Trajectory Estimation of the Hayabusa Sample Return Capsule Using Optical Sensors

TRAJECTORY ESTIMATION OF THE HAYABUSA SAMPLE RETURN CAPSULE USING OPTICAL SENSORS

Michael A. Shoemaker∗ and Jozef C. van der Ha† Kyushu University, Fukuoka, Japan ∗Ph.D. Candidate, Department of Aeronautics and Astronautics, [email protected] †Professor, Department of Aeronautics and Astronautics, [email protected]

Abstract

The sample return capsule for the Japanese Hayabusa asteroid mission will return to Earth in 2010. Because the capsule will reenter the atmosphere at night, it will appear as a bright light source during the high-heating portion of the trajectory. The present study describes the development of an operational capability to optically observe this part of the reentry capsule’s descent through the atmosphere. The trajectory is estimated via an Extended Kalman Filter (EKF), using ground-based and/or aerial measurements of the capsule’s angular position. The EKF is tested with simulations of the Hayabusa reentry, as well as NASA’s Stardust reentry from 2006. 1 NOMENCLATURE X = state vector = angle of attack, rad

t = topocentric right-ascension angle, rad

t = topocentric declination angle, rad C = axial force coefficient A = Earth gravitational parameter, m3/s2 CD = drag force coefficient = air density, kg/m3 C = lift force coefficient L 3 0 = reference air density, kg/m CN = normal force coefficient 2 n = capsule position from sensor n in ℱi, m d = drag acceleration in ℱi, m/s ! = Earth angular velocity in ℱ , rad/s 2 i dt = drag acceleration in ℱt, m/s

ℱi = inertial (J2000) reference frame ℱt = Earth-relative-velocity reference frame 2 INTRODUCTION ℎ0 = reference altitude, m ℎ = altitude above ellipsoid, m ellp The main mission objective of the Japanese H = scale height, m Hayabusa spacecraft is to collect samples from an 2 l = lift acceleration in ℱi, m/s asteroid and return those samples to Earth for analysis. The spacecraft was launched in 2003, l = lift acceleration in ℱ , m/s2 t t rendezvoused with asteroid Itokawa in 2005, and m = mass, kg is currently on a return orbit to Earth. The sam- r = capsule position vector in ℱi, m ple return capsule (SRC) is scheduled to reenter the atmosphere and land in Australia in June, rn = position vector of n-th sensor in ℱi, m it 2010. Because the SRC will reenter the atmo- R = rotation matrix from ℱt to ℱi sphere at night, the capsule and surrounding air S = reference area, m2 will appear as a bright light source (i.e. “ﬁreball”) during the portion of the trajectory with high t1i, t2i, t3i = x, y, z axes of ℱt, expressed in ℱi aerodynamic heating. Kyushu University, in col- v = inertial velocity vector in ℱ , m/s i laboration with the Japan Aerospace Exploration ver = Earth-relative velocity in ℱi, m/s Agency (JAXA), is developing an optical sensor and trajectory estimation system to observe this

