Cross-Validation of GPS and FFRF-Based Relative ... - CiteSeerX

CROSS-VALIDATION OF GPS- AND FFRF-BASED RELATIVE NAVIGATION FOR THE PRISMA MISSION O. Montenbruck(1), M. Delpech(2), J.-S. Ardaens(1), N. Delong (2), S. D’Amico(1), J. Harr (2) (1)

(2)

Deutsches Zentrum für Luft- und Raumfahrt (DLR), German Space Operations Center (GSOC) 82234 Wessling, Germany Email: [email protected]

Centre National d’Etudes Spatiales (CNES), 18 Av. Edouard Belin, 31401 Toulouse cedex 9, France Email: [email protected]

ABSTRACT Scheduled for launch in mid 2009, the Swedish PRISMA mission will enable an in-depth flight demonstration and validation of advanced formation flying technologies. Among its key instruments is the radio frequency formation flying (FFRF) sensor, which has been contributed to the PRISMA mission by the French National Space Agency (CNES) in partnership with the Spanish Centre for the Development of Industrial Technology (CDTI). The FFRF sensor is a fully self-contained navigation system for relative positioning and pose estimation. It does not depend on Global Navigation Satellite System (GNSS) signals and can therefore operate at arbitrary distances from the Earth. The FFRF sensor will thus be vital for astronomical formation flying missions such as PROBA-3 and SIMBOL-X. Missions in low earth orbit (LEO) like PRISMA, in contrast, benefit greatly from the availability of GPS, which enables high precision absolute and differential navigation. To that end the two satellites will be equipped with a dedicated GPS navigation system developed and contributed by the German Aerospace Center (DLR). The GPS navigation system will provide the primary reference for absolute and relative position measurements and thus serve the validation and calibration of other navigation sensors. In preparation of the PRISMA flight, and as key step towards future formation flying missions, extensive ground tests and simulations have been performed by DLR and CNES to assess the achievable relative navigation accuracies of the two sensor types and the potential for in-flight validation of FFRF data using differential GPS. This paper provides an overview of the cross-validation strategy, a description of the joint hardware-in-the-loop simulations performed to assess the FFRF and GPS relative navigation accuracy, and a comparison of the expected real-time and post-facto navigation results in the context of the PRISMA mission. 1. INTRODUCTION Different classes of formation flying missions are currently under discussion within the European engineering and science community: technology demonstration missions (e.g. PROBA-3), synthetic aperture interferometers and gravimeters for Earth observation (e.g. TanDEM-X, postGOCE), dual spacecraft telescopes which aim at the detailed spectral investigation of astronomical sources (e.g., XEUS, SIMBOL-X), multi-spacecraft interferometers in the infrared and visible wavelength regions as a key to new astrophysics discoveries and to the direct search for terrestrial exoplanets (e.g., DARWIN, PEGASE). These missions are characterized by different levels of complexity, mainly dictated by the payload metrology and actuation needs, and require a high level of on-board autonomy to guarantee the safety of the formation during all phases. A common denominator of astronomical formation flying missions is the deployment of a self-contained relative navigation system, able to operate at arbitrary distances from the Earth without external aid (e.g. from GPS, ground control, etc.), which could serve the fundamental needs of distributed Fault Detection, Isolation and Recovery (FDIR), formation deployment and acquisition as well as safe mode operations. Theoretically both optical (laser) and Radio Frequency (RF) signals could be exploited to accomplish these tasks, but in practice only the latter is considered a feasible option. In contrast to an optical sensor, RF technology does not need movable transmitters (narrow and coherent beams), is not affected by high heat generation and is not prone to mechanical stress and failures. The adoption of several Transmitters/Receivers (Tx/Rx) distributed on the participating spacecrafts avoids the implementation of a movable mechanical system, at the expense of a more complicated characterization of the multipath environment and calibration procedures. As a consequence, optical sensors are envisaged as fine metrology sensors to be used for scientific data collection after the formation has been locked (i.e., Science mode activities), while RF constitutes the most suited baseline for a coarse metrology safe-mode instrument. Two national space agencies are independently working on the development and validation of such a RF formation flying sensor. NASA plans to embark its Autonomous Formation Flying (AFF) sensor on the Terrestrial Planet Finder (TPF) mission, currently scheduled for launch in 2015 [1]. The AFF technology validation plan is based on sophisticated ground testbed activities and does not foresee flight heritage prior to its launch with TPF. In parallel the NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)

