Attitude and Interlock Angle Estimation Using Split-Field-of-View Star Tracker

An efficient Kalman filter based algorithm has been proposed for the spacecraft attitude estimation problem using a novel split-field-of-view star camera and three-axis rate gyros. The conventional spacecraft attitude algorithm has been modified for on-orbit estimation of interlock angles between the two fields of view of star camera, gyro axis, and the spacecraft body frame. Real time estimation of the interlock angles makes the attitude estimates more robust to thermal and environmental effects than in-ground estimation, and makes the overall system more tolerant of off-nominal structural, mechanical, and optical assembly anomalies. Introduction Spacecraft attitude determination is the process of estimating the orientation of a spacecraft from on-board observations of line-of-sight vectors to other reference points such as celestial bodies, the direction of the Earth’s magnetic field gradient, etc. [1]. Generally, a redundant set of these observations is used to generate more accurate estimates of the spacecraft attitude. If these observations are error-free, then the spacecraft attitude can be determined with small errors limited only by errors in the catalog directions of the reference vectors. But, in practical problems, these vector observations are not error-free, as some kind of sensor noise is always associated with these measurements. Typically star catalog position errors are a fraction of a micro-radian, whereas random measurement errors are one to two orders of magnitude larger. The Journal of the Astronautical Sciences, Vol. 55, No 1, January–March 2007, pp. 85–105 85 Presented as paper AAS 04-120 at the 14th AAS/AIAA Space Flight Mechanics Meeting, Maui, Hawaii, February 9–13, 2004. Assistant Professor, Department of Mechanical & Aerospace Engineering, University at Buffalo, NY 14260, Member AAS and AIAA. Analytical Structural Dynamics Department, Sandia National Laboratories, Albuquerque, NM 87185. StarVision Technologies sponsored Graduate Student, Ph.D. Candidate, Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843. Distinguished Professor, holder of George J. Eppright Chair, Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, Fellow AAS. Several attitude sensors are discussed in the literature, including three-axis magnetometers, Sun sensors, Earth-horizon sensors, global positioning sensors, rate integrating sensors and star cameras [1]. The accuracy of the attitude estimation depends on the quality of the attitude sensor used. For example, the attitude estimate accuracy that can be achieved with Sun sensors is approximately 0.015 degrees for two-axis attitude estimation (direction of the Sun in body and inertial frame) with the best available instruments; however, for a star camera this number for three-axis attitude can be estimated to within 0.0005 degrees. For higher accuracies, star measurements are used as the key inputs for the attitude estimation as their position with respect to the inertial frame is fixed and centroiding de-focused light from these small point sources enables high precision. The spacecraft attitude is determined by taking digital images of the stars by using Charge Coupled Device (CCD) or Complementary Metal Oxide Semiconductor (CMOS) sensor based star cameras. Pixel formats on the order of or larger are commonly used to provide good resolution images wherein the stars can be identified using one of several robust algorithms which have been developed [2, 3]. Attitude estimation accuracies in the sub-arc second range are possible using star data and gyro data, but the drawbacks are cost of the star camera, computation complexity, and extensive software and calibration requirements. Two star cameras are usually required to reduce the star dropout probability and especially to improve the geometry that enables precise three-axis attitude estimation. Most of the expense is associated with the camera head (focal plane electronics, processor, temperature control and interfacing). A novel split-field-of-view star camera is being developed to reduce the overall cost of attitude estimation without compromising the attitude accuracy. This star tracker was adopted for the recently canceled EO-3 Geostationary Imaging Fourier Transform Spectrometer (GIFTS) mission. However, the split-field-of-view design has been licensed by Broadreach Engineering and various algorithms designed for the GIFTS mission (the star identification, camera calibration, and attitude estimation algorithms) have been licensed by StarVision Technologies to develop a commercial star tracker technology for future missions. The basic idea of splitfield-of-view star camera is shown in Fig. 1(i). The split-field-of-view star camera has the capability to simultaneously image two nominally orthogonal portions of the sky using a single camera head with only one CMOS detector. Since a single focal plane, electronic sub-system, power subsystem and processor are required, the split-field-of-view star camera design offers significant advantages in mass, power, and cost in comparison to using two conventional trackers to achieve comparable accuracy. However, doing so makes the attitude estimation problem more complicated as the accuracy of the attitude estimates implicitly depends on the knowledge of the interlock angle between two fields of view (FOVs) of the star camera. A significant penalty