NAVIGATION PERFORMANCE PREDICTIONS FOR THE ORION …

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NAVIGATION PERFORMANCE
PREDICTIONS FOR THE ORION
FORMATION FLYING MISSION

Philip FERGUSON, Franz BUSSE, and Jonathan P. HOW

Space Systems Laboratory
Massachusetts Institute of Technology
philf@mit.edu, teancum@stanford.edu, jhow@mit.edu

ABSTRACT – This paper presents hardware-in-the-loop results that exper-
imentally demonstrate precise relative navigation for true formation flying
spacecraft applications. The approach is based on carrier-phase differential
GPS, which is an ideal navigation sensor for these missions because it pro-
vides a direct measure of the relative positions and velocities of the vehicles in
the fleet. In preparation for Orion, a planned microsatellite formation flying
mission, four modified GPS receivers were used in the NASA GSFC Forma-
tion Flying Testbed to demonstrate relative navigation. The results in this
paper show unprecedented levels of accuracy (
2cm position and <0.5mm/s velocity) which validate the use of a decentralized estimation architecture and offer high confidence in the success of Orion. » 1 - INTRODUCTION Autonomous formation flying of satellite clusters has been identified as an enabling technology for many future NASA and the DoD missions [1, 2]. The use of fleets of smaller satellites instead of one monolithic satellite should improve the science return through longer baseline observations, enable faster ground track repeats, and provide a high degree of redundancy and reconfigurability in the event of a single vehicle failure. If the ground operations can also be replaced with autonomous onboard control, this fleet approach should also decrease the mission cost at the same time. However, there are many control, navigation, and autonomy technologies that must be developed and demonstrated before these advanced science missions can be flown. The Orion microsatellite mission was designed to address many of these concerns for formation flying in LEO [3, 4]. This paper discusses the current spacecraft design and recent results on the decentralized relative navigation using differential GPS that has been developed for Orion. The Orion mission will consist of two identical cube satellites that have been designed to be launched from the Shuttle cargo bay (although other options are possible) and perform experiments for 50 to 90 days. There will be three primary operational stages [4]: ² ² ² Formation Stabilization: During this stage, the vehicles will be de-tumbled and the Orion vehicles will be maneuvered into their first formation (100m in-track separation). In-Track Experiments: In this stage, the two Orion spacecraft demonstrate tight for- mation flying with one vehicle following the other. The goal is to demonstrate a precise 5m error box centered at a point formation with one Orion remaining within a 5m 100m (in-track) from the other Orion. Elliptical Formation Experiments: In this final stage, the spacecraft will be controlled to stay within error boxes that traverse passive apertures (closed-form ellipses) in the LVLH frame (e.g., as governed by Hills equations). 10m £ £ Fig. 1: Orion spacecraft interior showing one of the propulsion tanks and associated plumb- ing. A torquer coil can be seen at the top. Fig. 2: Internal structure showing CDH CPU (middle bottom), GPS (top), HP prop (middle back) and LP Prop (lower left). 2 - THE ORION SPACECRAFT The Orion structure is a 44.5cm cube composed of T-6061 aluminum honeycomb. The main load-bearing portion of the microsat consists of a top faceplate, a bottom faceplate, and a set of panels that form an internal “X.” These honeycomb plates are each 1.27cm thick and are bound together with aluminum L-brackets and stainless steel bolts. Four 0.64cm honeycomb plates cover the remaining four sides of the cube. These panels are non-load-bearing. The solar cells will be bonded to a Kapton-insulated facesheet, which will then bond to the outside panels. Figures 1 and 2 show the internal structure. The Orion propulsion system uses GN2 stored in three composite wrapped aluminum tanks (see Fig. 1). The system is designed to provide the satellite with the maximum ∆V for the given volume and mass budgets. Most of the parts used are COTS in order to simplify