments. In this method, the mean value and standard deviation of the semi-major axis change in different time intervals were first calculated according to historical data. Then, these two parameters, the mean value and standard deviation of the semi-major axis change, are chosen as basis variables and combined as an anomalous criterion. For orbit objects with different characteristic, anomalous thresholds were given in different time intervals for identifying the anomalies of the orbital objects. Finally, this method is used for low earth orbit (LEO) satellites and American–Russian breakup debris. By adopting this method, the characteristics of the orbit change were given. The accuracy rate of anomaly analysis for LEO satellites and American– Russian breakup debris can reach to 100%, which demonstrates that the method was rapid and valid. Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Orbit anomaly; Semi-major axis changes; Standard deviation
1. Introduction Orbit anomaly discrimination of space objects is an important job in space debris research field. Space objects are classified into two kinds: (1) objects that can be controlled, such as operational satellites; (2) debris that cannot be controlled, such as the dead satellites, rocket debris and breakup debris. There are two main causes for the orbit anomaly. One is the collisions between two space objects, breakup by burn leakage and explosion (Patera, 2006) and the other is the environmental orbit anomaly (Johnson, 2002). TLE (Two Line Element) is a kind of orbit element published publicly which can update twice a day with small errors (Kelecy et al., 2007). Much effort is currently being made to use TLEs to discriminate the orbit anomaly for space objects in the space debris collision warning field (Patera, 2008; McNeill et al., 2009). It is meaningful to find
⇑ Corresponding author.
E-mail address: [email protected] (W.D. Song).
the orbit anomaly of space objects timely and accurately, which can make it convenient to master the status of space objects, analyze and identify the dangerous intersections. Especially for non-deliberate orbital anomalies, the factors that may cause abnormalities can be analyzed immediately after the anomaly detection.
2. Definition of the semi-major axis change The orbital changes are regular for space objects in earth orbit which is affected by earth gravitation and other perturbations. When these objects undergo external forces or dramatic changes in the space environment, their orbits will change anomalously, causing some abrupt changes of orbit elements. There are two kinds of external forces for these objects. One is a sudden impulse force with a short duration, which can be ignored for such a short time, and the other is a small thrust which has a period of duration. Whether it is an impulse or a thrust, there will be a velocity change (called velocity increment) in these objects, which
0273-1177/$36.00 Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2011.10.007
W.D. Song et al. / Advances in Space Research 49 (2012) 386–391
can induce orbit elements changes. The relationships between the orbit elements and the velocity increments can be given as following (Montenbruck and Gill, 2000): 8 pffiffiffiffiffiffiffi n 1e2 > Da DmU ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > 2 ð1þ2e cos f þe2 Þ > > < pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a ð1þ2e cos f þe2 Þ cos f þe n DmN ¼ sin E pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Da De 1e2 > ð1þ2e cos f þe2 Þ > > > p ffiffiffiffiffiffiffi > 2 2 : DmW ¼ nar cos1e Di u ð1Þ where DvU, DvN and DvW are the velocity increments of the along-track, in plane and out plane, respectively. From the above equations, it can be seen that the along-track velocity increment can cause changes in the semi-major axis; the in-plane velocity increment can lead to the changes in the semi-major and eccentricity, and the out-plane velocity increment usually only causes changes in the inclination. 2.1. Analysis step of the semi-major axis change The semi-major axis change can be caused by the changes of the along-track and in-plane track velocity additions. The changes of the eccentricity and inclination are caused by the velocity increment of in plane and out plane. However, it is difficult to identify the cause for the velocity changes of in-plane and out-plane, respectively. Whether it is the collision, the explosion breakup or the orbit manoeuvre, there will be obvious changes in the semi-major axis. In order to detect the orbit anomaly of an object, the most common method is to find the orbital mean motion or the semi-major axis anomalous changes. In the current paper, the semi-major axis change is taken as an anomalous parameter for analyzing the orbit anomaly of the space objects. Obviously, the semi-major axis change is not a TLE parameter, but it is derived from a TLE parameter, mean motion, which is also used to derive the total energy (Patera, 2006, 2008; McNeill et al., 2009). The anomalous analysis steps are outlined as follows: (1) Taking the data of the last three months (or longer) before the analysis period as samples and considering the orbital data at any time as a basis. Then, calculating the time and semi-major axis change of the other data relative to the basis and obtaining a series of time intervals Dt and semi-major axis changes Da. (2) After gaining the time and semi-major axis changes, these changes are classified by time. Here, the time interval is rounded off and the absolute value of the semi-major axis change is taken, namely |Da|. So, these absolute values are chosen as analysis variables. (3) For the sample of each integer day time interval, the mean value jDaj and standard deviation rðjDajÞ of the analysis variables are calculated. Therefore, a threshold for the semi-major axis changes at the integer time intervals for any space object is given, that is kðjD aj þ 3rðjD ajÞ (k P 1)).