associated with the split-field-of-view optics, however, is the loss of about 50% of the light. This can be accommodated with an appropriate integration time. To further complicate attitude estimation, we may not know precisely the orientation of the gyro axis with respect to the star camera reference axis. In order to achieve high precision attitude determination, comparably precise estimates of these interlock angles are required. Generally, ground-based testing is 512 512 86 Singla, Griffith, Katake, and Junkins http://www.broad-reach.net. http://www.starvisiontech.com. used to calibrate the space systems, but this process requires the systematic testing in expansive high precision laboratories. In addition, the environmental changes over the life of the mission may result in calibration changes that are difficult to predict. Therefore, the precise knowledge of these interlock angles are best-determined from on-orbit measurements in the actual operational environment. In addition, an on-orbit calibration approach has the advantage that the algorithms can be invoked at any time when a sensor health-monitoring algorithm determines that sensor calibration accuracy has been diminished to an unacceptable degree. In this paper, a new approach is presented that allows us to estimate all interlock angles on-orbit along with the spacecraft attitude. The structure of the paper is as follows. First, various reference frames required to solve the attitude estimation problem using a split-field-of-view star camera are introduced followed by a brief review of the star camera and gyro models. Next, a new algorithm is presented to compute the spacecraft attitude along with various interlock angles on-orbit. Finally, the proposed algorithm is validated by simulating various space mission scenarios. Reference Frames Generally, at least two coordinate systems are defined for the attitude determination process: an inertial frame, and a body-fixed frame. For most problems, the inertial reference frame is a nonrotating frame fixed associated with an equatorial plane and equinox axis of a prescribed date (e.g. J2000). The projection of the orthogonal image frame axes onto the inertial frame axes is given by an orthogonal matrix, C, called the attitude matrix. Now, the attitude determination problem requires us to determine a set of attitude coordinates that uniquely parameterize the orthogonal attitude matrix, C. The various attitude sensors provide the measurement data in their own independent frame, generally known as the sensor frame. For academic purposes, the body frame of the spacecraft and the sensor frame are frequently assumed to be the same. Unfortunately this assumption is not generally true, and a precise knowledge of the interlock angle between body frame and sensor frame is necessary for a high precision attitude determination problem. This is due to the fact that the body frame is usually associated with an optical bench on which critical science instruments are mounted. Attitude and Interlock Angle Estimation Using Split-Field-of-View Star Tracker 87 FIG. 1. Dual Field of View (FOV) Camera Concept. To solve the attitude determination problem using a split-field-of-view star camera and a rate gyro, the following five reference frames are used: 1. The inertial frame fixed to the center of the Earth denoted by N. 2. A frame with z-axis parallel to the boresight axis of the front FOV denoted by 3. A frame with z-axis parallel to the boresight axis of the side FOV denoted by 4. The gyro axis frame (the frame in which gyro data is available) denoted by G. 5. The star camera reference frame denoted by (same as the spacecraft (body) frame) defined as follows: DEFINITION OF STAR CAMERA REFERENCE FRAME. If the set denotes three directions of the star camera reference frame and and denote the boresight directions (unit vectors) for the front and side FOV respectively as shown in Fig. 1(ii), then 1. The x-direction of the frame is along the unit vector that bisects the boresight unit vectors; i.e. 2. The z-direction is along the unit vector normal to the plane of boresight vectors; 3. The y-direction is along the unit vector that completes the right hand set; i.e. We mention that the derived frame has been defined in such a way that the output attitude from is least affected by sensor noise, residual calibration errors in interlock, and errors in rotation about the front and side boresights. Given measurements in a single FOV, it should be noticed that the boresight rotations typically are one order of magnitude less precisely determined than the direction of the boresight vector. Thus, the frame is based upon the truth that the two boresight vectors, are the two best determined body-fixed vectors, and deriving the body frame from them seems logically well-justified. Of course, final interlock rotation to various other science sensor frames remains to be estimated. However, this must be addressed in a mission specific fashion. Sensor Model Development of the mathematical models for the attitude sensor is an important task in determining the spacecraft attitude solution. Generally, these mathematical models are parameterized by some poorly known parameters, which are estimated by using the sensor measurements and an estimation algorithm. In this section, a brief review of the star camera and the gyro measurement models are presented which will be used later in the estimation algorithm.