CNES French National Space Agency is developing the Formation Flying Radio Frequency (FFRF) sensor, provided to PRISMA in partnership with the Spanish Centre for the Development of Industrial Technology (CDTI). This sensor will be first validated in space as part of the CNES’ participation (named the “FFIORD experiment” [2]) on the PRISMA technology demonstration mission, scheduled for launch in June 2009 [3]. In this context, the Swedish PRISMA mission acquires a unique role to validate sensor and actuator technologies related to formation flying and to demonstrate experiments for proximity operations and rendezvous. Key sensor and actuator components [4] comprise a GPS navigation system developed by the German Aerospace Center (DLR), two vision based sensors (VBS) provided by DTU, Denmark, two CNES FFRF sensors, and a hydrazine mono-propellant thruster system. These will support and enable the demonstration of autonomous spacecraft formation flying, homing, and rendezvous scenarios, as well as close-range proximity operations. The PRISMA spacecraft are named MAIN (or Mango) and TARGET (or Tango) and will be injected by a DNEPR-1 launcher into a sun-synchronous orbit at 700-km altitude and 98.2° inclination. A dusk-dawn orbit with a 18 h nominal local time at the ascending node (LTAN) is targeted. Following a separation from the launcher, the two spacecraft will stay in a clamped configuration for initial system checkout and preliminary verification. Once the spacecraft are separated from each other, various experiment sets for formation flying and in-orbit servicing will be conducted within a mission lifetime of ca. ten months. Spacecraft operations will be performed remotely from Solna, near Stockholm, making use of the European Space and Sounding Rocket Range (Esrange) ground station in Kiruna in northern Sweden. The S-band ground-space link to MAIN supports commanding with a bit rate of 4 kbps and telemetry with up to 1 Mbps. In contrast, communication with the TARGET spacecraft is only provided through MAIN acting as a relay and making use of a MAIN-TARGET intersatellite link (ISL) in the ultrahigh-frequency (UHF) band with a data rate of 19.2 kbps. The MAIN spacecraft has a wet mass of 150 kg and a size of 80×83×130 cm in launch configuration. In contrast to the highly maneuverable MAIN spacecraft, TARGET is a passive and much simpler spacecraft, with a mass of 40 kg at a size of 80×80×31 cm. Electrical power for the operation of the MAIN spacecraft bus and payload is provided by two deployable solar panels delivering a maximum of 300 W, whereas TARGET relies on one body-mounted solar panel providing a maximum of 90 W. The MAIN spacecraft implements a three-axis, reaction-wheel based attitude control and three-axis delta-v capability. The TARGET spacecraft applies a coarse three-axis attitude control based on magnetometers, sun sensors, and GPS receivers, with three magnetic torque rods as actuators. The DLR’s GPS navigation system will provide the primary reference for absolute and relative position measurements and thus serve the validation and calibration of other navigation sensors. In preparation of the PRISMA flight, the assessment of the achievable GPS and FFRF relative navigation accuracy is being performed in a joint effort by DLR and CNES. The ultimate goal is to evaluate and fully exploit the potential for in-flight validation of FFRF data using differential GPS. This paper provides an overview of the GPS and FFRF subsystems, and a description of simulations performed to assess their respective relative navigation accuracy in the context of the PRISMA mission. 1.1 GPS Navigation System Each of the PRISMA satellites is equipped with a cold-redundant set of GPS receivers. The receivers are each equipped with a low noise amplifier (LNA) and cross-connected via a relay to a pair of GPS antennas on opposite sides of the spacecraft (Fig. 1). In this way, GPS tracking can be ensured in all foreseen attitude modes of the PRISMA formation. x

