Trans. JSASS Aerospace Tech. Japan Vol. 14, No. ists30, pp. Pj_13-Pj_20, 2016
Progress of Search Operation for IKAROS by means of Open-loop Tracking Data
By Shota KIKUCHI,1) Hiroshi TAKEUCHI,2) Osamu MORI,2) Yuya MIMASU,2) Yoji SHIRASAWA,2) Hideki KATO,2) Naoko OGAWA2) and Sho TANIGUCHI3)
1)Department of Aeronautics and Astronautics, The University of Tokyo, Tokyo, Japan 2)Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Japan 3)Fujitsu Limited, Tokyo, Japan
(Received July 30th, 2015)
The latest re-acquisition of IKAROS, which rebooted after hibernation mode, was achieved on April 23, 2015. In this re-acquisition, post-processing of open-loop tracking data was performed to search for IKAROS. The open-loop method enables signal processing, even under difficult communication conditions. The algorithm for processing open-loop tracking data is proposed and is applied for actual signal from IKAROS. It is demonstrated that the signal can be well analyzed by removing the Doppler shift effect because of the orbital and spinning motion of IKAROS, even when the signal is too weak to be acquired by real-time operation. Using the method proposed in this study, estimating the spinning motion of a spacecraft and acquiring various data are possible as well as detecting signal. This research can be applied not only to a spinning-type spacecraft, such as IKAROS, but also to those with uncertain attitudes.
Key Words: IKAROS, DFT, Spin Modulation, Open-loop Recording, Search Operation
Nomenclature The latest re-acquisition was achieved by the off-line post-processing of data stored by an open-loop recorder. t : time Unlike closed-loop, real-time signal detection, open-loop f : frequency recording enables repeating signal processing many times f : resolution band-width (RBW) under different conditions. This capability can be highly s : signal advantageous when signals are weaker, less stable, or at a S : Fourier spectrum different frequency than expected, and thus open-loop 2) P : power spectrum recording has been used in several deep space missions. For N : number of DFT points example, it was used in a radio science mission of the Galileo probe during its entry into the Jovian atmosphere.3) SNR : signal to noise ratio Additionally, the Mars Exploration Rovers used open-loop T : DFT time window length recording for communication during the entry, descent and x : modeled signal landing phases.4) In these two examples, open-loop systems handled the uncertainty in the spacecraft motion and 1. Introduction frequency shifts caused by the atmosphere. Open-loop recording is also used for very long baseline interferometry to IKAROS is the world’s first interplanetary solar sail determine the delay of quasar or spacecraft signals.5) spacecraft and was launched by JAXA in 2010. It successfully In this research, the use of open-loop tracking data to search completed all of its nominal missions and has continued to for a lost spacecraft is proposed. In the search operation for operate in additional missions (Fig. 1). However, IKAROS ran IKAROS, open-loop recording was useful because uncertainty out of propellant for attitude control, and thus it is no longer exists in the spacecraft motion because of SRP. Moreover, the able to control its attitude. Consequently, IKAROS shifted to post-processing of open-loop tracking data enables complex hibernation mode and lost communication with ground and iterative signal processing to remove the Doppler shift stations in January 2012 because of a lack of solar power. effect caused by the spinning motion of the spacecraft, which IKAROS subsequently became capable of generating is called spin modulation. Using this method, the orbital and sufficient power again because of a decrease in the sun angle, and eventually, communication was re-established in September 2012.1) This occurred because of the search operation that was used to predict the attitude motion of IKAROS, which can be changed dynamically by solar radiation pressure (SRP). The hibernation mode and re-acquisition were later repeated, and IKAROS was re-acquired again on April 23, 2015. Although this was the fourth acquisition, success was achieved in a different way than in the previous three times. Fig. 1. The solar sail spacecraft IKAROS.
Copyright© 2016 by the Japan Society for Aeronautical and Space Sciences and1 ISTS. All rights reserved.
