ATTITUDE DETERMINATION Active attitude control actuators (e.g. control momentum gyros, reaction wheels, offset thrusters, magnetic torque rods, etc.) are the mechanisms that keep spacecraft properly oriented. Measurements from closed-loop attitude control feedback sensors (e.g. magnetometers, horizon sensore, sun sensors, gyroscopes, star trackers, etc.) determine the orientation of the spacecraft and through computer controls order attitude corrections to be performed by the actuator. A GPS receiver can provide attitude and attitude rate data to the actuator for real-time, autonomous attitude determination and control. The benefit of using a GPS sensor is the elemination of different sensors and their interfaces. This in turn can reduce costs, power requirements, weight, complexity, and increase system reliability [Lightsey, 1995, p.461]. An array of GPS antennas (at least three, but four preferable) oriented in the same direction are placed on the rigid structure of a spacecraft. Software controlled multiplexing allows for signals being received at all antennas to reach a single receiver. The carrier phase measurements are used to determine differential range between the "master" antenna and each of the other antennas in the direction of the line of sight from a GPS satellite to the master antenna. The components of baseline vectors between antennas in the spacecraft body-fixed frame and integer ambiguity resolution are required. Additional on-board code computes attitude from successive carrier phase measurements for real-time determinations. Given data about the dynamics of the spacecraft, a Kalman filter can be used to improve attitude estimates. The main performance issues are: - update rate - how often is attitude data being feed into the loop, - antenna placement - the further apart the antennas are, the better the result and the more antennas that are receiving signals from the same satellites the better the result, - ambiguity resolution - since carrier phase observations are begin collected the correct integer ambiguities must be resolved (see e.g. Cohen [1995]), and - multipath - the largest contributor to the noise in the measurements. The CRISTA-SPAS mission, using a Tans Vector receiver, for a 24 hour period produced rms attitude variations around mean motion of 0.19( in roll, 0.15( in pitch and 0.26( in azimuth [Brooke et al., 1995]. Attitude determination accuracy estimated to be 0.5( rms was produced in the RADCAL mission [Lightsey et al., 1994]. Results from the two Tans Vector receivers on-board the GADACS experiment assembly have not yet been published, but attitude determination on the order of 0.1( to 0.5( was expected [Bauer et al., 1994]. The planned Gravity Probe-B satellite will use a Tensor receiver as a back-up attitude sensor with an accuracy requirement of 0.1( rms over one second [Uematsu et al., 1995]. References Cohen, C.E. (1995). "Attiude determination." In Global Positioning System: Theory and Applications (Eds. B.W. Parkinson and J.J. Spilker Jr., Assoc. Eds. P. Axelrad and P. Enge). Progress in Astronautics and Aeronautics Vol. 164 (Ed. P. Zarchan). American Institute of Aeronautics and Astronautics, Inc., Washington, D.C., 643 pp. Lightsey, E.G. (1995). "Spacecraft attitude control using GPS carrier phase." In Global Positioning System: Theory and Applications (Eds. B.W. Parkinson and J.J. Spilker Jr., Assoc. Eds. P. Axelrad and P. Enge). Progress in Astronautics and Aeronautics Vol. 164 (Ed. P. Zarchan). American Institute of Aeronautics and Astronautics, Inc., Washington, D.C., 643 pp. CLOCK SYNCHRONISATION At the time of GPS signal acquisition by a GPS receiver, the crystal oscillator (usually a TCXO)-based receiver clock is synchronised with GPS time by means of pseudorange measurements and the GPS navigation message. A spacecraft bus architecture can be used to supply GPS-derived time to synchronise all spacecraft subsystem clocks. In this manner, daily clock updates from ground stations will not be required and precise time-tagging of downloaded satellite data will be possible [Bauer et al., 1995]. Once receiving GPS signals, a GPS receiver is capable of a GPS time clock synchronisation accuracy of approximately 300 nanoseconds with SA engaged. This accuracy is quite sufficient for many satellite missions. The sychronisation of spacecraft system clocks by GPS time transfer can be accomplished by means of a feedback loop. A computer monitors the difference between the GPS time and local clocks. The computer then uses this information to advance or delay the local clocks (i.e. by means of a phase microstepper) Klepczynski [1995]. The GADFLY experiment to be launched on the SSTI-Lewis spacecraft requires a precise timing reference of 1 millisecond [Bauer et al., 1995]. Given the previous discussion, this is a conservative estimate. Other missions have more stringent specifications. It is predicted that the receiver onboard Gravity Probe-B will have a clock sychronisation with GPS time in the order of 100 ns [Uematsu et al., 1995]. Two notes should be made in conclusion. The accuracy of the GPS-derived time reference is strongly correlated with the ability