Attitude Estimation for a Flexible Spacecraft in an Unstable Spin

Anattitudereconstruction algorithm hasbeendeveloped fora e exiblesounding rocketwhosespin vectornutates unstablyaboutitsminorinertia axis.Theattitudeestimatesareneededforposte ightanalysisoftherocket’ sscience data. An additional goal of the work is to show that a e exible-body model can be used in a Kalman e lter or in a smoother. The attitude is estimated using a smoother whose dynamic model includes a main rigid body and a pair of elasticbooms. Boom e exure is the principal causeof nutation instability. Boom bending is modeled by a Markov process, but the laws of mechanics are used to determine its ine uence on the attitude dynamics. This smoother achieves a better attitude estimation accuracy than can be achieved using a rigid-body model. The peak attitude error is estimated to be 4 deg, and the principal error source seems to be the limited accuracy of the rocket’ s attitude sensors. HIS work deals with the poste ight attitude determination for a sounding rocket mission, the Cleft Accelerated Plasma Experimental Rocket (CAPER). CAPER was launched from the Andoya Rocket Range in Norway in January 1999. Its e ight lasted slightly longer than 1200 s and reached an apogee altitude of 1360 km. The goal of this mission was to study the behavior of the ionosphere during auroral events. Attitude information is needed to transform CAPER’ s measurements of electric e eld components into geodetic coordinates. An attitude accuracy of from 2 to 4 deg is considered acceptable for the mission. From an attitude determination standpoint, the important characteristics of the CAPER sounding rocket were as follows: Its attitude sensors were a vector sun sensor with a slit e eld of view, a e xed-head horizon crossing indicator (HCI), and a three-axis magnetometer that was mounted on a short boom. The rocket’ s attitude was passively spin stabilized with the nominal spin vector directed along its minor inertia axis. CAPER deployed several booms after exit from the atmosphere and after the e nal stage motor burn. The longest of these were two e exible 3-m booms that deployed perpendicular to the nominal spin axis and in opposite directions from each other. A schematic diagram of this cone guration appears in Fig. 1. Minor-axis spin stabilization is often used in sounding rocket experiments. Near the dawn of the space age, the Explorer-1 mission demonstrated that such a cone guration has an unstable nutation mode due to energy dissipation in the e exible booms. 1 In many sounding rocket experiments it is acceptable for the nutation amplitude to grow as long as the resultant coning half-angle does not become too large by the end of the e ight. There are two major challenges in doing poste ight attitude determination for CAPER. The e rst is the lack of rate-gyro data. This challenge dictates the use of an Eulerian dynamics model to propagate the attitude and rates between measurement sample times. The model becomes especially important toward the end of the e ight, when only magnetometer data are available. The attitude estimate in rotation about the magnetic e eld vector is based solely on dynamic model propagation during this phase, and model inaccuracy