Pj_13 Trans. JSASS Aerospace Tech. Japan Vol. 14, No. ists30 (2016) spinning motion of a spinning spacecraft can be estimated axis and the antenna boresight. This spin modulation effect accurately, even under difficult communication conditions, makes it difficult to decode data or even detect a signal from such as weak signals and large spin rates. In addition, despite the spacecraft, especially when the spin rate is high. Moreover, such severe conditions, the decoding of ranging or telemetry the spinning motion is also affected by SRP, and the spinning data may be possible with an open-loop recording method. state is difficult to predict; as a result, the estimation of the The method proposed here can be applied not only to a spin modulation effect also becomes difficult. spinning-type spacecraft but also to one whose attitude is The open-loop recording method proposed in this study uncertain because of some problems. Therefore, this method enables communication with the spacecraft, even under such can provide flexibility and redundancy in spacecraft operation. severe conditions. 2.2. Communication requirements 2. Outline of Search Operation To communicate with IKAROS, the following conditions must be satisfied.1) 2.1. Difficulty in operation of IKAROS 1. Sun angle: less than 60 deg The solar sail spacecraft IKAROS has a cylindrical body and 2. Earth angle: less than 80 deg a square sail membrane with a surface of approximately 200 m2, 3. Pointing error of a ground antenna: less than 0.015 deg as shown in Fig. 2.1) The large sail membrane of IKAROS Here, the definitions of the Sun and Earth angles are given in enables the solar photon acceleration by SRP because of the Fig. 3. reflectivity of the aluminum evaporated on the surface of the The first requirement is needed for the solar arrays on the membrane. IKAROS is a spinning-type solar sail, and the top of the body to generate sufficient power. During extension of the large sail is maintained by the centrifugal force hibernation mode, if this condition is satisfied, IKAROS generated by the spinning motion of the spacecraft. Such a reboots automatically and can communicate with a ground spinning-type solar sail does not require masts to sustain a large station. It should be noted that the upper limit of the sun angle membrane, and thus, the weight of a spacecraft is minimized. varies according to several factors, including the solar distance These characteristics of IKAROS cause difficulties and the age and temperature of the solar arrays. regarding communication. First, IKAROS is accelerated by The second requirement is needed for the antenna of SRP, and its attitude is varied everyday by SRP torque, which IKAROS to point in the direction of the Earth. This Earth affects its orbital motion. Therefore, it is difficult to accurately angle restriction applies to one of the two LGAs mentioned in predict the IKAROS’s orbit. Consequently, after having lost the previous section. As indicated in the introduction, communication with a ground station, the re-establishment of IKAROS ran out of propellant for attitude control, and thus, communication is highly difficult. whether these two requirements are satisfied depends Another difficulty is related to the spinning motion of the completely on the natural motion of the spacecraft. spacecraft. As shown in Fig. 2, there are four antennas In addition to the antenna on the spacecraft, an antenna on a mounted on IKAROS, two of which are LGAs used for ground station must point in the correct direction; this is the normal operation because of their broader beam width. These third requirement. To satisfy this condition, the orbital motion antennas are fixed on the body without despin mechanisms, and attitude motion of the spacecraft must be estimated with and thus, the signals from the spacecraft includes spin adequate accuracy. Another approach for this requirement is modulation effects because the difference between the spin to try as many different antenna offset patterns as possible within the limited operation time; this approach can be efficiently implemented using the open-loop recording method proposed here. Based on this approach, IKAROS can be acquired, even when some ambiguity exists in the orbital and attitude predictions, as accomplished in the latest acquisition. 2.3. Past search operation results Figure 4 shows the trajectory of IKAROS, and Fig. 5 shows the Sun and Earth angle histories. These figures contain information 1) Fig. 2. IKAROS Configuration. about the past and future. As of May 2015, IKAROS has been
