Star Pattern Recognition for Real Time Attitude ...

The Journal of tho Astronautical Sciences, Vol. XXV, No.3, pp. 251·270, July-September, 1977

Star Pattern Recognition for Real Time Attitude Determination' John L. Junkins, Chelsea C. White, III, James D. Turner? Abstract In this paper, we discuss an attitude determination approach for autonomous, on-board, near-real-time determination of spacecraft attitude with sub-ten-arc-second precision. The method employs a systematic pattern recognition procedure for identifying stars sensed by, for example, charged coupled device (CCD) electrooptical star sensors. An extended Kalman filter is used to predict spacecraft attitude at each data gathering epoch. A parallel processing division of the computations and logic associated with data acquisition/editing, pattern recognition/attitude determination and optimal prediction functions is proposed. Three intermittently communicating parallel processes are proposed which appear to optimize the rate and precision of attitude estimation, subject to the contraints of on-board computation. Numerical experiments are summarized which support the validity and practicality of the proposed star pattern recognition/attitude estimation strategy.

Introduction In a recent presentation [I]. we proposed a three-process strategy. called UV ASTAR, for determination of spacecraft attitude. UVAST AR utilizes star co-ordinate and magnitude data measured by an electro-optical star sensing system (see Figure I) and a priori estimate of spacecraft attitude in order to determine an improved and updated a posteriori estimate of spacecraft attitude. The star pattern recognition strategy implicit in UV ASTAR represents a generalization of the approach proposed by Rupert [2). Several star sensors/trackers are currently under development (e.g. the lPL STELLAR sensor [3] and the BBRC DIGISTAR sensor) which employ a charged coupled device (CCD) array to digitize starlight. The DIGISTAR CCD light sensitive I Presented at the 1977 AAS/AIAA Astrodynarnics Conference, Jackson Lake Lodge. Grand Teton National Park, Wyoming, September 7-9,1977. 1 The University of Virginia, Charlottesville, Va, 22901.

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FIG. I. UV ASTAR - An Electro-Optical/Software System Capable of Real Time Readout of Digitized Star Coordinates, and Ultimately, Autonomous, Near-Real Time Star Pattern Recognition and Attitude Determination

element is a 11.4 mm. X 8.8 mm. matrix of about 2 X 105 light-sensitive subelements, or pixels, accurately embedded (to I part in 10,(00) in a microcircuit chip (see Figure 2). The starlight is defocused to spread a typical star's image over a 4 X 4 subset of pixels. The star centroids can be determined with errors less than 10 arc-seconds in the orientation of the vector toward typical stars. The attitude determination strategy summarized below assumes an electro-optical star sensing system composed of two such CCD arrays and associated optics and signal processing electronics. The CCD arrays serve as the "film" for a new generation of digital "stellar cameras" which can digitize starlight with near-negligible lag from real time. As is observed in Reference [3], these CCD sensors represent new levels of precision, reliability and versatility. In both the STELLAR and DIGISTAR systems, digitized starlight is analyzed by a programmable microprocessor which determines star image centroid coordinates and magnitudes and associates time with these measurements. The microprocessor also applies calibration corrections and

253

Star PlIttern Recognition for Real Time Attitude Determination

outputs star image coordinate and magnitude data in near-real-time (current projections for DlGISTAR indicate about 5 sets of star image centroids will be output per minute), and can be programmed to detect and delete obviously spurious images which are subject to unreasonable magnitude variability and/or erratic motion (e.g. spacecraft debri reflecting sunlight). At present, star measurement error and the frequency and character of spurious measured images can be simulated using Monte-Carlo methods. It is expected, however, that a prototype CCD star CCD AR~Y (488 x 380 pixels) ("Defocused'· negative Image)

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sensor (a single CCD array DIG1STAR system) will be flown on a Space Shuttle Mission during calendar year 1980. Orbital flight test data can then form the basis for evaluating the CCD star sensor hardware and validating the attitude determination strategy described below.