387
(4) For the analysis period, the time interval Dt and the corresponding absolute value of the semi-major axis change jDaj are derived. Comparing the result with the above threshold, if it is larger than the threshold, it is considered as abnormal, or it is abnormal. 2.2. Method of deleting outliers For surveillance and other reasons, there are many anomalous and outlier points for a series of TLEs which need to be deleted during the anomalous analysis. For the sample data, both the outlier and anomalous points need to be deleted before deriving the normal changes of the semi-major axis. For the analysis data, the outliers need to be deleted from the anomaly analysis results. (1) Deleting the outlier and anomalous point of sample data: For simplicity, the outlier and anomalous points are not usually larger than 20% of the total sample. So, 20% of the sample data with larger values are deleted. (2) Deleting the outlier of analysis data: The outliers usually have the following characteristics: (1) The outlier point is the anomalous one. (2) The product of the changes of the semi-major axis for the outliers of the adjacent TLE data points is negative. (3) The sum of the changes of semi-major axis for the outliers of the adjacent TLE data points is very small. All the outliers can be deleted according to the above characteristics. 3. Anomalous analysis of operational satellites in LEO orbit According to the orbital information of operational satellites obtained from UCS (Union of Concerned Scientists) Satellite Database in July 2009, 426 satellites in LEO orbit were analyzed. The TLE data from January 1, 2009 to July 1, 2009 were chosen as a sample and the data from July 1, 2009 to December 1, 2009 were analyzed. Totally, 401 out of 426 operational satellites had TLE data. 3.1. Threshold determination of anomalous analysis The maximum time intervals of the adjacent TLE data were obtained by anomalous analysis. Then, these maximum time intervals were regarded as the largest time interval of the sample. Because update frequency of the satellite in orbit is usually faster, the time interval of TLEs is not larger than seven days. The update frequency of most satellite is one or two days. For the anomalous threshold kðjDaj þ 3rðjD ajÞÞ, 99.74% of the analysis data should be within the threshold when k = 1. However, the change of the semi-major axis is much
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larger than the normal change when satellite orbit anomaly occurs. k is not only related to the orbital and physical characteristics, but also related to the reason for satellite anomaly, such as the magnitude and the time of the maneuver thrust force. Because it is usually difficult to get the above information, the value of k can be adjusted by comparing the SACM results with the human judgment results in the analysis. k = 3 is finally identified, so the anomaly threshold 3ðjD aj þ 3rðjD ajÞ can be used for the satellite in LEO orbit. However, the outliers in the anomalous results need to be deleted. When the product of adjacent semi-major axis changes is negative and the sum of the adjacent semi-major axis change is less than k 2 jD aj (jDaj is the mean of the semi-major axis change and k2 is equal to 5 according to experience), it is a outlier and needs to be deleted. That means the outlier satisfies the following conditions: DaðjÞ Daðj þ 1Þ < 0 ð2Þ jDaðjÞ þ Daðj þ 1Þj < 5jD aj
Table 2 Statistical results of the anomalous operational satellites. Anomalous object number (SACM result)
Comparison of orbit change segments between SACM result and human judgment Equal
Less
Larger
190
120
14
56
Table 3 Analysis results of non-anomalous satellites. Non-anomalous object number (SACM result)
Judged by human Anomalous object number
Non-anomalous (human judgment)
211
21
190
(3) There are 211 non-anomalous objects in SACM results shown in Table 3. By analyzing their orbit mean motion of 211 objects, there are 21 objects with orbit anomaly, including 50 orbit change segments.