to collect good-quality GPS observations. And with the imminent demise of SA, the dithering forced on the GPS clocks will cease and therefore the integrity of receiver-produced timing capabilities will improve. References Klepczynski, W.J. (1995). "GPS for precise time and time interval measurement." In Global Positioning System: Theory and Applications (Eds. B.W. Parkinson and J.J. Spilker Jr., Assoc. Eds. P. Axelrad and P. Enge). Progress in Astronautics and Aeronautics Vol. 164 (Ed. P. Zarchan). American Institute of Aeronautics and Astronautics, Inc., Washington, D.C., 643 pp. RELATIVE POSITIONING The main application of relative spaceborne GPS positioning is, as noted in the previous section, for real-time spacecraft rendezvous and docking. Automated GPS-based systems are seen as a promising technique to be used for this evolving and expanding application. Table 2.1 and Appendix I highlight more of these applications. The methodologies put forward are analogues to terrestrial differenced and relative GPS positioning. The former involves orbit determination being performed on both spacecraft and the "target" spacecraft (e.g. a space station) transmitting its solutions to the "chaser" spacecraft (e.g. a space shuttle) for differencing. The latter involves processing the single-difference observations (observations differenced between pairs of pseudorange measurements of a common GPS satellite) or double-difference observations (observations differenced between pairs of single differences for the same epoch) and transmitting the raw measurements from the target to the chaser for computation of relative position and velocity [Ambrosius et al., 1993, and DiPrinzio and Tolson, 1994, p. 37]. Relative positioning accuracy has been determined from a number of simulations, including approximately 3 metres rss using high-precision, single-differenced pseudoranges [Ambrosius et al., 1993], and approximately 0.4 metres rss after 1000 seconds using pseudorange and accumulated-phase data with an integrated Kalman estimation filter [Cox and Brading, 1995]. In a simulation by DiPrinzio and Tolson [1994], given a "visible" constellation of seven GPS satellites, 15° measurement noise and the use of double-differencing, C/A code relative positions were determined with accuracies of 20 metres 3d rss for baselines greater than 2 kilometres (while chaser is "homing in" on target) [DiPrinzio and Tolson, 1994, p. 42]. For baselines shorter than 2 kilometres, 3 cm 3d rss relative position accuracies were determined using ambiguity resolved carrier phase measurements [DiPrinzio and Tolson, 1994, p. 42]. To allow for ambiguity resolution, the relative position between the two spacecraft was required to remain steady and a Kalman filter was employed to estimate the initial integer ambiguities from the double-difference phase observable [DiPrinzio and Tolson, 1994, p. 42]. In a trial, orbits were determined independently with two receivers, one on the Wake Shield Facility-02 and one on the Space Shuttle. These one hour arcs were formed from double difference observations between the on-orbit receivers and IGS network receivers. Pseudoranges were observed with one receiver and carrier phase with the other. The distance between the two receivers was computed by Shuttle instruments. 10 metre relative positioning accuracy was attained in this post-processed experiment. For the proposed RADARSAT-2 mission, highly accurate relative position of orbital passes will be required for proposed interferometric synthetic aperture radar (INSAR) measurements [Ahmed, 1996]. Regular SAR provides two-dimensional images based on slant ranges from the SAR to the ground and the relative along-track position of the SAR. INSAR utilises an additional antenna (either a physically separate antenna or the same antenna on a different orbital pass) to measure the differential phase to each image pixel [Dixon, 1995]. In reality, this relative position accuracy is a function of absolute orbit determination. For a "typical" remote sensing satellite at an altitude of several hundred kilometres, centimetre level relative positioning is required for repeat orbit separations of 1 kilometre to determine absolute height errors of less than 1 metre. If only relative height errors of less than 1 metre are required in the image (i.e. absolute determinations made via ground control points), 1 metre relative positioning accuracy is required for a 1 kilometre baseline [Fuk and Goldstein, 1990]. Results from the orbit determination study of the TurboStar receiver on board MicroLab-1 (section 5.5) indicate that the latter requirements can be met. It has been stated that absolute height accuracies of 1 metre can also be determined with centimetre level 1 kilometre relative position with GPS [Zebker et al., 1994] given the orbit determination results from the TOPEX / Poseidon mission. References REAL-TIME OD Under the terms of the contract, we were requested to investigate the use of GPS as a sensor for orbit determination. The rationale for requiring real-time, on-orbit, orbit determination (OD) is varied. Autonomous OD would for example reduce or potentially eliminate