the manufacturing process. There are 12 cold gas thrusters clustered in four groups of three to provide full 3-axis attitude and station-keeping control. Each thruster has the capability of providing approximately 60mN of thrust. The 3 cylindrical fuel tanks, each pressurized to 3500psi are predicted to provide a total ∆V capability of approximately 25m/s. The EM propulsion system has been extensively tested to demonstrate that it will meet the Shuttle Safety (e.g., verification procedure to show valve closure and tank certification) and mission performance goals (leak tests of the high and low pressure sides). The position and attitude determination system for Orion is comprised of two parts: A magnetometer (for coarse attitude determination) and a GPS receiver system (with the capa- bility of determining attitude as well as position). Orion will use a Honeywell HMC2003 3-axis magnetometer (40µG resolution) to provide feedback to the torquer coils during detumbling. The GPS receiver for Orion (see Fig. 2) is a modified version of Zarlink (Mitel) Semiconduc- tor’s OrionT M GP2000 chipset [3] (discussed in more detail later). To simplify the attitude determination process, a second RF front end was added to each board. Each RF front end can be programmed to use any of the 12 available correlator channels. There are total of 6 GPS antennas (36 channels) on each Orion. The Attitude Control System (ACS) consists of two distinct subsystems. A magnetic damping controller is included to slow the spacecraft rotation sufficiently for GPS signals to be acquired. Dedicated hardware, consisting of a three-axis magnetometer and torquer coils, allows the detumbling to be performed without GPS information. The torquer coils can be seen at the top of Fig. 1 and 2. The second attitude controller uses the GPS attitude solution and the thrusters. It is designed to keep the top face (with three GPS antennas) pointing “up” for the best GPS sky coverage. A Kalman filter is used to estimate the full attitude state. The Command and Data Handling (C&DH) system is responsible for all low-level tasks onboard the spacecraft. These tasks include decoding ground and inter-satellite communication, forwarding commands to distributed subsystems, controlling power switching for subsystems and experiments and gathering health and telemetry data. The CPU is a SpaceQuest NEC V53 with a 10MHz processor and 1MB of EDAC Ram, and it will run the Space Craft Operating System (SCOS) by BekTek. Both the CPU hardware and operating system have spaceflight heritage. Fig. 2 shows the C&DH integrated into Orion. The Communications subsystem must handle all data transfer between the ground and Orion as well as between each Orion vehicle. Crosslink between spacecraft will operate in half-duplex while the down/uplink will operate in full-duplex mode. Both crosslink and up/downlink communications will be conducted at 9600 baud. The modems for Orion are manufactured by SpaceQuest and have been used successfully on past spaceflights. The communications system makes use of an omni directional antenna pattern with circular polarization. The Science Computer is a 200MHz StrongARM 1110 RISC based microprocessor called the “nanoEngine” (built by Brightstar Engineering). The nanoEngine has three RS-232 communi- cation ports and 20 general purpose IO pins for controlling other hardware. A CompactFlash memory disk will be used for mass storage. At full usage, the entire nanoEngine board draws 1700 MIPS/W). The nanoEngine weighs only 76g (without an interface card) less than 2W ( and is smaller than a credit card. The operating system for the Science Computer is embedded Linux. The Science Computer will perform the navigation computation and fleet coordination. » With the hardware design essentially complete, the goal of recent work on the Orion mission has been to develop a simple, decentralized, real-time GPS filter that meets the performance targets, as specified by the control analysis [6]. As discussed in the following, the capabilities of this filter have been demonstrated on a 4-vehicle, hardware-in-the-loop simulation. 