ESA GNC Conference Papers Repository

High accuracy pointing attitude determination estimator system of the future infrared astronomy satellite SWARM interferometer
D.B. Bhatia, U.B. Bestmann, P.H. Hecker
Presented at:
Salzburg 2017
Full paper:

InfraRed Astronomy Satellite Swarm Interferometer (IRASSI) is an aperture synthesis interferometry mission that consists of a free-flying 3D swarm of 5 telescopes orbiting the Sun-Earth Lagrange point 2 in a halo orbit. The scientific objective of this mission is to image circumstellar disks and protoplanetary regions which are fertile grounds for star and planet genesis, and are visible only in far-infrared (FIR) range of electromagnetic (EM) spectrum. Hence, IRASSI operating in FIR frequency range of 1-6 THz and spannnig wavelengths between 50-300µm would be able to quantitatively analyze the physical and internal chemical structure of these regions by obtaining their spectral maps at an unprecedented high angular resolution of 0.1 arcsec. IRASSI's mission outline was sketched based on the concepts and studies of precursor FIR and space-based interferometer mission such as ESPRIT, SPIRIT, TALC, DARWIN, Terrestrial Planet Finder and Pegase. Focused on this centuries-old quest of discovering Earth-like habitable planets in extrasolar systems has led to the launch of many single-space telescopes operating in various ranges of EM spectrum namely Hubble, Kepler, Spitzer, Herschel and upcoming James Webb Space Telescope (set to be launched in 2018). But none of these missions meet both the requirements of achieving a sub-arcsec angular resolution of 0.1 arcsec and operating in IRASSI's frequency range. Hence there is a research gap in the unexplored FIR wavelengths at high angular resolutions as a consequence of the challenges of imaging this EM spectrum. In order to address manifold science and engineering challenges that affronts the observation in this frequency range led to the inception of IRASSI mission. First, attenuation of FIR spectrum due to the Earth's atmosphere calls for the need of a space-based observatory. Second, imaging these regions with an unprecedented high angular resolution below 1 arcsec demands for a prohibitively large collecting surface of atleast 20 m diameter (adapted from Thinned Aperture Light Collector (TALC) mission concept), due to the inverse relationship of angular resolution with the diameter of the collecting dish. This leads to other challenges like launch, deployment and operation of such massive structures due to their mass and sheer size. Hence, space interferometers are the best solution so far to overcome this challenge in which wavefronts collected at different heterodyne receivers are superimposed to generate an interference signal. Swarm based interferometer overcomes another important challenge of single-spacecraft system in case of subsystems failure or complete shutdown leading to the complete mission failure. Swarm missions in such scenario will not lead to total mission failure since only the affected satellite is eliminated with the rest of the system operating normally. IRASSI constellation relishes and utilizes this advantage as it is composed of 5 identical spacecraft. IRASSI's dynamically changing baseline distances, with distance ranging between 7-850 m during scientific observations helps in measurement of astronomical target signal at different locations thus providing abundant astronomical data points by virtually filling the synthetic aperture. This imposes high requirement on the spatial resolution that should be proportional to the observed wavelength, which for FIR is in the order of micrometer level. Therefore the baseline distances of IRASSI telescopes must be determined to micrometer accuracy. Another constraint imposed by the science requirement is on the pointing accuracy of IRASSI telescopes. IRASSI telescopes are single receivers, i.e. the focal plane of each telescope is not filled with detector elements, rather has just one receiver feed horn that collects the observed source signal. These signals from all telescopes are then correlated to get the final visibility functions. For uniform illumination of the primary dish, the main lobe of the power pattern provides the highest sensitivity. And since the telescope beamwidth has inverse relation to the telescope diameter, the demand on the pointing accuracy depends on the high end frequency of the operating FIR spectrum of IRASSI, i.e. at 6 THz. At this frequency the high power beam width (HPBW) of the main lobe is minimum. This imposes a stringent requirement on the Absolute Pointing Error of each spacecraft to be atleast 0.4 arcsec with a goal of 0.2 arcsec such that the target remains within one tenth of HPBW of each telescope. Achievement of such high attitude accuracy requires selection of appropriate high performance sensor suite and optimal attitude estimation algorithms. Missions requiring attitude accuracy of better than milli-arcsec employ mission specific Fine Guidance Sensor (FGS) (used on Hubble, Chandra, JWST etc.), which is an interferometric instrument whose construction is complex (as compared to a