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Maneuver Detection of Space Object for Space Surveillance

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Maneuver Detection of Space Object for Space Surveillance MANEUVER DETECTION OF SPACE OBJECT FOR SPACE SURVEILLANCE Jian Huang*, Weidong Hu, Lefeng Zhang $756WDWH.H\/DE1DWLRQDO8QLYHUVLW\RI'HIHQVH7HFKQRORJ\&KDQJVKD+XQDQ3URYLQFH&KLQD (PDLOKXDQJMLDQ#QXGWHGXFQ ABSTRACT on the technique of a moving window curve fit. Holzinger & Scheeres presented an object correlation Maneuver detection is a very important task for and maneuver detection method using optimal control maintaining the catalog of the orbital objects and space performance metrics [5]. Kelecy & Jah focused on the situational awareness. This paper mainly focuses on the detection and reconstruction of single low thrust in- typical maneuver scenario where space objects only track maneuvers by using the orbit determination perform tangential orbital maneuvers during a relative strategies based on the batch least-squares and long gap. Particularly, only two classical and extended Kalman filter (EKF) [6]. However, these commonly applied orbital transition manners are methods are highly relevant to the presupposed considered, i.e. the twice tangential maneuvers at the maneuvering mode and a relative short observation gap. apogee and the perigee or one tangential maneuver at In this paper, to address the real observed data, we only an arbitrary time. Based on this, we preliminarily consider the common maneuvering modes and estimate the maneuvering mode and parameters by observation scenarios in practical. For an orbital analyzing the change of semi-major axis and maneuver, minimization of fuel consumption is eccentricity. Furthermore, if only one tangential essential because the weight of a payload that can be maneuver happened, we can formulate the estimation carried to the desired orbit depends on this problem of maneuvering parameters as a non-linear minimization. Therefore, choices in the modes of least squares problem. To obtain a more sensible and orbital maneuver are limited. The thrust imposed on accurate result, the prior knowledge is incorporated the tangential direction is an efficient maneuvering into the iterative solving process calculated by SOCP mode for minimizing fuel consumption, which is algorithm. Finally, the performance and efficiency of commonly applied in the process of various orbital our method are validated by the theoretical analysis maneuvers [7]. In particular, the maneuvering positions and some observations. are usually chosen at the apogee and perigee point [7]. The studies in this paper are based on all the above- 1 INTRUDUCTION mentioned hypothetical maneuvering modes. Nowadays, there are at least 20000 trackable objects in Furthermore, due to the limited coverage of the sensors, earth orbit and among them 1300 have the capability of the small and regular observation gap couldn’t be performing orbital maneuver [1]. When the orbital guaranteed, which may be from hours to many days. maneuver occurs unexpectedly during the gaps, how to Therefore, it is more meaningful and expected that the detect and reconstruct the abnormal event will directly performance of the proposed maneuver detection affect the capability of space situational awareness. method will be little affected by the observation gap, Particularly, the available observations collected by the especially the large gap. Certainly, we also hope to current space surveillance systems, such as the AFSSS reconstruct the maneuvering parameters precisely (US Air Force Space Surveillance System) [2], which when the maneuver event occurs during a small gap. has a long gap between the neighboring observations, This paper presents a novel and stepwise algorithm to are generally discrete in the spatial-temporal domain. handle these problems as follows. In section 2, the The problem of maneuver detection during observation maneuvering modes and maneuvering parameters are gaps brings much more difficult, in contrast with that estimated preliminarily according to the change of commonly encountered in real-time tracking semi-major axis and eccentricity. If there is only one applications. tangential maneuver during the gap from the result, we Regarding the problem of maneuver detection, the formulate the estimation problem of maneuvering corresponding methods are the varieties with respect to parameters as a non-linear least squares problem. Thus, different modes of orbital maneuvering and detection a more precise result can be obtained by solving the metrics. Storch estimated the maneuvering parameters constrained non-linear least squares iterative process of a collocated satellite in geosynchronous orbit by using SOCP (Second Order Cone Programming) using nonlinear least squares [3]. In [4], the energy per algorithm in Section3. Section 4 is the simulation unit mass was computed to detect a space event based results and performance analysis. Section 5 is the _____________________________________ Proc. ‘6th European Conference on Space Debris’ Darmstadt, Germany, 22–25 April 2013 (ESA SP-723, August 2013) conclusion. 