re-acquired four times. The yellow regions in Fig. 5 represent the periods when the Sun and Earth angle requirements stated in the previous section are satisfied. It should be noted that these regions are given based on calculations, and thus, do not necessarily match the days on which communication with IKAROS was actually achieved. Although the search operation is affected by several difficulties, as previously stated, the IKAROS operation team has successfully acquired and re-established communication after each hibernation mode so far. This research actually contributed to the latest re-acquisition, confirming that the proposed method is valid and highly useful. Fig. 3. Definition of the Sun and Earth angles. The next re-acquisition will be possible around November
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fsmp f (5) N Sk is called the Fourier spectrum and encodes the information about the amplitude and phase of the corresponding frequency component fk . Practically, the power spectrum of fk given by the next equation indicates the energy of the frequency and is essential for signal analysis 2 Pk Sk (6) Signal quality can be evaluated by the signal-to-noise ratio (SNR). In this paper, SNRk is given by the next equation and is used to compare the performance of each DFT. Fig. 4. Trajectory of IKAROS in the Sun-Earth fixed coordinate.1,6) Pk P SNRk The points expressed as diamonds represent the dates when IKAROS n 1 (7) was re-acquired. The terminal point of the trajectory represents the (P P)2 n i approximate date on which IKAROS will be next re-acquired. i1 where n 1 P Pi (8) n i1 To analyze the power spectrum of a whole signal whose frequency changes over time, each DFT is performed over a short time period and successively along the time axis. The
period can be overlapped if necessary. This method is Fig. 5. Sun angle and Earth angle history.1,6) The yellow regions show sometimes called short-time Fourier transform. In this period, the times when the Sun and Earth angles requirements are satisfied. the time of each DFT is defined as follows.
t0 tN 1 2016, and at this time the Earth distance will be nearer than at any (9) 2 other past re-acquisition. Therefore, much more data concerning Even when a signal of a spacecraft is weak, or the SNR is IKAROS are expected to be obtained. large, in practice, the SNR can be improved by summing a
successive power spectrum for a certain time period as shown 3. Conventional Method in the following equation.
j 3.1. Discrete Fourier transform ~ P ( ) P ( ) (10) To analyze the spectrum of a signal from a spacecraft, k j k n ni discrete Fourier transform (DFT) is widely used. Since the Here, this time period is called integration time and is computation of DFT requires large calculation costs, an expressed as follows. algorithm called fast Fourier transform (FFT) is typically t (11) applied. int j i The improved SNR over some integration time can be Time series data of a discrete received signal can be k ~ expressed as obtained by replacing Pk in Eq. (7) with Pk in Eq. (10). 3.2. Problem sn In iQn (1) The analysis results obtained by applying DFT are given in where I and Q represent in-phase and quadrature n n this section. Figure 6 shows the analysis result of the actual components of the signal, respectively. The DFT performed signal from IKAROS on April 23, 2015, which is the day on on this signal is given as follows.7) N 1 which IKAROS was re-acquired. The signal processed in this i2fk tn analysis was a continuous wave, and thus, the signal intensity Sk sne (2) n0 was relatively high. This figure is called a spectrogram and where presents the time history of the power spectrum corresponding k T to each frequency component. fk , tn n (3) The upper spectrogram in Fig. 6 has a peak frequency trend T N which shifts over time. This Doppler shift is caused by the Here, N represents the number of DFT points and T relative orbital motion of the spacecraft with respect to a represents the time length of the DFT, which are related to the ground station whose position changes according to the sampling rate f as follows. smp rotation of the Earth. The lower figure is a magnified image of N fsmp (4) a portion of the upper figure. The lower figure shows that the T peak frequency shift mentioned above has a sinusoidal From Eqs. (3) and (4), the resolution band-width (RBW) is component because of the spin modulation resulting from the given by the following equation. spinning motion of IKAROS. Therefore, the angular
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Fig. 7. Spectrogram of a weak signal.