1 part of the reentry capsule’s descent through the detailed trajectory estimation function. NASA’s atmosphere. Genesis capsule reentered during daylight, thus This optical sensor system, which will primar- the trajectory could not be measured relative to ily consist of ground-based cameras, is planned for the star background. But, ground-based optical deployment in various sites around the Australian cameras (visual and infrared) were used to observe desert where the SRC will land. The two primary the varying luminance as the capsule tumbled, purposes for this system are: (1) to provide real- allowing the capsule’s attitude to be inferred[2]. time trajectory estimates to the JAXA ground Also, aircraft-mounted optical sensors were used teams for capsule recovery, (2) to allow for post- to photometrically measure the capsule’s surface- flight verification of capsule performance. These averaged temperature[10]. optical measurements may play an important role On the other hand, the reentry of NASA’s Star- in reconstructing the trajectory, because the SRC dust capsule in 2006 was observed during dark- lacks onboard data (e.g. accelerometer) recording ness, allowing the trajectory to be imaged against due to mass restrictions. Post-flight evaluation of the star background (see Fig. 1). The Star- the capsule flight performance may be useful in the dust sample return capsule, carrying samples from design of future interplanetary and Earth reentry comet Wild-2, entered the atmosphere at an iner- missions. tial velocity of 12.9 km/s (the fastest reentry for a The development builds on the lessons learned man-made object to date), and made a soft land- from the observation campaigns for the Genesis ing with parachutes in Utah. Because this super- and Stardust reentry vehicles in 2004 and 2006, orbital reentry occurred during darkness, it was a respectively[1][2]. The Genesis and Stardust op- good opportunity for conducting optical observa- tical observation campaigns included some trajec- tions of the capsule’s heating. These observations tory reconstruction capabilities, but the primary were driven by a desire to study the thermal pro- requirement was to evaluate the thermal protec- tection system, which is applicable to the design tion system performance. In contrast, the present of the Orion Crew Exploration Vehicle[11]. study focuses on the development of a trajectory estimation capability using ground-based and aerial measurements of the SRC angular position. The SRC angular position will be measured by first taking images of the trajectory against the star background, then relating the SRC position in the images with the known star positions. An Extended Kalman Filter (EKF) is developed to estimate the SRC state during reentry. Similar EKFs have been developed in the past, for applications such as estimating the reentry trajectories of low Earth orbit (LEO) space debris[3][4] and ballistic missiles[5][6][7]. First, Section 3 describes past studies on observing super-orbital rentry missions. Section 4 gives an overview of the Hayabusa and Stardust reentry missions. The formulation for the EKF and the Figure 1: Stardust “fireball” image (from [1]). system model for this study are given in Section 5, and the simulations are discussed in Sections 6 and 7. Measurements collected during the Stardust reentry have been used by others for trajectory re- 3 PREVIOUS WORK construction. Visible and infrared video cameras were used to determine the time of parachute deployment and compare the observed reentry with There are several past examples of observing pre-flight predictions[12]. A DC-10 aircraft op- super-orbital reentry vehicles. The reentry of the erated by NASA and the University of North Apollo 8 spacecraft in 1968 was observed by one of Dakota, outfitted with numerous optical sensors, the Apollo/Range Instrumented Aircraft[8][9], but made observations of the capsule [1]. Video of the these observations were not used to perform any capsule against the star background, along with

2 GPS time stamps, were recorded from this air- 5 SYSTEM MODEL craft. Because the position of the aircraft was estimated from the onboard flight logs, and the angular position of the stars are very accurate, the anal- 5.1 Estimator Dynamic Model ysis of images from this video allowed the time his- The equation of motion of the capsule is tory of the tracking angles to be measured. These angular measurements are used in this study to ¨ r = − 3 r + l + d (1) test our trajectory estimation method. r where the 2-body gravity, lift, and drag accelerations are considered. Figure 2 shows these forces 4 REENTRY OVERVIEW acting on the body, and several reference frame definitions. Frame ℱi is the inertial frame centered on the Earth, here taken to be the J2000 reference frame. Frame ℱt is centered on the cap- 4.1 Hayabusa Reentry sule, with the x-axis aligned with the capsule’s Details of the Hayabusa capsule design and reen- Earth-relative velocity vector ver, the y-axis in try sequence can be found in [13] and [14], respec- the cross-track direction, and the z-axis complet- tively. The Hayabusa capsule will separate from ing the right-handed coordinate system. The unit the main spacecraft several hours before reentry. vectors along these three ℱt axes, expressed in ℱi, are: The capsule reaches atmospheric interface (defined ver t1i = (2) by JAXA to be 200 km altitude) with an iner- ∣ver∣ tial velocity and flight path angle of approximately t × r 12.1 km/s and -12 deg, respectively. At approx- t = 1i (3) 2i ∣t × r∣ imately 10 km altitude, the fore heat shield and 1i aft cover will jettison, and the main parachute t3i = t1i × t2i (4) and beacon antenna will deploy. JAXA’s pri- The Earth-relative velocity, expressed in ℱi, is de- mary method of locating the capsule after landing fined as: is direction-finding of the beacon signal. Radar- ver = v − ! × r (5) reflective material was also applied to the edges of the parachute canopy to allow tracking with the radar infrastructure in Australia. The optical tracking described in this paper represents an ad- ditional layer of backup landing-point prediction.