'DH 32 ' cos I HHDDH (2) 'DD 1 H2 2 H'H 2 ESTIMATION OF MANEUVERING MODE When we want to obtain the sensible values of the As we know, the orbits often have the unexpectable maneuvering true anomaly I and velocity 'Y , the changes due to undertaking the various tasks. The most solution of Eq. 2 must satisfy: frequent orbital maneuvers are implemented to keep 1cddosI 1 (3) the spacecraft at the prearranged orbit, especially the semi-major axis D and eccentricity H which determine However, Eq. 3 can’t be always satisfied, i.e. only one the orbital shape. Generally, these two orbital tangential maneuver can’t simultaneously adjust the parameters are controlled more rigorously than any semi-major axis and eccentricity arbitrarily. Therefore, other parameters, and they are usually not allowed to multiple maneuvers should be applied, one efficient fluctuate with respect to the time. The common and mode of which is that twice tangential maneuvers at efficient maneuvering mode is to exert an additional the apogee and perigee point which could minimize the tangential velocity at a proper point or the perigee and fuel consumption. apogee point [7]. However, one tangential maneuver can’t simultaneously adjust the semi-major axis and 2.2 Twice tangential maneuvers at the eccentricity arbitrarily, while two tangential maenuvers perigee and apogee at the apogee and perigee can do that. They are both the common applying maneuvering modes. Therefore, Most of the orbits of space objects have small the maneuvering mode and the corresponding eccentricities and can be approximated as circle orbits. maneuvering parameters can be estimated preliminarily Thus, the item H2 in Eq. 1 can be omitted. Eq. 1 can be according to the change of semi-major axis and transformed into: eccentricity. ­ 2 12 °QD' 2 12HIcos H'Y ® (4) 2.1 One tangential maneuvering mode 2 12 ¯°QD'HY 2 12HIcos H cos IH ' If the observed semi-major axis and eccentricities changed obviously at different times, the maneuver Firstly, the 'Y is used to adjust the eccentricity H at detection should be taken into account. Based on the the perigee or the apogee, i.e. I 0D or I 180D . hypothesis of one tangential maneuvering mode, we This maneuvering velocity is denoted as . should reconstruct the maneuvering velocity as well as 'Y H judge that where the maneuver occurs and whether D When I 0 , we can get ''YQ DH 2 . When only one tangential maneuver can realize this change of H D these parameters. I 180 , ''YQ H DH 2 . According to the perturbation motional formula, a After the adjusting of eccentricity H , the semi-major tangential impulse velocity 'Y exerted at an arbitrary axis D should be modified a value 'D to adapt the point I during the orbit will simultaneously change final change. 'D includes two parts: the first is the value of the semi-major axis 'D and eccentricity original changed value 'D ; the second is the deviation 'H as Eq. 1: dD H caused by the adjusting of H . Thus, the current D ­ 2 12 value is 'DD ' dD H . Therefore, when I 0 , 'DY 2 ' ° 12HIcos H D ° QH1 2 'D 'D H 1 DH' ; when I 180 , 'D 'D ® (1) 2 H 1 DH' . In addition, when the signs of 'D and ° 21 H 2 12 'HY 12HIcos H cos IH ' D ¯° QD 'H are the same, we choose I 0 ; while they are different, we choose I 180D . Accordingly, the value Where QD P 3 , P 3.98600436u1014PV 3/ 2 is the of 'D will be reduced and the fuel consumption is earth gravitational constant, I is the true anomaly. saved. Once the 'D and 'H are known, we can calculate the In order to adjust the 'D , we exert an equivalent maneuvering parameters I and 'Y . Dividing the each once at the apogee and second equation by the first equation at Eq. 1, we can tangential velocity 'Y D obtain that: perigee respectively. In this case, the eccentricity H will not be changed while adjusting D according to Eq. 4. We can obtain that 'Y D QD' 4 . Finally, twice tangential maneuvers at the perigee and apogee ) m 350 k can be utilized to achieve the arbitrary change of ( eccentricity H D de and the semi-major axis . The tu ti 300 concrete formats are as follows: al l ta (1) When the sign of 'D and 'H are the same, bi 250 2 7 12 17 'DD ' 1 H D'H, and the first tangential impulse Or Time(circle) ty D ci 0.01 'Y1 is exerted at I 0 , the second tangential impulse i D ntr 'Y2 is exerted at I 180 , where 0.005 ecce l ta ­ QD''H QDDD ' 1 H 'H bi 'YQ 0 ° 1 Or ° 24 4 2 7 12 17 ® (5) Time(circle) QD'' D 1 H D'H °'YQ )LJXUH2EVHUYDWLRQVDWWKHILUVWWLPH ¯° 2 44 7DEOH$QDO\VLVUHVXOWVRIWKHILUVWREVHUYDWLRQV (2) When the sign of 'D and 'H are different, Circle 1 to Circle 2 Circle 2 to Circle 16 'DD ' 1 H D'H, and the first tangential impulse Maneuver Maneuver Maneuver Maneuver D velocity position velocity position 'Y1 is exerted at I 180 , the second tangential (m/s) I(°) (m/s) I(°) D Mode 1 X X X X impulse 'Y2 is exerted at I 0 , where -15.5 180 -17.4 0 Mode 2 ­ QD''H QDDD ' 1 H 'H -15.5 0 3.9 180 °'YQ1 From Tab.
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