the need for expensive ground tracking stations. The performance of a spacecraft's attitude determination and control system (ADACS) can be greatly improved with on-board position estimates of better than 1 kilometre [Unwin and Sweeting, 1995]. In the context of remote sensing satellites, real-time OD accuracies of better than 20 to 30 metres can reduce the OD error contribution in the total pixel localisation error for nadir-looking directions to an almost negligible level [Potti et al., 1995]. On-orbit, OD is invariably performed in real-time or near real-time in the GPS receiver. And conversely, to perform real-time orbit determination with GPS, it is most efficient to incorporate the OD software into the receiver. This involves absolute position determination with a GPS receiver. These determinations can be performed in real-time with GPS receivers that have software capability to track GPS signals from fast moving space platforms. The range of the received Doppler frequency signals are about 100 kHz in a LEO spacecraft, as compared to a receiver on the ground for which this width is approximately one tenth as wide [Ichikawa et al., 1995]. By utilising its pseudorange and carrier phase observations, the receiver can determine its position and velocity in real-time as does a receiver operating on the earth's surface. This is its navigation solution or state vector. It must be observed that the accuracies of these solutions are difficult to assess due to the lack of known position information. Software code in the receiver or in another system on-board the satellite must convert the receiver-derived state vector to an orbit determination. The simplest case is an osculating ellipse for a single epoch. A more comprehensive orbit determination would involve the use of a satellite force model with the state vectors and a Kalman filter. Such a technique is used in the GPS/MET TurboRogue in order to schedule occultation times (refer to section 4.2.2). Figure 6.1. A generic real-time, on-orbit, orbit determination architecture [after Potti et al., 1995]. Figure 6.1 illustrates a generic real-time, onboard, orbit determination architecture flowchart design from research by Potti et al. [1995]. GPS signals are received at the antenna (1) and are tracked in the data acquisition section (2) as described in section 4.1.1. If single frequency data are being collected, ionosphere corrections are required if ionospheric propagation delay of the signals is to be removed. Gold et al. [1994] suggest averaging the code and phase data to eliminate the first order ionosphere induced errors. The state vector of the GPS satellites is predicted (3) from the GPS navigation message obtained by the data acquisition section (2) for the design matrix computation. The state vector and its covariance matrix for orbit determination must be initialised from input parameters. One such initialisation method is to fit orbit models to the point positions generated by the receiver's navigation solution [Gold et al., 1994]. The propagation of the state vector (4) and the state vector error covariance matrix (5) are performed by analytical and/or numeric integration. A change in the GPS satellite constellation being tracked would require a re-initialisation of the state vector elements pertaining to the specific satellite(s) involved. An orbit dynamics model is incorporated at this stage. The measurement processing section (6) utilises an extended Kalman filter (EKF), due to the non-linear formulation, to predict the states between two updates. These predicted states are differenced from the measured observables to determine the measurement residuals. The observation matrix is determined. An EKF is used to update the state vector (8) and the covariance matrix (9). Finally from the updated state comes the orbit determination (10). 6.2 Current capabilities Real-time, on-orbit, OD results are found sparingly in the literature. Therefore, navigation solutions, post-processed and simulated results are also included in this review. As such, Table 6.1 describes the potential real-time OD accuracy attainable with GPS receivers on-board various satellites or the results for data used to determine the orbits. The comments made are expanded upon in the following paragraphs. Satellite Solution accuracy Comments MicroLab-1 46 m navigation solution WSF-02 62.6 m post-processed l.s. fit of an orbit to nav. sol'n. DARPASAT 350 m navigation solution compared to range vectors SFU 200 m ( < 200 m real-time, on-orbit OD PoSAT-1 1.5 km receiver turned on for only one orbit per day EUVE 10 to 15 m post-processed in a simulated real-time scenario Table 6.1. Orbit determination accuracies attainable with GPS receivers on board various satellites. For the TurboStar receiver on MicroLab-1, the receiver navigation solution was shown (in section 4.4) to have a 3d rss mean error of approximately 46 metres, compared to precise orbit determination with the same receiver. These results were collected over a six hour period and are considered typical of the receiver navigation solution [Schreiner, 1996b]. As indicated, the TurboStar is a dual frequency, eight