4.2 Stardust Reentry

See [1],[11], and [12] for detailed descriptions of the Stardust reentry. The Stardust capsule had an inertial velocity and ﬂight path angle at entry (de- ﬁned by NASA to be 125 km altitude) of 12.9 km/s and -8.2 deg, respectively. As mentioned in Sec- tion 3, aircraft-mounted cameras recorded video of the capsule, from which angular measurements were derived. These measurements cover the capsule’s descent from 97 to 46 km altitude, over a Figure 2: Reentry dynamics and reference frames time span of 55 s. The measurements were provided at a rate of 1 Hz. The time history of the aircraft’s latitude, longitude, and altitude were also provided over the same time span, at a rate of The lift and drag accelerations can be easily ex- 0.5 Hz. The aircraft position was interpolated to pressed in ℱt: match the frequency of the angle measurements. ⎡ 0 ⎤ No uncertainties were available for the angle mea- lt = ⎣ 0 ⎦ (6) surements or the aircraft positions. 1 2 − 2m verSCL

3 ⎡ 1 2 ⎤ − 2m verSCD dt = ⎣ 0 ⎦ (7) 0

These accelerations are expressed in ℱi using the it it it rotation matrix R , i.e. l = R lt and d = R dt, where: it R = t1i t2i t3i (8) The atmospheric density is modeled with the COSPAR International Reference Atmosphere (CIRA-72) exponential model:

ℎ − ℎ = exp − ellp 0 (9) 0 H where 0, ℎ0, and H are defined over 10-km altitude bands, resulting in a piecewise-continuous density variation. Reference [15] pp. 537 gives a Figure 3: Sensor measurement geometry table of these parameters. Although the lift and drag accelerations in Eq. 1 use CL and CD, respectively, the nominal capsule 6 HAYABUSA REENTRY aerodynamics are usually described with the axial SIMULATIONS force coefficient CA and normal force coefficient C . The present analysis assumes 0 deg angle of N 6.1 Hayabusa Simulation Design attack, allowing us to use CA and CN directly. See [16] for a detailed description of the EKF. The EKF is tested via computer simulation of The state vector X is written as the Hayabusa scenario described in Section 4.1. T The drag coefficient is assumed constant at 1.14 X = r r˙ (10) throughout reentry, for both the truth and estimated states. Noise is added to the density model which is estimated using the dynamics model de- defined by Eq. 9 to mimic density fluctuations ver- scribed earlier, as well as the measurement model sus altitude. These differences between the true described next. density and the model predictions are caused by time variations in wind, temperature, etc. Our 5.2 Estimator Measurement Model study simulates the density variations as a random walk versus altitude (see [17] for details). Optical sensors are distributed around the reentry The simulations assume that the Hayabusa cap- area, each having index n, n = 1,...,N, where N sule will have sufficient brightness for optical ob- is the total number of sensors. Figure 3 shows a servations from approximately 110 to 35 km al- single optical sensor with position vector rn, and titude. Thus, the observation time span is 60 s. the position vector from the sensor to the capsule Simulations are run at 1 Hz and 20 Hz measure- n, such that r can be written as ment frequency, to test the effect on estimation accuracy. The initial state estimate covariance r = rn + n (11) matrix and the process noise covariance matrix are chosen by trial-and-error tuning of the EKF. Each sensor measures the capsule’s angular po- Three ground sites are chosen that are capable of sition in topocentric right-ascension and declina- viewing the assumed visible portion of the nominal tion angles relative to the known star positions. reentry trajectory. The measurement angles from sensor n are

tan−1 ( / ) 6.2 Hayabusa Simulation Results Y = t = n2 n1 (12) n sin−1 ( /∣ ∣) t n n3 n Figure 4 shows the results of a single run of the T Hayabusa simulation at 1 Hz and 3 ground sites. where n = n1 n2 n3 . The time scale is shown in elapsed seconds from