FOV

S67-1575-20 GPS Antenna

Phoenix GPS Receiver

z y

LNA 5V DC

GPS antennas

R/F Switch

5V DC S67-1575-20 GPS Antenna

LNA Phoenix GPS Receiver

FOV

Fig. 1 Fault tolerant architecture of the PRISMA GPS system for the PRISMA mission (left). Identical systems are used on the MAIN and TARGET spacecraft. The antenna accommodation is illustrated in the right panel, which shows the PRISMA satellites in their stacked configuration shortly after launcher separation. The Phoenix-S receiver adopted for the PRISMA mission is a miniature GPS receivers for space and high-dynamics applications [5] that has been developed by DLR based on a commercial-off-the-shelf (COTS) hardware-platform (SigTec MG5001). It employs a Zarlink GP4020 baseband processor which combines a GP2021 12-channel L1 C/A code correlator an a ARM7TDMI 32-bit microprocessor kernel with auxiliary peripheral modules such as UARTs and a 32-kbit on-chip RAM memory. Dedicated thermal-vacuum and radiation tests have demonstrated that the receiver can NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)

cope with the space environment. In particular, it can tolerate a total ionization dose of up to 14 krad [6], which enables extended operation in low Earth orbit (LEO) up to 800 km altitude. The receiver offers a low power consumption (0.8 W begin-of-life) and form factor (check-card size), which makes it attractive for micro-satellite missions with restricted on-board resources. Aside from PRISMA, the receiver has been selected for ESA’s PROBA-2 mission as well as various national (TET-1, Flying Laptop) and international (XSat, RSSP) projects. The software of the Phoenix-S receiver is specifically designed for use on LEO satellites and offers acquisition aiding, precision timing and low noise measurements. Carrier tracking is controlled by an FLL assisted 3rd-order phase-locked loop while a low bandwidth Doppler aided delay-locked loop is employed for the C/A code tracking. At a representative carrier-to-noise (C/N0) level of 42 dB-Hz pseudorange and carrier phase measurements with a standard-deviation of 0.5 m and amount to 0.7 mm have been obtained in pre-flight qualification tests [7] conducted in a signal-simulator testbed. For use in carrier-phase differential GPS (CDGPS) applications the receiver design ensures integer doubledifference ambiguities by resolving the 180° phase ambiguity caused by the use of a Costas tracking loop. Aside from the kinematic navigation solution, the receiver outputs raw pseudo-range, carrier phase and Doppler measurements one every ten seconds to the onboard computer system. These data are used for real-time absolute and relative navigation of the PRISMA satellites within the MAIN GNC software [8] and also sent to ground for offline processing as part of the telemetry data stream. 1.2 FFRF Navigation System 1.2.1 FFRF Sensor Presentation The Formation Flying Radio Frequency (FFRF) subsystem developed by Thales Alenia Space is in charge of the relative positioning of 2 to 4 satellites on formation flying (FF) missions. It produces coarse measurements of relative position, velocity and line-of-sight (LOS). As the first element in the FF metrology system chain, the FFRF sensor ensures initial good relative navigation accuracy for the subsequent optical metrology subsystems (i.e., coarse optical lateral metrology, fine optical metrology, and fine longitudinal metrology). The subsystem comprises one transmitterreceiver RF terminal and up to 4 sets of antennas on each satellite of the constellation. Destined specifically for future non-LEO formation flying missions, the FFRF terminals are manufactured using only space qualified components. It also undergoes severe environmental acceptance testing in order to qualify for long duration missions in high elliptic orbits (HEO) or at the Lagrangian points (L1 or L2). The FFRF subsystem relies on an architecture inherited from GPS receiver technology. Using multi-antenna bases (triplets) and TDMA sequencing, each terminal transmits and receives a GPS like navigation signal modulated on two S-band carrier frequencies (S1 and S2). Since every terminal is equipped with both transmitter and receiver, each satellite is able to make ranging and LOS measurements with every other satellite. First, coarse measurements are produced using ranging obtained from the C/A code, and then fine measurements with centimetre accuracy are performed using carrier phase measurements. Three types of raw measurements come from the Rx/Tx antennas: pseudo code, phase on S1, and phase on “wide-lane” obtained by combination of S1 and S2 carriers. Raw data coming from Rx antennas are twofold: delta phase measurement on S1 carrier, delta phase measurement on wide-lane. The dual frequency allows the system to perform carrier ambiguity resolution using a wide lane, while 2-way measurements are used to account for the relative clock drift of the platforms. LOS measurements are made by measuring the carrier phase difference between the master and slave antenna on the triplet antenna base. Relative attitude, though, is not measurable in a 2 satellite configuration and it has to come from an external attitude sensor such as a star tracker.