3 - STATE DEFINITIONS The goal of the relative navigation is to estimate the state of the formation, i.e., where the vehicles are located with respect to each other. The vehi- cle states include the position ri and velocity ˙ri, which are expressed in the Cartesian Earth Cen- tered Earth Fixed (ECEF) frame (see Fig. 3). All calculations and integrations are also performed in the ECEF frame. A specific GPS antenna on one of the vehicles is typically selected as a formation reference point. The vehicle associated with this reference point will be referred to as the “master” or “reference” vehicle, with the rest called “followers”. For state estimation, the selection of the reference is arbi- trary (it could be any vehicle in the formation). Fig. 3: Defines absolute r and relative ∆r position for a formation. Absolute states are expressed in the ECEF frame. Subscripts denote the user vehicles, where the reference vehicle will be indicated with the sub- script “1”; superscripts are used to denote the GPS NAVSTAR satellites. For example, the absolute position of the master user is r1, and the absolute velocity of GPS satellite m is ˙rm. The formation state can be expressed equivalently in absolute states (relative to the center of the earth) or in relative states (relative to the reference point in the formation). The relative states (∆X12 = X2 X1) between the vehicles are of much greater interest for formation flying, leading to a basic formation state of the form (n vehicles) ¡ (1) (2) £ 3.1 - Measurement Model X T 1 ∆X T 12 ∆X T 1(n 1) − ¢ ¢ ¢ T ¤ Each vehicle has a GPS receiver, which collects its own independent set of measurements at each time step. The GPS receiver provides three measurements: Code phase, carrier phase, and the Doppler shift on the carrier phase. Absolute navigation uses the code and Doppler measurements, but for orbital relative navigation, only the carrier phase measurement is needed. The carrier phase measurement, φ, for each visible GPS satellite by the receiver is where = range between user i at measurement time and GPS satellite m at time φm i = rmi k ri k ¡ + bi + Bmi + βm I m i + νφ i ¡ ri k ¡ rmi k bi Bmi I m i βm i νφ of signal transmission = clock offset for user i = clock offset for GPS satellite m at time of transmission = ionospheric delay = carrier phase bias for user i = other noises (including receiver noise and multipath) This measurement is a function of the user state, the GPS satellite state, the ionosphere, and other noise sources. Besides the user estimate, all of these terms have errors associated with them. (For absolute state estimation, the biases also present some difficulty, and are generally determined by combining carrier phase with code phase). As an alternative, measurements between two receivers from the same NAVSTAR satellite can be subtracted, which is referred to as the single difference measurement, ∆φm φm ij = φm i . In the case of relative navigation, these measurement sets would be from receivers on different vehicles, and the single difference provides a direct measurement of the relative state between the two vehicles. More specifically, the single difference is j ¡ ∆φm ij = rmi k ri ¡ k ¡ k ¡ k rmj (ri + ∆rij) + ∆βm ij + ∆bij + ∆Bm ∆I m ij + ν∆φ (3) ij ¡ where ∆rij ∆bij ∆Bm ij = differential position between users i and j = differential clock offset between users i and j = differential clock offset for GPS satellite m, between the transmitting states for users i and j ∆I m ij ∆βm ij ν∆φ = differential ionospheric delay = differential carrier phase bias between users i and j, on signal from m = remaining differential noises Note that the errors in these differential terms are typically much smaller than in the corre- sponding absolute terms. These single differences provide a direct measure of the relative state between vehicles, but do not provide an absolute state estimate. A single difference measurement can be created for each GPS satellite that is commonly visible to each pair of receivers i and j. With N commonly visible GPS satellites, there are N single difference measurements for this pair, which are grouped at time, tk as Of course, since both the users and GPS satellites move rapidly in their orbits, the list of commonly visible GPS satellites will change very frequently. £ yk = ∆φ1 ij(tk) ∆φN ij (tk) ¢ ¢ ¢ T ¤ 3.2 - Environment and State Definitions For each physical measurement, ∆φ, the terms on the right hand side of Eq. 3 must be modeled or