established, and a command is uplinked to turn off the modulation. Because of the weakness of the signal, no trend in the peak frequency appears in Fig. 7. However, the following part shows that a trend can be seen in the same time-frequency space using improved algorithm. It can be concluded that the signal processing method involving DFT with small RBW and a short integration time is not suitable to directly trace a
frequency shift as shown in Fig. 6, when the signals are Fig. 6. Spectrogram of a strong signal. comparatively weak. The search operation was actually performed on April 16, Table 1. Calculation conditions (Overlap: overlap rate, RODS: 2015, but the operation team was unable to identify a signal re-moving orbital Doppler shift effect, RSM: removing spin modulation using a spectrum analyzer at a ground station. Thus, real-time effect). signal processing has limitations that are basically the same as Figure 6 7 11,12 13,14 18,19,20 those described above. Date Apr 23, Apr 16, 2015 2015 4. Open-loop Recording Method Modulation off on fsmp [kHz] 50 200 200 200 200 4.1. Concept N 215 217 213 213 217 When the signal is very weak, a long integration time can f [Hz] 1.5 1.5 24.4 24.4 1.5 be used to improve the SNR in practice. However, the t [sec] 0.2 0.2 300 300 300 int frequency of a spinning-type spacecraft, such as IKAROS, Overlap 0.5 0.5 0.5 0.5 0.5 changes over time because of orbital Doppler shift and spin RODS × × × RMS × × × × modulation, and thus, the power of a signal disperse around a peak frequency when the integration time is long.
To solve this problem, a method to remove the orbital frequency of this sinusoidal shift is identical to the spin rate of Doppler shift and spin modulation effects from open-loop the spacecraft. recording data is proposed. If these effects are removed from a The calculation conditions used for the analysis shown in signal, the frequency of the processed signal will become Fig. 6 are listed in Table 1, which also presents the calculation constant with respect to time, and the use of long-time conditions of the signal processing described below. It should integration becomes possible. be mentioned that in order to see a spin modulation effect, Figure 8 shows the frequency model of an original received RBW f must be sufficiently smaller than the spin signal from a spinning-type spacecraft. The frequency change amplitude of the spacecraft which is usually approximately caused by orbital Doppler shift and spin modulation can be 20–30 Hz. The integration time tint must also be sufficiently well modeled by the equations given in this figure. It is small relative to the time scale of the spinning motion of the important to estimate the parameters (a, b, c, A, B, C) to spacecraft. For the window function, the Hamming window is remove these effects, and the estimation algorithm is proposed used for all of the DFT analyses performed here. in the following part. Another result obtained by applying DFT to the open-loop The analysis process for open-loop recording data is shown tracking data from April 16, 2015, is shown in Fig. 7. This in Fig. 9. According to each process, several types of highly was the day before communication with IKAROS was important information about a spacecraft can be obtained. re-established. The communication subsystem of IKAROS is Initially, the orbital Doppler shift effect is removed from the programmed to transmit a signal with modulation after data by DFT analysis with sufficiently large RBW to avoid the rebooting from hibernation mode. Therefore, the signal from spin modulation effect. If a signal can be detected by this the space-craft is very weak before communication is process, a spacecraft can be acquired. Once the orbital
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Fig. 10. Process of computing a spectrum by DFT.
corresponding to fk f ( ) . If an analytical expression xn could completely model a real signal sn , the spectrum would include only the component corresponding to f0 . Therefore, if sn is well Fig. 8. Frequency model of a received signal. modeled, the frequency of sˆn becomes constant with respect to time, and the power spectrum of the signal can be integrated, as shown in Eq. (10), even for a long integration ˆ time. Once a spectrum Sk is calculated, a spectrum Sk of an original signal sn can also be obtained from Eq. (15). The relationship between each signal and spectrum is expressed in Fig. 10. Parameters (a, b, c, A, B, C) in Eq. (12) should be optimized by numerical calculations. The optimized parameters must satisfy the following condition at time .