channel, cross-correlating receiver. Unfortunately, the real-time ODs computed by the receiver were not available for this study. However, the continuous collection of position determinations of this accuracy would indicate that ODs to the 50 metre level are possible. A TurboStar identical to the GPS/MET receiver was flown on the second Wake Shield Facility mission (WSF-02). The navigation solution was produced with pseudorange observations in the presence of SA. In the post-processing mode, an orbit was fit to one hour of such solutions in a least squares process. No dynamic modelling was performed. The fit of the navigation positions produced a 3d rss value of 62.6 metres [Schroeder et al., 1996]. The DARPASAT spacecraft contains a six channel AST-V, dual frequency receiver, without an AS circumvention capability. 28 sets of 20 minute navigation solutions were collected from C/A code observations and compared against ranging data. At least 30 minutes separated the GPS data sets and the receiver was turned off at these times so as to produce independent data sets through the re-initialisation of the receiver's filter. These data sets contain solutions that contain filter converged data, good GPS satellite geometry with no viewing constellation changes, and low solution variances. Ionospheric corrections from the navigation message were applied to pseudoranges. The ranging data were propagated to the times of the GPS solutions by incorporating a spacecraft state with the ranging data. Force models used during this propagation were a 36(36 geopotential field, luni-solar gravitation, solar radiation pressure, and atmospheric drag. The accuracy of these ephermerides are predicted to be one kilometre in position, but are degraded over time. The 3d rss difference between the GPS navigation solution and the propagated ranging data was determined to be approximately 350 metres [Mitchell et al., 1996]. It must be noted that the GPS position error determined in this study is one-third the size of the predicted error in the benchmark solution. A more accurate benchmark would have perhaps produced different results. The Space Flyer Unit (SFU) contains an Hitachi, Ltd. five channel, single frequency (L1 and C/A code) GPS receiver (GPSR). The GPSR has two telemetry modes, point positioning and filter mode, which can be changed by up-link commands. The point position mode utilises GPS satellite ranging data, whereas the filter mode estimates orbital elements of SFU with an Extended Kalman Filter (EKF). The EKF contains an SFU dynamics model and a GPSR clock model. The benchmark OD solutions used are earth-based results from radiometric data. The results of the on-orbit point positioning for four and a half hours is approximately 400 metres with a variance of less than 20 metres. For on-orbit OD, the SFU receiver produced position errors at a level similar to the point positioning error, 200 metres. The variance of the position error in the GPSR orbit differenced from the earth-based OD is less than 200 metres. However, the authors caution that more data are required for a full analysis, since only three hours of data were used in this comparison. The effects of SA and the ionosphere were not removed from this on-orbit GPS OD experiment [Ichikawa et al., 1995]. For the PoSAT-1 spacecraft, it was determined that continuous GPS OD was not required for 1.5 km OD accuracy. Also, to reduce power consumption the six channel, C/A code Trimble TANS receiver is only activated for one orbit each day. To determine the accuracy of the receiver navigation solution, GPS determinations were propagated to radar tracking points (the method used has not been publicly described). The 3d rss position error is approximately 150 metres 2( for one half hour of data. PoSAT-1 generates mean orbital elements in orbit by converting individual position and velocity data to osculating elements, and then transforming these osculating elements to mean elements through the use of an SGP4 analytical propagator. Successive element sets are then combined over time through a least squares fit to obtain a single mean orbital element set. When compared to NORAD elements, the 3d rss for over 15 weeks of data was approximately 1.5 kilometres [Unwin and Sweeting, 1995]. Navigation solutions from the twelve channel, single frequency (L1, P-code) GPSDR receiver on board the EUVE satellite were post-processed in a simulated real-time, on-orbit OD strategy. No onboard filter was used to compute the state from past navigation solutions. Simplified dynamic models are used including a sphere rather than a box wing model, no atmospheric drag, earth and solar radiation, and earth tides models. A 12(12 earth gravity field is used. An ionospheric correction is applied to range data to the first order by averaging the code and the phase data. An EKF is used for the OD process along with a reduced dynamic solution, the latter which reduces the effects of dynamic modelling errors by stochastic force estimation. The resulting OD differed from metre level OD with LEO receiver and ground GPS receivers by 10 to 15 metres 3d rss, even in the presence of SA [Gold et al., 1994].