FFRF antennas

Fig. 2 Accommodation of FFRF antennas on the PRISMA mission (left). Graphical representation of the Rx/Tx antenna triplets available on the MAIN and TARGET spacecraft (right). On PRISMA, MAIN is the only satellite equipped with a full antenna triplet enabling LOS measurement and PositionVelocity-Time (PVT) computation. TARGET S/C, on the other hand, carries three single Rx/Tx antennas mounted with 120° pointing difference to ensure full space coverage (cf. fig. 2). The FFRF subsystem is specified to provide the following information every second: range (expected accuracy = 1 cm), azimuth and elevation of line-of-sight between NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)

two satellites (expected accuracy < 1°), time bias between the two satellite clocks. This accuracy assumes a successful sensor initialization that includes some Integer Ambiguity Removal (IAR) operation. This process is to be performed first on LOS then on range and requires a rotation of the MAIN S/C. 1.2.2. FFRF-based Relative Navigation FFRF sensor provides only a relative position snapshot that constitutes the main input of a Relative Navigation function implemented in the MAIN S/C on-board computer. This function is executed at 1 Hz and provides the MAIN S/C relative state (position and velocity) in the local orbital frame attached to TARGET and is always active whenever FFRF sensor is powered on. The navigation algorithm is based on an Extended Kalman Filter (EKF) that includes a model of each satellite absolute dynamics. The EKF state vector comprises MAIN S/C position and velocity coordinates in the Spacecraft Local Orbital (SLO) frame as well as two bias values associated to the LOS measurements. FFRF sensor performance is affected by some electrical and multi-path biases that can be reduced by ground calibration (multi-path cartography) and in-flight characterization. Some electrical bias residuals are expected to remain on-board and LOS bias estimation has been therefore implemented to improve the overall performance. The estimation of these exogenous inputs is feasible since relative orbital dynamics is taken into account inside the filter. The computation of the predicted measurements is based on the filter state vector, the MAIN and TARGET attitude estimates and the attitude of the TARGET Local Orbital Frame computed by the RF Navigation Function. State propagation relies on the dynamic model of MAIN and TARGET satellites and the knowledge of MAIN accelerations during thrust (provided by dedicated accelerometers). All these data are provided with their time-tag expressed in GPS time in order to perform their synchronization. This synchronization is made possible by the measurement of the time difference between on-board GPS time and local FFRF time. The Relative Navigation includes also the FFRF sensor management that involves (1) the computation of aiding data to be transmitted to both satellite terminals, (2) the monitoring of its functioning, (3) a reset capability in case of specific anomalies. 1.3 Cross-Validation Concept The PRISMA mission offers an ideal testbed to compare and cross-validate GPS- and FFRF-based relative navigation products. As depicted in Figure 3 various products will be generated on a routine basis during the mission lifetime. GPS measurements generated by the Phoenix-S receivers will be used on-board to perform real-time (R/T) absolute and relative orbit determination [8]. The GPS-based real-time navigation software contributed by DLR represents an integral part of the GNC system and supports most of the PRISMA experiment activities providing continuous position and velocity of the formation flying satellites. The GPS receiver data are sent to the ground as part of the telemetry data stream and will be used offline for routine post-facto Precise Orbit Determination (POD) at DLR. The POD function will be executed daily in a fully automated manner. As a baseline all necessary spacecraft input data for POD (e.g., GPS data, attitude and orbit maneuver info) will be available within three hours after they have been generated on-board, so to allow a rapid assessment of the function of onboard sensors and experiments. Due to the typical latency of the required precise GPS orbit and clock solutions (i.e., 0.5-2 days), the POD process will provide trajectory files within one day after availability of all input data. The precise orbit solutions delivered by DLR will represent the primary reference for absolute and relative position measurements and thus serve the characterization of the FFRF sensor. Precise GPS-based orbits will also be generated by CNES and will contribute to the overall quality assessment of the DLR real-time and offline products. POD POD (DLR) (CNES)