4 the beginning of the observations. The errors in the position and velocity estimates relative to the truth state are plotted with time, along with the reported 3- uncertainties from the state estimate error covariance matrix. In general we see that the position and velocity converge over the simulation time span. Figure 5 shows the results from 30 Monte Carlo (MC) simulation runs, with measurements taken at 1 Hz. The three lines in Fig. 5 represent the results using a diﬀerent number of sensor sites. It is clear that the estimation error decreases as the number of sensor sites is increased. For a single sensor, we see that the velocity error temporarily increases between 30 and 40 seconds, which corre- sponds to the peak deceleration. After this peak deceleration, the velocity error decreases again. Figure 6 shows MC simulation results using the same sensor sites, but with the measurement fre- Figure 5: Hayabusa position and velocity errors quency increased to 20 Hz. There does not appear (1-), 1 Hz, 30 MC runs to be a signiﬁcant advantage in using a higher measurement frequency, other than the faster conver- gence time.

Figure 6: Hayabusa position and velocity errors (1-), 20 Hz, 30 MC runs

7 STARDUST REENTRY Figure 4: Hayabusa position and velocity errors SIMULATIONS and 3- uncertainties, single simulation run 7.1 Stardust Simulation Design The EKF is also tested on the Stardust reentry, using the angle measurements described in Sec- tion 4.2. For these tests, we try two diﬀerent state vector formulations: one with the CD assumed known, and one where CD is added to the state vector from Eq. 10. The drag is modeled as

5 an integral of stationary white noise (i.e. random walk), using the method described in [3]. The ﬁlter uses the same tuning parameters that were used for the Hayabusa simulations. Even though there is no truth state available, one of JPL’s trajectory estimates is used to compare with the EKF’s estimates. This trajectory estimate is based on pre-entry orbit estimates and numeri- cal simulations of the atmospheric reentry. The trajectory is available online from NASA’s NAIF website, and accessible via the SPICE ephemeris toolkit[18]. The JPL trajectory is used as the initial state estimate. The predicted aerodynamic performance of the Stardust capsule is obtained from Ref. [19] and used to compare with the Figure 8: Stardust velocity error (1 sensor site) EKF’s estimates of CD.

7.2 Stardust Simulation Results and 10 deg. The CD estimate varies around 10 to 20% of the assumed truth value. One poten- Figure 7 shows the error in the position for the tial reason for this error is that variations in the Stardust simulations, defined as the difference be- atmospheric density could appear as variations in tween the EKF state estimates and the JPL state the aerodynamic coefficients (see Eqs. 6 and 7). estimates. Also shown in the figure are the 3- po- Reference [20] describes possible density variations sition uncertainties reported in the state estimate from the GRAM-95 model of up to 25% at high error covariance matrix. We see that the position altitude. Therefore, future versions of this work error stays around 1 km for most of the observa- will investigate adding the atmospheric density to tions, then approaches 2 km after 57 s. Figure the state vector. 8 is similar to Fig. 7, but here the velocity error is shown. We see that the velocity estimates diverge, with the error increasing from less than 0.01 km/s to nearly 0.15 km/s in the case where CD is estimated. These results suggest that this version of the EKF has trouble estimating the position and velocity with only angle measurements from a single sensor site.

Figure 9: Stardust CD estimates, with NASA predicted values from [19]

Lastly, Fig. 10 shows the measurement residuals from the Stardust data. The increase in the residuals at the end of the observation span is likely caused by two factors: the increasing error Figure 7: Stardust position error (1 sensor site) in the state estimate, and the increasing measurement noise due to blooming in the CCD camera. Figure 9 shows the estimated CD, its reported The blooming causes measurement noise because uncertainties, and the predicted values at of 0 as the capsule becomes brighter, it ﬁlls up a larger

6 number of pixels in the image, which increases the Tetsuya Yamada, and Kazuhisa Fujita of JAXA errors in extracting the centroid of the bright ﬁre- for the helpful discussions on the Hayabusa reentry ball (recall Fig. 1). operations.

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