estimated. In our work, the absolute state estimate, r1, is determined in a simple absolute 20m accuracy). The GPS navigation filter on the GPS receiver (least-squares point solution, states include the position, velocity, clock offset, and clock drift, for each visible NAVSTAR satellite. These are determined from ephemerides that are broadcast by the GPS satellites themselves. A simple model is included in the filter of the ionospheric delay. Any differential ephemeris error, ionospheric model error, or other sensor noises remain as measurement errors. The full relative state to be estimated, x, at a given time step, tk, is then defined, ¼ xk = (∆rij(tk))T ∆bij(tk) (∆˙rij(tk))T ∆˙bij(tk) (∆βij)T (5) £ For N commonly visible GPS satellites, ∆βij is a vector of N differential biases. The full state vector has (8 + N ) states. Again, note that over time, as the number of commonly visible GPS satellites changes, the state vector dimension will change during the filtering process as well as the measurement vector. T ¤ 3.3 - Decentralized Form of the Filter Measurements When compared to centralized filters, decentralized filters offer the benefits of improved ro- bustness/reconfigurability and distributed processing effort. Fortunately, the nature of this application lends itself well to a decentralized filter. The single difference measurement, for the relative state of vehicle j with respect to the reference vehicle, as defined in Eq. 3, can be linearized for short separations to give where Hj is defined (when using the definition of y in Eq. 4 and of x in Eq. 5) as yj = Hjxj + ej Hj = LOSj 1 0 0 I £ ¤ and ej is a general error term. The dimension of Hj is (8+N) N. This is a valid simplification £ because the dominant term, by far, is the differential range between the vehicles. All of the remaining terms in Eq. 3 can effectively be lumped into the error term ej. These errors are typically so small when compared to the differential range, that they can be considered as a noise term, ν. In this case, combining all of the vehicle relative state measurements provides a formation measurement, H2 H3 0 . . .    ¼ y2 y3 ... yn x2 x3 ... xn ν2 ν3 ... νn    +   (8)     For a formation with n vehicles, there are n 1 single difference blocks, since the absolute state of the reference vehicle is determined separately. If the noises ν2, ν3, . . . , νn are uncorrelated                             Hn ¡ 0 (4) (6) (7) and independent, the noise covariance matrix for a centralized filter would be block diagonal. In this case, because of the block diagonal nature of the observation matrix, H, the filter could be decentralized without any loss of accuracy, and a centralized and decentralized filter would provide exactly the same results. However, a decentralized filter is an approximation for this application because the noise terms are correlated: 1. Since each vehicle forms single differences with respect to the same reference, these sin- gle differences will be correlated. However ground testing has shown that this level of correlation is relatively small (carrier phase noise level 2-5mm); and 2. Recall that all other measurement errors in the remainder terms of Eq. 6 are lumped into the noise term, νj. Although forming a single difference cancels out many of the common mode errors, any residual errors will be correlated between vehicles. ¼ However, if these correlations are relatively small, they can be ignored, resulting in decoupled measurements that can be used to form a decentralized estimator. As discussed, decentraliza- tion offers many benefits and a key aspect of this work was to investigate whether a decentralized estimator could be used to meet the relative navigation goals set by the fuel usage [6]. The discussion presented in this section was based on a linearized version of the measurement equations. Linear filters are useful for formations with small separations, but, in general, a nonlinear measurement update is required [7]. However, this decoupling in the measurements that leads to a decentralization estimator also holds for the nonlinear extended Kalman filter. 