The UVASTAR Parallel Processes With reference to Figures 3 and 4, the UVASTAR system consists of three parallel processes whose macroscopic descriptions are briefly described as follows: Process A consists of two CCD star sensors and associated electronics, and a dedicated micro-processor. The function of process A is to digitize the starlight, and therefrom, determine best estimates of the centroid location (on the CCD image plane) and the magnitude of each star image. Process B operates upon the Process A output (a time, star image coordinates and magnitudes), and a priori spacecraft attitude estimate, to determine an updated, a posteriori attitude estimate. Process B, implemented on-board in a dedicated microprocessor, employs a star pattern recognition method to identify two or more of the measured stars as specific stars stored in a catalogue; and having identified the stars, the spacecraft attitude is determined which brings the simulated star coordinates into least square agreement with the measured coordinates. Process C accepts as input the discrete attitude estimates from Process B (available several times per minute, with a corresponding lag from real time), attitude control system commands, and perhaps other on-board measurements (such as gyro-angular rate measurements). Using a discrete Kalman filter formulation and a dynamical model for spacecraft rotational motion, real time best estimates of the spacecraft orientation are calculated. The output of Process C is continuously addressable for on-board use in generating control system commands, for feedback to Process B, or to ground telemetry. Each of these three parallel processes is now discussed in greater detail.

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255

Star Pattern Recognition for Real Time Attitude Determination

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Process A One specific realization of Process A is now considered in more detail. Two identical DIGIST AR star trackers [1] are rigidly attached to a spacecraft, with their optical about 90° apart. With reference to Figure 2, each 70 rnm leas images starlight upon a Fairchild 11.4 X 8.8 mm light sensitive charged coupled device (CCD). TIle CCD is a matrix of 488 X 380 silicon pixels accurately imbedded (to 1 part in 10,000) in a microcircuit chip. Each pixel develops a charge which is a function of the intensity and spectral properties of the starlight incident upon it. 3 High speed analog circuits scan the response of each pixel, comparing it to a threshold response level. When a pixel exceeds the threshold response level, the response level is passed through an analog-to-digital conversion and stored (along with the x-y address of the illuminated pixel) in a buffer. Once each scan is complete, a programmable microprocessor (a Motorola 6800) calculates the centroid of each cluster of starlight and sums the response of each cluster to determine an instrument magnitude measure. About OJ second is required to complete a scan of the CCD. Typically, 3 to 6 stars will be detected on each of the two CCDs. The 'Instrumental star magnitudes, i.e. the star magnitude as perceived by the instrument, for DIG1STAR will be available from BBRC for all stars of visual magnitude 4 or brighter and for many stars having visual magnitude between 4 and 6, using star spectral data obtained from Kits Peak Observatory [4 J. Instrumental star magnitudes for other stars which may be in the visual range of DlGISTAR can be determined using the less accurate instrumental star magnitude approx imation procedure proposed in Reference (5).

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cent I fy tn,! eee s ureo , (J, t/J) estimates of step I-E are accepted as valid. If none of the remaining measured stars are predicted to within 20 arc-seconds, then the (i,j)th pair is rejected as a false hit. The next set of [(i,j), (I,J)] star pairing indices from Table I (discussed in step I-D) is then considered until a successful star pairing, followed by a successful prediction of one or more additional star image locations, is achieved. If all star pairs are exhausted, or if the mean cycle time of Process A is exceeded, a new set of data from Process A is taken as fresh input, and control is returned to step I-A. II. Final Attitude Estimation: A. If 10 arc-second class precision is acceptable, then the final estimates derived from step I-E and confirmed by step I-F are accepted without further

267

Star Pattern Recognition for Real Time Attitude Determination

refinement as output, along with the corresponding time, for access by Process C. B. If maximum precision is desired, then the least square differential correction of step I-E is redone, where all measured stars which were confirmed in step I-F by a 20 arc-second or closer prediction are considered. Suppose, for example, that three (six) measured stars were confirmed in FOV 1 (FOV 2 ) . Then, the least square process would find the (eJ>, (J, "') estimates and bring the predictions [using Eqs. (I) and (4)] of these nine stars into least square agreement with their corresponding observed values. This particular system of 9 X 2 == 18 equations involving the three unknowns (1jJ, (J, "') typically results in I0/Vf8 == 2 arc-second variance in the converged estimates. We note that due to the one to two arc-second systematic error in the DIGISTAR sensor configuration considered here, considering more than roughly ten stars does not significantly improve the converged estimates.