maximize J (a, b, c, A, B, C) SNR0 ( ) (16) Fig. 9. Achievable status according to each process. Here, J is the objective function, and SNR0 is calculated ˆ from Eqs. (6) and (7) by substituting Sk of Eq. (15) into Sk Doppler shift effect can be removed, more precise analysis of Eq. (6). This algorithm requires iterative numerical with small RBW to remove the spin modulation effect can be calculation in principle, and thus, the open-loop recording performed. Several types of useful data can be subsequently method is necessary. obtained, such as in-formation about the spinning state of a spacecraft, range rate data and beacon data. 5. Analysis Result Furthermore, if the phase of a signal is synchronized, it will also be possible to obtain range data and telemetry data, even 5.1. Removing the orbital Doppler shift effect when the signal is weak enough to prevent obtaining these A long integration time is necessary for processing a weak data by real-time processing. However, this process has not signal. In this section, DFT analysis results obtained with been implemented yet and should be investigated in the future. large RBW to avoid the spin modulation effect are shown. 4.2. Algorithm Figures 11 and 12 show the result obtained by processing First, the frequency of an input signal sn ( ) is modeled by the same signal shown in Fig. 7 with longer integration time the equation below. and without removing the orbital Doppler shift effect. The 2 f (t) a bt ct Acos(B Ct) (12) peak of the signal frequency can be clearly seen in Fig. 11, Then, the modeled signal at time is given as follows. although no such peak appears in Fig. 7. This DFT analysis
i2f ( )tn used an integration time of 5 minutes, as stated in Table 1, and xn e (13) thus, the practical SNR is sufficiently improved to show a A modified signal sˆ is defined by the following equation, n peak trend. Figure 12 shows the power spectrum of each * sˆn sn xn (14) frequency at 2:20, which is called a periodogram. A peak * where xn denotes the complex conjugate of xn . If DFT is appears in the center of this periodogram, but the power is applied to the function given in Eq. (14), the Fourier spectrum dispersed and the peak has a wide band-width. This problem can be expressed by the equation below. ascribed to the orbital Doppler shift, which causes the peak N 1 frequency to not be constant. ˆ ˆ i2 f k t n Sk ( fk ) sne By contrast, Figs. 13 and 14 show the result obtained by n0 re-moving the orbital Doppler shift effect but using the same N 1
(15) integration time. These figures show that the peak becomes i2 ( f k f ( ))t n sne sharper and that the back ground noise becomes relatively n0 small. This analysis was based on a comparatively rough Sk ( fk f ( )) frequency shift prediction from the orbit propagation of 6) Eq. (15) indicates that the spectrum of a signal sˆn IKAROS. After per-forming this signal processing, however, corresponding to fk is identical to that of a signal sn a more accurate analytical frequency model can be obtained
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Fig. 11. Spectrogram of long-time integration DFT analysis. Fig. 15. Spectrogram of the whole pass.
Fig. 12. Periodogram of long-time integration DFT analysis. Fig. 16. Antenna offset pattern of the whole pass.
around 0 to 5 kHz and 15 to 10 kHz corresponding to two subcarrier peaks. These two peaks appear intermittently, mainly because the operation team attempted many antenna direction patterns to find IKAROS, as shown in Fig. 16. Comparing Figs. 15 and 16, the peaks appeared only when the antenna was directed using a single appropriate combination of right ascension and declination, which is expressed as the blue region in Fig. 16. Consequently, we successfully established communication between IKAROS during the next week operation on April 23, 2015, by applying this open-loop Fig. 13. Spectrogram of long-time integration DFT analysis by recording method. It should be noted that the peaks disappear removing the orbital Doppler shift effect. at approximately 2:30 and re-appear at approximately 3:00.