R/T GPS (Onboard)

Truth (Simulated)

R/T FFRF (Onboard)

Fig. 3 The cross-validation of the GPS- and FFRF-data is based on the comparison of various products generated in real-time on-board (GPS and FFRF R/T) and post-facto on-ground (DLR and CNES POD). During the testing and validation phase the simulated truth is used as reference to assess the accuracy of the different navigation results. In contrast to the real mission, where no true spacecraft motion is available and POD results have to be used as reference, the current test and validation phase offers the possibility to simulate the reality applying orbit and attitude NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)

model of arbitrary accuracy. The cross-validation concept is based on the definition of scenarios as representative as possible of the joint GPS-FFRF measurements campaigns. As shown in the sequel the simulated truth is used as reference to assess the accuracy of the difference navigation results and evaluate the potential for in-flight validation of FFRF data using differential GPS. For the GPS subsystem detailed hardware-in-the-loop (HWIL) simulations are set up, which employ a Spirent dual R/F output signal simulator as well as two engineering models of the Phoenix-S GPS receiver selected for PRISMA. The relative motion of the two simulated spacecraft is recovered using the same precise relative navigation software (FRNS) that will be employed in the PRISMA offline navigations support facility at DLR. The simulation and data analysis include representative models for GPS broadcast ephemeris errors, ionospheric path delays, antenna offsets and phase patterns as well as the orbit and attitude of the MAIN and TARGET spacecraft. In parallel to the GPS HWIL simulation run by DLR, consistent software simulations are conducted by CNES to generate FFRF sensor data (range and Line of Sight measurements). The simulation includes also the R/T navigation algorithm implemented in the MAIN on-board computer that uses FFRF sensor to compute an estimation of MAIN S/C relative state. Error models used in the FFRF simulation are based on sensor characteristics established with engineering models in laboratory tests and a multipath calibration campaign conducted in an anechoic chamber. 2. GPS-BASED PRECISE RELATIVE ORBIT DETERMINATION The Phoenix GPS receivers onboard the PRISMA satellites provide raw pseudorange and carrier phase measurements that are used on ground to reconstruct both the absolute and relative motion of the two spacecraft (Fig. 4). Other than in the PRISMA real-time navigation system the MAIN and TARGET orbits are not estimated concurrently but refined in a two stage process. In a first step the absolute orbit of each individual spacecraft is estimated using only measurements from the respective satellite. The precise orbit determination process employed for this purpose is inherited from geodetic space missions but adapted to the availability of single-frequency measurements. Signal simulator tests conducted with the Phoenix receivers indicate that a precision of about 0.5 m can be achieved in this way for the individual, single-satellite orbits.

Fig. 4 GPS based relative navigation of the PRISMA satellites For the relative navigation differential pseudorange and carrier phase measurements are formed for those GPS satellites that are commonly observed by the receivers onboard MAIN and TARGET. The differencing immediately eliminates the uncertainty of the GPS clock offset as an error source and greatly attenuates the impact of GPS orbit errors and atmospheric path delays. The differential measurements are then used to estimate the motion of the TARGET spacecraft relative to MAIN while fixing the motion of MAIN to the previously computed precise orbit determination result. Compared to the real-time navigation performed onboard the MAIN spacecraft, the ground processing benefits from the availability of accurate GPS orbit and clock products, Earth orientation parameters and atmospheric density information. A slight performance improvement is furthermore expected from refined attitude information that is required for the modelling of the GPS antenna location relative to the respective center-of-mass. Most notably, however, an integer ambiguity resolution is performed in the ground-based relative navigation filter which effectively converts the single-difference carrier phase measurements into high-precision relative range measurements. The onboard processing, in contrast, has intentionally been restricted to a float ambiguity estimation in a trade-off between computational load, robustness and accuracy.

NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)

2.1 GRAPHIC Based Single Satellite Orbit Determination The individual orbits of the PRISMA satellites are obtained in a least-squares batch orbit determination process that employs a ionosphere-free combination of single-frequency pseudorange and carrier phase measurements. Denoting the range between the GPS satellite and the receiver by ρ, the GPS and receiver clock offsets by cdtGPS and cdt, respectively, and the carrier phase bias by B, the basic Phoenix GPS measurements can be modelled as

ρ C/A ρ

L1

= ρ + c(δt − δt GPS ) + I

= λϕ = ρ + c(δt − δt GPS ) − I − B .

(1)

The ionospheric path delay I affects the pseudorange and carrier phase measurements in a similar manner but with opposite sign [9]. As noted by Yunck [10], this fact can be exploited to form a ionosphere-free “GRAPHIC” (Group and Phase Ionospheric Correction) measurement from a simple arithmetic mean

ρ * = ( ρ C/A + ρ L1 ) / 2 = ρ + c (δt − δt GPS ) − B / 2 ,

(2)

of the C/A code and L1 carrier phase. The combination even exhibits a 50% lower noise level than the pseudorange itself (i.e., about 0.25 m for the Phoenix receiver), but is affected by an unknown bias that is different for each channel and inhibits a direct use of GRAPHIC measurements for single point positioning. The GRAPHIC bias originates from the carrier phase bias and is generally constant during arcs of continuous carrier phase tracking. This enables an estimation of arc-wise bias parameters within a global adjustment process. Within the Reduced Dynamic Orbit Determination module (RDOD) of DLR’S GPS High Precision Orbit Determination Software Tools suite (GHOST) [11], a high-fidelity dynamical model is used to describe the motion of the LEO satellite. Aside from the aspherical gravitational potential of the Earth, which is described through a GGM01 gravity model with representative degree and order of 70x70, the RDOD models account for solid Earth, pole and ocean tides, relativistic effects, luni-solar third body perturbations, atmospheric drag and solar radiation pressure. Maneuvers are, furthermore, taken into account assuming a constant acceleration in an orbital reference frame over the predefined burn-duration. Remaining deficiencies of the deterministic trajectory model are taken into by supplementary empirical accelerations in radial, tangential and normal direction. The equation of motion and the (simplified) variational equations are numerically integrated using a variable-order variable stepsize multistep method, which ensures both computational efficiency and accurate results. As part of a least-squares estimation, RDOD adjusts the initial state vector, a drag and radiation pressure coefficient, maneuver velocity increments, piece-wise constant empirical accelerations at predefined time intervals, epoch wise clock errors and, finally, the GRAPHIC (or carrier phase) biases. For a 24 h arc and a 30 s measurement interval, a total of 4000 parameters (comprising some 3000 clock offsets, 500 dynamical parameters and 500 bias parameters) have to be determined in a single adjustment process. This is efficiently accomplished through a pre-elimination and back-substitution of clock-offset parameters, which notably reduces the size of the remaining normal equations [11]. In view of inevitable linearization errors, the least-squares estimation is iterated two to three times which ensures proper convergence within the limits implied by the measurement accuracy. In the absence of other errors, typical accuracies of 0.2-0.5 m have been demonstrated with the Phoenix-S GPS receiver in a signal simulator environment. For comparison, a 0.6-1.0 m orbit determination accuracy has been demonstrated for the TerraSAR-X satellite [12] using GRAPHIC measurements from the MosaicGNSS GPS receiver that exhibit an almost ten times higher noise level than the Phoenix-S receiver. 2.2 Carrier Phase Differential GPS Navigation For utmost accuracy in the reconstruction of the relative position of MAIN and TARGET, differential carrier phase measurements are processed in the Filter for Relative Navigation of Satellites (FRNS) of the GHOST tools suite ([13], [14]). Since the Phoenix-S receiver clock is always aligned to GPS time with an accuracy of better than a few hundred nanoseconds, the measurements of the MAIN and TARGET receivers can be differenced without a need for timetag alignment and extrapolation. Assuming a maximum difference of 0.3 μs between the true measurements epochs, peak along-track navigation errors of less than 2 mm are expected from this simplification at the orbital velocity of 7.5 km km/s. Other than in the single satellite orbit determination, a Kalman filter/smoother approach has been adopted for the PRISMA relative navigation. Due to the frequent measurement updates that are typically performed once every 10-30 s, the (relative) motion of both spacecraft has to be propagated only over very short time intervals, which reduces the impact of numerical or modeling errors. In addition, the sequential processing facilitates the handling of carrier phase ambiguities, since only a small number of ambiguities for the currently tracked satellites need to be treated at a time. The FRNS filter processes the measurements both in forward and backward direction and averages the results to obtain a smoothed solution which balances the impact of measurements before and after a given solution epoch. For PRISMA, a single-frequency version of FRNS is employed, which adjusts the relative state vector (position Δr and velocity Δv), the TARGET drag and radiation pressure coefficient (CD,2, CR,2), differential empirical accelerations (Δaemp), the differential clock offset (Δcδt) and float values of the single-difference carrier phase ambiguities (ΔΝ1,2). In NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)

