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Copyright by Noah Harold Smith 2012 Copyright by Noah Harold Smith 2012 The Dissertation Committee for Noah Harold Smith Certifies that this is the approved version of the following dissertation: Alignment Filtering of ICESat Flight Data Committee: Bob Schutz, Supervisor Glenn Lightsey Todd Humphreys Peter Shelus Sungkoo Bae Alignment Filtering of ICESat Flight Data by Noah Harold Smith, B.A.; M.S.E. Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy The University of Texas at Austin December 2012 Alignment Filtering of ICESat Flight Data Noah Harold Smith, Ph.D. The University of Texas at Austin, 2012 Supervisor: Bob E. Schutz ICESat consisted of the Geoscience Laser Altimeter System (GLAS) and a commercial spacecraft bus. The stability of the GLAS to bus alignment was unknown and significant for GLAS pointing. Pointing control was performed by the bus, and variations of the GLAS alignment were effectively pointing control errors. There were four star trackers making measurements sensitive to this alignment, two on GLAS and two on the bus. Tracker pointing variations during samples from seven years of flight data were estimated using an alignment filter. The states of an alignment filter represent multiple independent attitudes, enabling the fusion of measurements from an arbitrary number of trackers and gyro units. The ICESat alignment filter states were equivalent to four tracker pointing vectors, expressed in both the body and celestial frames. Together with a star catalog, the four pointing vectors were equivalent to predictions of the tracker measurements. The stars provided nearly ideal reference points, but filter performance was improved by detecting and handling deterministic star errors. The primary result was evidence for relatively large pointing variations of the two GLAS trackers, on the order of fifty arcseconds, with both periodic orbital variations and trends on long time scales. There was also evidence of correlations between the variations of the two GLAS trackers, suggesting that they reflected GLAS to bus alignment variations. iv Table of Contents I. Introduction ................................................................................................................. 1 a. Contributions to the Field ....................................................................................... 4 II. Literature Review........................................................................................................ 8 a. Attitude Estimation ................................................................................................. 8 b. Alignment Estimation ........................................................................................... 10 c. Star Measurements ................................................................................................ 12 III. ICESat Characteristics .......................................................................................... 27 a. Body North and Body West Coordinate System .................................................. 27 b. Flight Data ............................................................................................................ 30 c. Attitude Modes and Alignment Filter Dataset ...................................................... 35 d. Maneuvers ............................................................................................................. 37 IV. Alignment Filtering ............................................................................................... 42 a. Filter Structure ...................................................................................................... 43 b. Gyro Propagation .................................................................................................. 49 c. Star Tracker Alignment Process Noise ................................................................. 63 d. Star Measurement Update ..................................................................................... 73 e. Output and Star Pass Residuals............................................................................. 77 V. Star Results ............................................................................................................... 96 a. Tracker Errors ....................................................................................................... 97 b. Position Biases and Bad Stars ............................................................................. 104 c. Instrument Magnitude Prediction ....................................................................... 123 VI. Alignment Results ............................................................................................... 145 v a. Uncertainties ....................................................................................................... 145 b. Alignments .......................................................................................................... 161 VII. Conclusion .......................................................................................................... 187 VIII. Appendix ............................................................................................................. 189 a. Scaled Tangent Coordinates for Unit Vectors .................................................... 189 b. Three-component Rotation Representations ....................................................... 192 c. Gyro Calibration Maneuvers............................................................................... 193 IX. References ........................................................................................................... 199 vi I. Introduction ICESat consisted of the Geoscience Laser Altimeter System (GLAS) and a commercial spacecraft bus. The stability of the GLAS to bus alignment was unknown and significant for GLAS pointing. Pointing control was performed by the bus, and variations of the GLAS alignment were effectively pointing control errors. There were four star trackers making measurements sensitive to the GLAS alignment, two on GLAS and two on the bus. Tracker pointing variations during samples from seven years of flight data were estimated using an alignment filter. The states of an alignment filter represent multiple independent attitudes, enabling the fusion of measurements from an arbitrary number of trackers and gyro units. Tracker pointing in the body frame was represented using latitude and longitude-like body north and body west coordinates, as shown in Figure 1. These coordinates aided physical interpretation of tracker pointing variations in terms of GLAS alignment, and were independent of the relatively inaccurate estimated rotations of the trackers about their pointing vectors. Correlations in the pointing of the two GLAS trackers suggest that there were significant variations of the GLAS alignment. Figure 1. ICESat, body north and body west coordinates, and approximate tracker pointing vectors. The combined states of the alignment filter represented the individual attitudes of all four ICESat trackers, relative to both the body and celestial frames. Individual filter states 1 included alignment rotations for each of the four tracker frames, and an attitude rotation for the body frame. For each tracker, a tracker pointing vector represented the tracker optical axis relative to the celestial frame based on three frame rotations: from the celestial frame to the body frame (attitude state), from the body frame to the reference tracker frame (constant), and from the reference tracker frame to the estimated tracker frame (alignment state). Star tracker measurements are less sensitive to rotations about the tracker optical axis. The sensitivity to rotation about the optical axis for a star on the axis is zero. Representing the tracker attitudes as pointing vectors made the results independent of the less sensitive tracker axes, and aided physical interpretation. Together with a star catalog, the tracker attitudes were equivalent to predictions of the tracker measurements. If the differences between tracker measurements and filter predictions were small, then the estimated tracker pointing vectors were accurate. For the primary results presented here, the BST1 tracker frame was tied to the body frame by holding the BST1 alignment states constant. In others words, there was a constant rotation between the body frame and the BST1 frame. The body frame was identified with the gyro unit. The individual tracker alignment states were small variations from a set of reference alignments. The alignment filter could run with the all of the tracker alignment states held constant at the reference values, but this resulted in relatively large star measurement residuals on the order of tens of arcseconds. With the tracker alignment states updating to follow alignment variations, the filter residuals were an order of magnitude smaller. The stars provided nearly ideal reference points to compare with the filter states via tracker measurements. In the flight data sample used here, the spacecraft was normally rotating at a constant rate about the GLAS to bus axis and the four star tracker pointing vectors followed one another along a great-circle around the celestial sphere, from near the celestial north pole to near the celestial south pole and then back. The same stars passed through all four tracker fields of view within a sixteen minute period. Variations of the
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