3.4 - State Dynamics Model The state estimate is propagated between measurements using a model of the vehicle dynamics, which includes the basic forces acting on the vehicle. This work used a very simple set of dynamics based on Kepler’s differential central gravitation model ∆¨r1j = µ r3 1  r1 ¡ r3 1 (r1 + ∆r1j) 1 + 2r1∆r1j + ∆r2 r2 1j + 2ωe ∆˙r1j + ωe (ωe ∆r1j) + w∆r (9) 3  £ £ £  q¡  where µ is the earth’s gravitational constant and ωe is the earth’s rotation rate. All other forces, such as differential drag and higher order gravity terms, are lumped together into the process noise, w∆r. The clock offset and drift dynamics are modeled only as ∆¨b1j = w∆b. The carrier phase bias states are considered constant, and so they have no dynamic propagation over time. Note that the unknown or unmodeled relative dynamics errors are much smaller than the corresponding absolute dynamics errors. ¢ 3.5 - Test Equipment and Conditions The GPS receivers used for this work are identical to the ones planned for Orion. The chipset has space heritage [5] and has been used extensively by the authors on terrestrial formation applications. It has variable gain Phase Lock Loop (PLL) carrier tracking loops. Special mod- ifications were also made to allow operation at orbital altitudes and velocities. A simple orbit propagator insures the ability to acquire navigation fix even in orbit, which is necessary because of the larger Doppler search space. For relative navigation we use simultaneous measurements (rather than interpolating over time), and so the receiver clock actively steers to GPS time. These modifications make this receiver an ideal orbital relative navigation sensor. The NASA Goddard Space Flight Center has a state-of-the-art Formation Flying Testbed (FFTB). At its heart is the Spirent STR Series Multichannel Satellite Navigation Simulator. It uses a Compaq DS10 workstation to simulate the motion of the NAVSTAR constellation and up to 4 independent vehicles. The workstation sends these states to two STR4760 RF signal generators. These signal generators create the GPS signals that would be observed by the four user receivers (with two RF outputs per generator). Many scenarios have been run using this simulator (base orbit has altitude of 450km, ec- centricity of 0.005, and 28.5◦ inclination). The simulations use a tenth-order gravity model and an atmospheric drag model (Lear’s). For the measurements, a diverging ephemeris and clock model was used and a standard orbital ionospheric model, as specified in NATO Standard Agreement STANAG 4294 Issue 1. There is no multipath noise in the simulation, but this is not expected to be a significant error source for microsatellites. All vehicle models are identical, with a surface area of 1m2, drag coefficient of 2, and 0.1 metric tonne (the smallest mass in the simulator). The antenna is at the center of gravity, and the vehicle maintained a nadir earth-pointing attitude. A standard hemispherical antenna gain pattern was used. » The decentralized filter for these demonstrations used the nonlinear update and propagation models [7]. Only carrier-phase single differences measurements were used. The update rate was 1Hz. Several formations were considered: 1. 100m and 10km In-track. Here the vehicles were in the same orbital path, all separated from one another by the prescribed amount in-track. 2. 1km and 10km In-plane ellipses. This formation is considered our baseline demonstration for meeting our performance targets. One vehicle followed the reference orbit. The other three vehicles moved about the master vehicle in an evenly spaced ellipse, staying within the orbital plane. The elliptical path in the local frame was 1km 2km. 3. 1km Out-plane ellipse. Similar motion, but now the relative motion ellipse is oriented out of the orbital plane, leading to greater differential J2 disturbances (larger process noise). £ 4 - RESULTS This section presents the results from real-time hardware-in-the-loop experiments using the GSFC FFTB facility. For all experiments, data storage of the raw measurements began after all four of the receivers achieved navigation fixes. The receivers performed “warm” starts, where they were provided almanac information for the NAVSTAR constellation, a rough current position guess (often wrong by several hundred kilometers) and a rough current time guess (off by up to fifteen seconds). The receivers can reliably and repeatedly lock on (accomplished hundreds of time during the course of