addition a zenith ionosphere delay (ΔΙ0) is estimated which is used to account for differential ionospheric path delays. If unaccounted, these might introduce baseline errors of up to relative navigation errors of several centimeters when considering baselines of several kilometers and/or high ionospheric activity. In the absence of a fully realistic model for the ionospheric path delays at the spacecraft altitude, a simple mapping function m( E ) =

2.037

(3)

sin 2 E + 0.076 + sin E

proposed by Lear [15] is employed to describe the dependence of the ionospheric path delays on elevation E. Modelled differential path delays can then be obtained by multiplication of the zenith ionosphere delay with the difference of the mapping functions for the MAIN and TARGET spacecraft. The zenith delay itself is treated as an exponentially correlated random variable. Its estimation can thus constrained by assigning an appropriate steady state covariance in accord with the expected differential delays for a given spacecraft separation. To fully exploit the benefits of carrier phase differential GPS, use has to be made of the fact that double-difference carrier phase measurements exhibit an ambiguity that is an integer multiple of the carrier phase wavelength. To this end, an ambiguity resolution process is performed after each measurement update. Here double difference ambiguities and their associated covariance are first formed from the single difference values estimated in the filter. The Least Squares Ambiguity Decorrelation method (LAMBDA) is then used to find the best matching set of integer ambiguities along with suitable confidence parameters. If a reliable determination of integer ambiguities is indicated by the LAMBDA method, the resulting values are fed back into the filter as supplementary constraints using a pseudo measurement update. Following a successful ambiguity resolution, the associated carrier phases can effectively be processed as extremely low noise pseudorange. Ultimately this enables mm-level navigation accuracies in the absence of other errors. 2.3 Precise Orbit Determination at CNES As for DLR, CNES precise orbit determination consists of a two step process, each one using the Least Square Method. The absolute orbit determination of both satellites considered independently is first performed using pseudo range and carrier phase measurements. The drag and solar radiation pressure coefficients are estimated at the same time, as well as the receivers clock biases. The second step is the relative TARGET/MAIN orbit estimation. In this step, the MAIN orbit and estimated coefficients are fixed to the absolute solution. For this relative estimation, the carrier phase single difference is used first to obtain a floating relative orbit where the carrier phase ambiguities are estimated as floats. The state vector also consists in position and velocity of TARGET, clock biases, drag and radiation pressure coefficients, and empirical acceleration, constant in the local orbital frame on predefined time intervals. This floating relative orbit is accurate enough for the integer ambiguities to appear, and for fixing their values. It also allows the detection and compensation of the carrier phase jump and the reconstitution of the GPS pass (also useful in case of TM gap), to detect and remove absurd measurements. After this floating estimation, the fixing of the ambiguities allows a very accurate relative estimation, using the full accuracy of the carrier phase measurements. It is also possible to do a stochastic estimation of the empirical accelerations, where the accelerations are modeled as a first order Markov process. The advantage is to avoid compensation of measurement errors and to be sure that estimated accelerations have more physical interpretation. 3. FFRF DATA ANALYSIS FFRF data analysis will be performed on the ground by comparison with the GPS POD product regarded as reference This analysis will focus on the main following operations: 1. Flight calibration (LOS and distance) 2. Ambiguity resolution phase 3. Data collection over a wide dynamic/geometric range combined with R/T relative navigation FFRF sensor performance is very sensitive to residual biases essentially due to propagation delays in the RF components and multi-path effects. In a large part, these biases can be assessed through specific calibrations on the ground (cables, antennas). A significant effort has been also invested to assess multi-path using PRISMA satellite mockups in an anechoic chamber (Figure 5). On top of this, an additional calibration will be performed during flight to determine the LOS and distance biases dependency with relative attitude and these results will be compared to the ones collected on the ground. This data is to be then synthesized in calibration tables that are uploaded in the FFRF sensor to improve performance. Requirements on GPS POD accuracy for this operation are the most challenging since a 2-3 mm level is to be achieved while the GPS antennas will be pointed away from Zenith by a few tens of degrees. Integer ambiguity resolution will be the major contributor to performance and the ability to perform it successfully will greatly depend on the accuracy of the calibration tables (some auto-calibration process is also run continuously but it concerns only the propagation delays inside the sensor RF stages). IAR on LOS should be an easy task even though it requires an attitude slew of the MAIN satellite (ambiguity is roughly 15°). On the other hand, IAR will be particularly critical on distance since success imposes to reduce all biases to less than 1 cm on the wide-lane. In this phase, NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)