This occurred because the ground station swept its frequency during that period, and as a result, IKAROS locked onto the signal from the ground; thus the transmitting frequency of IKAROS changed every moment during the sweep. These figures show that the signal from IKAROS could not be acquired by the real-time operation, and therefore, many antenna direction patterns were tried. However, when the open-loop tracking data were post-processed, the clear peaks became evident after long-time integration with the appropriate calculation conditions. We conclude that the
Fig. 14. Periodogram of long-time integration DFT analysis by post-processing method proposed here using open-loop removing the orbital Doppler shift effect. tracking data is highly advantageous compared with real-time processing. by solving parameters (a, b, c) in Fig. 8 and Eq. (12). 5.2. Removing the spin modulation effect Figure 15 shows the result of processing the whole The analysis described in the previous section used large open-loop tracking data obtained from the search operation on RBW to avoid the spin modulation effect, and therefore an April 16, 2015. This DFT analysis was performed over a analysis with smaller RBW after removing this effect must be wider frequency range and using the same calculation per-formed to obtain further information, as shown in Fig. 9. conditions as in Fig. 13. Briefly, Fig. 15 is a zoomed-out The first step of this analysis is to determine optimal (a, b, c, A, B, C) spectrogram of Fig. 13. Two peak frequency trends appear parameters which satisfy Eq. (16) by
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Pj_18 S. KIKUCHI et al.: Progress of Search Operation for IKAROS by means of Open-loop Tracking Data convergent calculations. Initial solutions are required for this parameters (a, b, c, A, B, C) are well estimated, and the calculation, and those of a, b and c, which express the orbital frequency of the signal is well modeled. Additionally, this Doppler shift effect, can be immediately obtained based on the process makes long-time integration possible, even when the results of the previous analysis. Parameter A expresses the peak frequency shifts over time because of the combination of spin amplitude, and even a comparatively rough initial the orbital Doppler shift effect and the spin modulation effect. 2 solution is known to provide valid optimization calculation The power spectrum Sk ( fk f ( )) can also be obtained, results. By contrast, parameters B and C , which express as shown in Fig. 19. Compared with Fig. 13, more detailed the phase of the spinning motion and spin rate, respectively, frequency analysis which is sufficient to trace a sinusoidal determine the shape of the sinusoidal frequency wave, and the peak frequency shift can clearly be achieved. From this figure, calculation results largely depend on the initial solutions of it can be concluded that even when a signal is very weak, its these two parameters. frequency can be analyzed by applying DFT, as for the strong In order to obtain appropriate initial solutions for B and signal case shown in Fig. 6. Moreover, range rate data can C , a grid search calculation should be performed before the also be obtained immediately because the data can be used to convergent calculation. Figure 17 shows the grid search observe Doppler shift. calculation result. DFT analysis was implemented on the data Figure 20 is the periodogram at 2:20, which has a wider collected on April 16, 2015, with an integration time of 5 frequency range than that in Fig. 19. Two frequency peaks minutes and a RBW of 1.5 Hz. In this calculation, corresponding to subcarriers appear in this figure and can also (a, b, c, A) are fixed at appropriate values, and (B, C ) are treated as variables corresponding to the horizontal and vertical axes of Fig. 17, respectively. This figure presents the contour map with respect to the value of SNR0 evaluated at 2:20. In this analysis, B is changed every 5 deg and C is changed every 0.05 rpm. The global maximum appears at B 255 deg , C 5.7 rpm in the figure, and thus, these values are used as the initial solutions of the next convergent calculation. This figure proves that the solution space is multimodal and that the calculation result is highly sensitive to parameters B and C . The initial solutions of a , b and c are given by Fig. 13, A is given as 10 Hz, and B and C are given by Fig. 17. Fig. 18. Spectrogram of long-time integration DFT analysis by Using these values, convergent calculations to solve all of removing the spin modulation effect (before frequency restoration). these parameters can be performed. As a result of this calculation, the spinning motion of IKAROS can be estimated as shown in Table 2. The analyses so far allow DFT to be performed on the IKAROS signal by removing both the orbital Doppler shift effect and spin modulation effect. The analysis results are shown in Figs. 18, 19 and 20. ˆ 2 Figure 18 presents the power spectrum Sk ( fk ) , which indicates that there is a constant frequency peak at 0 kHz; thus,
Fig. 19. Spectrogram of long-time integration DFT analysis by removing the spin modulation effect (after frequency restoration).