3.2. Anomalous results The SACM considers the semi-major axis change as the threshold in different time intervals to identify orbit anomaly, and at the same time the outliers are deleted. The SACM results are compared with that of human judgment method, which means that the results are judged by human by analyzing the curve change of the semi-major axis change with the time and the abnormal change of the semi-major axis can be easily judged by human brain according to the history change trend. In this paper, 401 operational LEO satellites were analyzed and the results were given as following: (1) After the outliers were deleted from the anomalous results, 190 objects are involved as anomaly and there are 1492 anomalous points for 190 objects. By analyzing the anomalous points, there are 332 segments of orbit change, while there are 394 segments of orbit changes by human judgment in Table 1. (2) It can be seen from Table 2 that for 190 objects, there are 120 objects have the same number of the orbit change segments for both SACM results and human judgment results. For 14 objects, the number of orbit change segments judged by human is less than that of SACM results. For 56 objects, the number of orbit change segments judged by human is larger than that of SACM results in Table 2. Table 1 Anomalous result of the operational LEO satellites. Anomalous points
Anomalous object number
Orbit change segments SACM
Human judgment
1492
190
332
394
4. Breakup event of Cosmos 2251 and Iridium 33 and anomalous analysis of its breakup debris Breakup event is a main source of space debris and a major category in orbit anomalous events. Usually after a large breakup event, the orbits of the space objects involved in the event can change abruptly. The extent and manner of orbit anomaly are related to the breakup intensity. The collision between Cosmos 2251 and Iridium 33 which happened in February, 2009 is a large orbit anomalous event, and is the first collision breakup happened between two intact catalog satellites. After the collision breakup, the orbits of the two satellites changed anomalously, including the semi-major axis, eccentricity and inclination. For this breakup event, the SACM was used to analyze the orbits of the breakup satellites and breakup debris and determine their anomalous orbit changes. Further the orbit anomalous changes of the breakup debris were classified. Their orbits were analyzed by the SACM. The analysis results could be used to indentify the collision breakup and understand the detection ability of SSN for breakup debris. 4.1. Orbit anomaly analysis of American–Russian satellites break events Before the collision of Cosmos 2251 and Iridium 33, their orbits changed regularly. Iridium 33 maintained its orbit periodically, the magnitude of orbit change was not large, and usually less than 0.5 km for each orbit change. Both orbits undergo abrupt changes at the collision time in Figs. 1 and 2. The mean change of semi-major axis is 3 km for Cosmos 2251 satellite (see Fig. 1), and 5 km for Iridium 33 which was uncommon compared with the usual
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The changes of the mean motion for the breakup debris with time from February 1, 2009 to March 1, 2010 were analyzed and the following results could be given: (1) The mean motion of most American–Russian debris had the ascending trends with time. (2) Some had periodic change trends. (3) The update frequency of the debris was different. Even for the same debris, the update frequency also had large difference for different analysis periods. (4) Some orbits of debris had some break, even some orbits happened abrupt change that means orbit anomaly. Orbit anomaly of American–Russian satellites breakup debris can be divided into three classes: Fig. 1. Semi-major axis changes of Cosmos 2251 satellite for breakup.
(1) The initial orbit was unsteady;Part of them was published in a short period after satellite breakup and their orbits were not stable. These debris orbits were densely distributed and hard to be detected and identified (see Figs. 3 and 4). (2) Orbit changes abruptly:Some orbits of the breakup debris change abruptly. If the changes were not caused by the collision or explosion, the catalog data were problematic (see Figs. 5 and 6).
Fig. 2. Semi-major axis changes of Iridium 33 satellite for breakup.
change (see Fig. 2). The intersection and anomaly analysis could help us to find the breakup event. 4.2. Orbit anomaly analysis of American–Russian satellites breakup debris Fig. 3. Semi-major axis changes of object 33757.
The American–Russian satellites breakup event produced a large quantity of debris with different velocity increments along different directions. Initially the breakup debris were concentrated in a small region. Then the debris gradually dispersed. Due to a short period of the concentration and the special characteristics of the breakup debris, such as the instability and the large area mass ratio, the American–Russian satellites breakup debris were hard to recognize. Generally, the breakup debris may undergo some abnormal changes caused by the errors in detection. By an anomaly analysis, SSN detecting rate can be given. So the data of breakup debris are abnormal for a short time after breakup. The SACM can be used to identify the orbit anomaly of the breakup debris. Then, orbit anomaly analysis is made for American–Russian satellites breakup debris.