development). A navigation fix was usually obtained, and active tracking began, in less than two minutes after the simulation began. ¼ Figures 4 and 5 show the position and velocity errors for the three relative solutions (shown as projections of the error into the Radial (R), In-Track (I), and Cross-Track (C) directions). The simulations start with large errors ( 2-5m) that result from the initial carrier phase bias errors. However, these biases are observable over time, and the position solution quickly converges. After the initial convergence, the biases on new measurements coming on-line are predicted from the current state estimate, but the results show that this initialization process does not disturb the position or velocity estimates [7]. To quantify the performance, the standard deviation and mean of the error was computed over the last half of the simulation in each dimension. Table 1 gives the root-mean-square of these means and standard deviations of the errors across the fleet’s three solutions. As shown, the position error has a mean of 0.2—1.1cm, and a standard deviation of 0.3—0.7cm. The velocity error has a mean of 0.03mm/s and a standard deviation of 0.3mm/s. Table 2 shows a list of results for different formations that were compiled in the same way. First, it is clear that for the close formations (1km or less), the performance is better than the target precision (performance approaches the noise floor as determined in the error analysis). » ) m i ( l a d a R 0.1 0 -0.1 0.1 0 -0.1 0.1 0 -0.1 ) m ( k c a r T - n I ) m ( k c a r T - s s o r C Relative Position Error,(LVLH) -3 x 10 Relative Velocity Error,(LVLH) 500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 2 0 -2 2 0 -2 2 0 -2 ) s / m i ( l a d a R ) s / m ( k c a r T - n I ) s / m ( k c a r T - s s o r C -3 x 10 -3 x 10 500 1000 2000 2500 3000 1500 Time (sec) 500 1000 2000 2500 3000 1500 Time (sec) Fig. 4: Relative position error (Radial, In-Track, Cross-Track) for three decentral- ized solutions (1km in-plane ellipse) during hardware-in-the-loop experiments. Table 1: Relative state estimation results: 1km in-plane elliptic formation. Pos. (cm) Mean 0.25 1.06 0.16 Vel. (mm/s) Std 0.156 0.275 0.107 Std Mean 0.032 0.45 0.001 0.66 0.017 0.29 Radial In-track Cross-track Fig. 5: Relative velocity error over time, projected in the Radial, In-Track, and Cross- Track directions. Error is less than 0.5mm/s. Table 2: Results for several formations — Tar- get: 2.0 cm (Pos.) and 0.50 mm/s (Vel.). Pos. (cm) Mean 0.93 0.83 1.03 5.76 2.83 Vel. (mm/s) Std 0.32 0.33 0.34 0.40 0.54 Std Mean 0.01 0.46 0.04 0.82 0.04 0.54 0.07 1.92 0.04 1.55 100m in-track 1km in-plane 1km out-plane 10km in-track 10km in-track As expected, the position accuracy degrades for the long separation formations. Velocity is good in all cases and has a low mean value, which is very important for the formation control. 5 - CONCLUSIONS This paper presented new results of the carrier-differential GPS relative navigation that has been developed for the Orion formation flying mission. These results validate the use of a decentralized estimation architecture and give further confidence in the success of this and future formation flying missions. REFERENCES [1] J. Leitner et al. “Formation Flight in Space,” GPS World, Feb. 2002, pp. 22—31. [2] A. Das and R. Cobb, “TechSat21 — Space Missions Using Collaborating Constellations of Satellites,” 12th AIAA/USU Conference on Small Satellites, Aug. 1998, SSC98-VI-1. [3] F.D. Busse, J.P. How, J. Simpson, J. Leitner, “Orion-Emerald: Carrier Differential GPS for LEO Formation Flying,” IEEE Aerospace Conference, Big Sky, MT, Mar 2001. [4] P. Ferguson, et al., “Formation Flying Experiments on the Orion-Emerald Mission”, AIAA Space Conference and Exposition, AIAA paper 2001-4688. [5] M. J. Unwin, et al., “Preliminary Orbital Results from the SGR Space GPS Receiver”, in Proc. of ION GPS, Nashville, Sept. 1999. [6] J. How and M. Tillerson, “Analysis of the Impact of Sensor Noise on Formation Flying Control,” American Control Conference, 2001, pp. 3986—3991. [7] F. D. Busse and J. P. How, “Real-Time Experimental Demonstration of Precise Decentral- ized Relative Navigation for Formation-Flying Spacecraft,” AIAA Guidance, Navigation, and Control Conf., August 2002, AIAA Paper 2002—5003.