An Example We now consider a specific numerical application of steps I-A through I-E. Table II gives simulated output of Process A. These simulated star image coordinates on the FOV 1 and FOV 2 CCD arrays were generated by specifying the true orientation (eJ>, 8, "') == (2.41254, 0.08454, 1.47654), and accessing a star catalog (the SAO star catalog [9] was used, where for simplicity it was assumed that instrument magnitude is identical to visual magnitude) for all seventh or brighter magnitude stars which would fall within the corresponding FOV 1 and FOV 2' Equations (I) TABLE II. Simulated DlGISTAR Output (Process A) Ordered image

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and (4) were then used to calculate the x-y coordinates of these stars on the CCO arrays, and Gaussian noise was added to simulate DIG1STAR error characteristics. The a priori estimates of (¢!, £J, 1/1) were assumed to be (2.46254, 0.03454, 1.42654), indicating a particularly large estimation error which is not likely to be exceeded in practice. Figure 6 displays all stars in sub-catalogs C1 and C2 , together with the true and a priori estimated boundaries of FOV, and FOV 2 • Steps I-A through I-E then yield a pairing of measured stars (1, 4) on the 49th cosine comparison. Using the ordering of Table I, this pairing actually was the second valid matching of star pairs. The (1, I) measured star pair is in fact the (1, I) catalogued star pair; but the particular measurement error sample from the random number generator resulted in this pair not being detected in the cosine comparison. Table III provides a numerical summary of the differential process of step I-E which recovered the true orientation to within 10 arc-seconds. Since the present simulation of Process A does not consider spurious images, it is apparent that this preliminary a posteriori attitude is confirmed by step I-E. Concluding Remarks A three parallel process strategy for autonomous attitude estimation has been proposed. Numerical results of simulations of the first two processes (data acquisition, and star pattern recognition/discrete attitude estimation) were presented. Several subjective judgements were made to define the tolerances employed in the star pattern recognition logic; the values used were selected using trial and error simulations. Future studies should employ Monte Carlo simulations with various tolerance settings to maximize reliability of the pattern recognition process. The calculations of the present paper were performed in a CYBER 172 computer system. The validity of the star pattern recognition approach is supported by these calculations; however, the issue of on-board implementation has not been rigorously addressed. It is anticipated that implementation of Process B in a microprocessor will be a straight forward developmental effort, since the computational require-

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Junkins et al.

ments are modest (a sequence of low dimensional data sorts, inner product calculations, logical tests, and inversion of 3 X 3 matrices). Implementation of Process C (the Kalman filter/state integration algorithm) presents the major unresolved problem area. Work is currently in progress [IO) which it is planned will validate the entire concept by implementation of Processes A, B, and C in microprocessors, culminating with Shuttle borne orbital flight tests during the early 1980's. References [I] JUNKINS, J. L, WHITE, C. c., and TURNER, J. D. "Star Pattern Recognition/Attitude Determination using Digital Star Sensing," Record of the Flight Mechanicsllistimation Theory Symposium (Goddard Space Flight Center, Greenbelt, Maryland, October, 1976). [2] RUPERT, P. R... 'SMART'-A Three-axis Stabilized Attitude Reference Technique," J. Spacecraft and Rockets, 8, 1971, 1195·1201. [3] SALOMON, P. M., and GOSS, W. C. "A Micro-Processor-Controlled CCD Star Tracker," AIAA Paper No. 76-116, AIAA 14th Aerospace Sciences Meeting, Washington, D.C., January, 1976. [4] Private communication with R. L Gutshall of BBRC, Boulder, Colorado. [5J GOTTLIEB, D. M. "SKYMAP System Description: Star Catalog Data Base Generation and Utilization," Computer Sciences Corporation, Report CSC/SD-76/6041, November 1976, Silver Springs, Maryland. [6] THOMPSON, M. M. Manual of Photogrammetry, American Society of Photogrammetry, 1, 1966, p. 469. [7] JUNKINS, 1. L Optimal Estimation of Dynamical Systems, Noorhoff International Publishing, Leyden, The Netherlands (in press), Ch. 1 and 5. [8] LIKINS, P. Elements of Engineering Mechanics, McGraw-Hill, N. Y., 1973. [9J Smithsonion Astrophysical Observatory Star Catalog, Part 1, Smithsonian Institution, Washington, D.C., 1966. [10] JUNKINS, J. L., and WHITE, C. C., III. "UVASTAR: A New System for Star Pattern Recognition and Spacecraft Attitude Estimation," RLES Proposal ESS-USAETL·1492·76, University of Virginia, October, 1976.