Fig. 17. Contour map of SNR with respect to the B-C plane.
Table 2. Spin states estimated by numerical calculation. Item Symbol Value Spin amplitude A 10.787 Hz Spin phase B 257.73 deg Fig. 20. Periodogram of long-time integration DFT analysis by Spin rate C 5.6978 rpn re-moving the spin modulation effect.
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Pj_19 Trans. JSASS Aerospace Tech. Japan Vol. 14, No. ists30 (2016) be seen in Fig. 15. Moreover, the frequency peak of a main are possible using the proposed approach, even under difficult carrier appears near the center of this figure which is buried in communication conditions. Furthermore, range and telemetry noise and does not appear in Fig. 15. This result also confirms data may be obtained from a weak signal of a spinning-type the validity and the usefulness of this method. The reason why spacecraft stored using an open-loop recorder; this is the the right peak has larger power than the other two is that the subject of a future study. orbital Doppler shift effect and the spin modulation effect This research can be applied not only to a spinning-type were removed based on the frequency of the right peak, spacecraft, such as IKAROS, but also to those with uncertain although Doppler shift effect differs slightly according to the attitudes. We conclude that the proposed method provides frequency. flexibility and redundancy in spacecraft operation. It should be emphasized that these signal-processing methods requiring long integration times and iterative References numerical calculation processes are possible because they are used for the post-processing of open-loop tracking data. 1) Mimasu, Y., Shirasawa, Y., Yonekura, K., Mori, O., Saiki, T., Tsuda, Y., Takeuchi, H., Funase, R. and Taniguchi, S.: Attitude and Orbit Prediction of IKAROS in Actual Flight Operation, 3rd 6. Conclusion International Symposium on Solar Sailing, Glasgow, Scotland, 2013. We successfully re-established communication with 2) Thornton, C. L. and Border, J. S.: Radiometric Tracking Techniques for Deep Space Navigation, John Wiley & Sons, IKAROS, which was rebooted after hibernation mode, on Hoboken, 2003. April 23, 2015. This was the fourth time that acquisition has 3) Folkner, W. M., Preston, R. A., Border, J. S., Navarro, J., Wilson, accomplished, but in this instance, re-acquisition was achieved W. E. and Oestreich, M.: Earth-Based Radio Tracking of the in a way that differed from the previous three times: by Galileo Probe for Jupiter Wind Estimation, Science, 275 (1997), pp. 644-646. post-processing open-loop tracking data recorded on April 16, 4) Pham, T., Chang, C., Fort, D., Satorius, E., Finley, S., White, L. 2015, a week before acquisition. and Estabrook, P.: Tracking capability for entry, descent and The algorithm of discrete Fourier transform (DFT) based on landing and its support to NASA Mars Exploration Rovers, ESA open-loop tracking data was proposed in this study. This 3rd Workshop on Tracking, Telemetry and Command Systems for algorithm utilizes the advantage of the open-loop recording Space Applications, Darmstadt, Germany, 2004. 5) Yuen, J. H.: Deep Space Telecommunications Systems method, which enables complex and iterative processing, and Engineering, Plenum Press, New York, 1983. long-time integration. The analysis results obtained by 6) Taniguchi, S., Imamura, O., Ohnishi, T., Mimasu, Y., Shirasawa, applying the proposed method to the actual signal from Y., Yonekura, K., Mori, O., Takeuchi, H., Ichikawa, T. and IKAROS are also shown. The signal was shown to be well Yoshikawa, M.: Orbit Determination and Evaluation of Prediction analyzed by re-moving the orbital Doppler shift and the spin Error to Acquire IKAROS, 57th Space Science and Technology Conference, Tottori, Japan, 2013 (in Japanese). modulation effect, even when the signal is too weak to be 7) Brigham, E. O.: The Fast Fourier Transform, Prentice-Hall Inc., acquired by real-time operation. Englewood Cliffs, 1974. In addition to detect signals, estimating the spinning motion of a spacecraft, and acquiring range rate data and beacon data
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