Autonomous Inertial Relative Navigation with Sight-Line- Stabilized Integrated Sensors for Spacecraft Rendezvous Hari B. Hablani * The Boeing Company, Huntington Beach, California 92647 DOI: 10.2514/1.36559 This paper presents a novel autonomous inertial relative navigation technique with a sight-line-stabilized integrated sensor system for midrange (20–1 km) spacecraft rendezvous. A continuous-discrete six-state extended Kalman filter is developed for this purpose. The integrated sensor suite onboard an active chaser satellite comprises an imaging sensor, a coboresighted laser range finder, the space-integrated Global Positioning System/inertial navigation system, and a star tracker. For high accuracy of the relative navigation, the Kalman filter state vector consists of the inertial position and velocity of the client satellite governed by a high-fidelity nonlinear orbital dynamics model. The error covariance matrix is formulated in terms of the estimation error in the relative position and velocity of the client satellite, consistent with the sensor measurements. Inertial attitude pointing and rate commands for tracking the client satellite are determined using the estimates of the client’s inertial relative position and velocity. To estimate the inertial attitude of the chaser satellite outside the space-integrated Global Positioning System/inertial navigation system, a new three-axis steady-state analytical attitude estimator is developed that blends the gyro- and the star-tracker-measured attitudes. The simulation results of a midrange spacecraft rendezvous using glideslope guidance validate this new six-state autonomous inertial relative navigation technique. The simulation results show that the imaging sensor’s sight line can be stabilized at the client satellite in midrange accurately enough to enable the laser range finder to measure the range occasionally, but these measurements are not necessary for the midrange rendezvous phase, because the extended Kalman filter can estimate the range with the angle measurements of the imaging sensor. I. Introduction T HE principal objective of this paper is to present a sight-line- stabilized integrated sensor system that enables novel autonomous inertial relative navigation of a passive client spacecraft for the midrange (20–1 km) phase of a spacecraft rendezvous. Bryan [1] explains various facets of autonomous rendezvous and docking, including its different phases and required sensors. The sensor suite considered here is based on the scenario that the client spacecraft is passive, disabled, or noncooperative, and so there is no cross-link communication between the two satellites nor are there any optical reflective geometry on the client satellite. As such, following [2,3], the selected sensor suite is an integrated sensor system composed of an imaging sensor with wide, medium, and narrow fields of view for relative angle measurements, a coboresighted (or collimated) laser range finder (LRF) for range measurement, and the space-integrated Global Positioning System/inertial navigation system (SIGI) for the active chaser satellite. A new autonomous relative navigation algorithm that this sensor ensemble facilitates is formulated in an inertial frame using a continuous-discrete extended Kalman filter (EKF). To enhance accuracy of attitude estimates of the chaser satellite, the SIGI Kalman filter is provided with star tracker measurements of the inertial attitude of the satellite. For attitude estimation outside the SIGI, a new three-axis steady-state attitude estimator is developed that optimally blends gyro and star tracker attitude measurements. The inertial relative position and velocity estimates of the client satellite are used to determine the pointing and rate commands for tracking. A three-axis attitude controller stabilizes the imaging sensor’s sight line and coboresighted LRF at the client satellite within the pointing-accuracy requirements. Whereas the field of view of an imaging sensor is large (4  4 deg for medium and 1  1 deg for narrow fields of view), the laser beam width is merely 0:25 mrad (0.014 deg) and has very low divergence (0:25 mrad) [3]. Therefore, whereas the pointing requirement to avoid jitter of the imaging sensor is loose, that for the LRF is stringent (15–30 rad). For accurate pointing, the imaging- sensor boresight and the coboresighted LRF must be aligned very carefully [2,3]. Because achieving this degree of alignment and pointing stability is expensive, a secondary objective of this study is to show that it is not necessary to measure the range for a midrange (20–1 km) rendezvous, because it can be estimated from the angle measurements under certain observability conditions [4,5]. The present proof-of-concept study differs from the studies and flight tests of the past in several respects. Kawano et al. [6] illustrated the use of relative Global Positioning System (GPS) and laser radar navigation for the relative approach phase (from 10 km to 500 m) and final approach phase (from 550 to 2 m) of autonomous rendezvous and docking of two engineering test satellites (ETS-VII). The satellites were equipped with GPS receivers and cross-link antennas. Similarly, Park et al. [7] developed a relative navigation Kalman filter for rendezvous of the space shuttle with the wake-shield facility, both vehicles having GPS receivers and the wake-shield facility transmitting its receiver’s output to the orbiter; the electro- optic sensors were not involved in this test. In their more recent demonstration of the Rendezvous and Proximity Operation Program, Clark et al. [8] illustrated the benefits of their relative navigation Kalman filter using an LRF when the two spacecraft were within the range of a few hundred meters. Here again, because of the short range, the pointing accuracy of the sensors was not a concern, and relative navigation was based on simple linear relative dynamics in the local-vertical/local-horizontal (LVLH) frame. Gaylor and Lightsey [9] emulated the SIGI Kalman filter for operation in proximity of the International Space Station, but they did not deal with relative navigation or electro-optic sensors and their pointing. Woffinden and Geller [10] formulated relative navigation using angles only, but their study was for very close range (25 m) in which Presented as Paper 5355 at the AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, TX, 11–14 August 2003; received 9 January 2008; revision received 28 May 2008; accepted for publication 29 May 2008. Copyright © 2008 by The Boeing Company. All rights reserved.. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0731-5090/09 $10.00 in correspondence with the CCC. * Technical Fellow, Integrated Defense Systems, Flight Sciences and Advanced Design; currently Visiting Faculty, Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 208 016, India. Associate Fellow AIAA. JOURNAL OF GUIDANCE,CONTROL, AND DYNAMICS Vol. 32, No. 1, January–February 2009 172