high precision precision commercial-off-the shelf (COTS) Star Tracker), as it constitutes extended optics that focuses the signal from the telescope main dish to provide high pointing accuracy information to the spacecraft for control. Construction, maintenance, on-orbit operation and calibration of FGS is complex, time consuming and expensive. However, owing to the single receiver construct of IRASSI telescope dish, FGS is not feasible for IRASSI mission. Hence achieving sub-arcsec to milli-arcsec attitude accuracy with already validated, reliable and high-precision commercial-off-the shelf (COTS) sensors is a choice for IRASSI and a step towards high-precision cheap attitude systems for satellites in general. Attitude sensors (especially Star tracker) and inertial sensor technology improvement and maturation over past 15-20 years now provides us with this opportunity. This paper describes the development and analysis of high accuracy Attitude Determination Estimator System (ADES) that achieves three-axes pointing estimation accuracy of atleast 0.04 arcsec. Scientific requirements of IRASSI impose twofold challenge on ADES system. First is the stringent pointing accuracy requirement of at least 0.4 arcsec which led to the goal of achieving an order better estimation pointing accuracy, i.e. 0.04 arcsec from the ADES which is unprecedented. An order better accuracy of 0.04 arcsec is aimed from attitude estimation system which leaves enough margin for control error and other errors like structural instabilities etc. Second challenge is to achieve this accuracy with commercial-off-the shelf (COTS) sensors without using FGS which is employed on missions requiring such high pointing accuracy. Achievement of this demanding pointing accuracy goal depends on careful selection of appropriate sensors and employing optimal attitude determination algorithms. Extensive sensor analysis led to careful selection of using two Ball Aerospace High accuracy Star Tracker (HAST) mounted perpendicular to each other and operating simultaneously along with a high accuracy wide bandwidth Northrop Grumman Hemispherical Resonating Gyroscope (HRG) during ‘fine-pointing mode' of IRASSI when scientific observations are conducted. During ‘Coarse Attitude acquisition', Coarse Solar Sensor (CSS) from Adcole are fused with the HRG. This work describes the sensor accuracies, other operating characteristics and number of sensor units required for each IRASSI spacecraft. Furthermore, sensor placement on board IRASSI satellite will be described thus providing the orientation matrix of each sensor frame w.r.t the spacecraft body reference frame, which is required for accurate attitude estimation. Mathematical measurement models of these sensors are described and modified appropriately for this mission. State-of-the art Multiplicative Extended Kalman Filter (MEKF) algorithm archived in the literature and implemented on several past and current missions is selected and implemented in MATLAB for sensor data fusion. MEKF is a modification of standard EKF that uses a multiplicative error quaternion rather than an additive quaternion error. A 6-state (attitude error and gyro bias estimates) mission-mode MEKF is developed in which unit quaternion is used as global attitude representation and local quaternion errors are represented by a 3-component multiplicative attitude error. Unit quaternion is the choice of attitude parameters for space missions because it has 1) a compact attitude representation (with only 1 redundant parameter) that avoids any singularities, 2) linear kinematics, 3) algebraic attitude matrix thus avoiding transcendental functions and 5) simple successive rotations operation analogous to successive matrix rotations. MEKF implemented during ‘Fine- pointing mode' and ‘Coarse Attitude Acquisition mode' uses measurements from star trackers and sun sensors respectively. High accuracy rate-integrating HRG is used as a dynamic model replacement that provides precise angular rate information and reduces computational burden. Computational burden is also minimized by simulating discrete-time equations of MEKF and employing Murrell's approach during correction. Furthermore, a robust form for state covariance propagation, known as Joseph's form is implemented which guarantees non-negative eigenvalues of state-covariance. MATLAB simulations of ‘fine-pointing mode' demonstrate an attitude accuracy of 0.04 arcsec (1s) with 1 star tracker and gyroscope fusion. Utilizing 2 star tracker measurements in ‘fine-pointing mode' achieve an accuracy of 0.03 arcsec (1s). Achievement of such high accuracy also requires sensor calibration which is performed prior to mission mode filter implementation as it counteracts the effects of calibration errors due to launch shocks, in-orbit thermal fluctuations and out-gassing effects. Three estimators implemented during two mission modes assume that the calibrations have already been performed. This work is financed by the German Ministry of Economy and Energy through the German Aerospace Center, Space Administration (DLR Bonn, Deutsches Zentrum für Luft- und Raumfahrt, FKZ 50NA1327).