Fig. 4. Semi-major axis changes of object 33762.
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of space objects is relatively small, the probability of orbit change induced by collision is very small. If the orbit anomaly caused by collision is not considered, the anomaly ratio of breakup debris may reflect the detecting ability of SSN. The following is the orbit anomaly analysis for American–Russian satellites breakup debris using the SACM. By adjusting the anomalous factor k, the optimal anomalous results can be obtained. Finally k = 10 is adopted. 4.2.1. Anomaly analysis of Cosmos 2251 breakup debris Orbit anomaly analysis of Cosmos 2251 breakup debris is listed as following: Fig. 5. Semi-major axis changes of object 34011.
(a) There were 49 anomalous objects for program results shown in Table 4. From Table 4, it can be seen that 39 anomalous objects were identified by human judgment, and the orbits of 10 objects changed rapidly (8 objects were in the decay period). The accuracy rate was 100% (49/(39 + 10)), if considering rapid orbit change as orbit anomaly (see Table 4). (b) In the 39 breakup debris with orbit anomaly of Cosmos 2251 (not considering the decaying object), there are 44 orbit change segments by SACM calculation, and 45 orbit change segments by human judgment. SACM results and human judgments have the same results for 38 objects. Only one SACM result is less than that of human judgment. Table 4 shows the comparison of SACM results with human judgment of anomaly objects for Cosmos 2251 breakup debris.
Fig. 6. Semi-major axis changes of object 34078.
4.2.2. Anomaly analysis of Iridium 33 breakup debris Orbit anomaly analysis of Iridium 33 breakup debris is demonstrated as following: (a) Table 5 shows that there were 8 anomalous objects and 2 of them were in the decay period. The accuracy rate was equal to 100% (8/(2 + 6)) if considering rapid orbit change as orbit anomaly. Table 4 Comparison between SACM results and human judgment results of anomaly objects for Cosmos 2251 breakup debris. SACM result
Anomalous object number
49
Human judgment result
Anomalous Rapid orbit change (not including reentry) Decay Sum
39 2 8 49
Fig. 7. Semi-major axis changes of object 34652.
(3) Outlier point of data:The main reason for the outlier points is usually attributed to the error of the detection (see Fig. 7). Orbit anomaly analysis is mainly used to identify the abrupt change of the second situation. Because the density
Table 5 Comparison of SACM results with human judgment results of anomaly objects for Iridium 33 breakup debris. SACM result
Anomalous objects number
8
Human judgment result
Anomalous Decay
6 2
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(b) In the 6 objects with orbit anomaly of Iridium 33, there are 6 orbit change segments by SACM calculation and 7 by human judgment.From the above analysis, some conclusion can be derived: (1) The SACM can identify the orbit anomaly of American–Russian breakup debris effectively. (2) k = 10 was effective for anomaly identification of American–Russian breakup debris.
5. Conclusion On the basis of the relationship between the change of orbit parameters and velocity increments, a semi-major axis change method (SACM) was put forward. An anomalous threshold was given in different time intervals for objects in different orbits. Orbit anomalous analysis was made for the LEO satellites and the American–Russian breakup debris and their orbit change characteristics were explored. The results indicated that the method was rapid and valid. The accuracy rate of the anomaly analysis for LEO satellites and American–Russian breakup debris can reach 100% with the SACM.
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Acknowledgements This paper is supported by the National Nature Science Foundation of China (91016013) and the Program for New Century Excellent Talents in University. References Patera, R.P. Space event detection method, AIAA/AAS Astrodynamics Specialists Conference AIAA 2006-6513, Keystone, Colorado, August 21–24, 2006. Johnson, N.L. Environmentally-induced debris sources, NASA Lyndon B. Johnson Space Center, Second World Space Congress, 2002. Patera, R.P. Space event detection method. J. Spacecraft Rockets 45 (3), 554–559, 2008. McNeill Jr., J.F., Coggi, J.M., Ailor, W.H., et al. Space situation monitoring laboratory: an integrated web-based environment for space environment information and analysis, in: Proceedings of the AAS/ AIAA Astrodynamics Specialist Conference, AAS 09-416, Pittsburgh, Pennsylvania, August 2009. Kelecy, T., Hall, D., Hamada, K., et al. Satellite Maneuver detection using two-line element (TLE) data, 2007,