requirements on GPS POD accuracy is much less stringent since the potential errors will be multiple of the carrier wavelength (λ =65 cm). Next, FFRF measurements will be collected over distances from 10 km down to 10-15 meters and with a few m/s relative rates. The objective is to cover a domain representative of rendezvous scenarii of future missions such as SIMBOL-X and determine what is the achievable accuracy of the FFRF sensor alone and in combination with the R/T relative navigation system. Here, the GPS POD accuracy must be one order of magnitude better than FFRF system over the whole domain of operation to enable its performance characterization.

Fig. 5 Multi-path calibration experiments with PRISMA mockups at CNES At first, analysis on the ground will involve the processing of FFRF raw data to make sure the sensor internal navigation unit is working properly. Raw data will be fed to a copy of the FFRF on-board software and its output will be compared to the measured PVT. Later, as long as there is no anomaly, data analysis will involve only PVT measurements and R/T FFRF navigation solution. 4. HARDWARE IN THE LOOP SIMULATION 4.1 GPS Signal Simulator Test Scenario The hardware-in-the-loop test presented in this paper makes use of a Spirent signal simulator STR7700 to generate artificial L1 GPS signals representative of those received by two co-orbiting spacecraft. The modeled PRISMA spacecraft are assumed to fly in a near circular orbit at 700-km altitude and 98.2° inclination. In accord with the envisaged “dusk-dawn” configuration, the ascending node is located at 18h local time. The epoch is (fictitiously) chosen as 2nd July 2006, 00:00:00 GPS Time, and coincides with the ascending node crossing of the MAIN orbit. Adopted orbital elements in the inertial J2000 reference system are given in Table 1 and the resulting spacecraft relative motion during the simulation is plotted in Fig. 6. Within the transformation from Earth-Centered-Inertial (ECI) to EarthCentered-Earth-Fixed (ECEF) a fictitious UT1-TAI difference of –35.0 s and pole coordinates of (x,y) = (0.0705",0.4077") are applied by the simulator. The orbit is propagated over the 48 h simulation period using a JGM-3 70x70 Earth gravity model as well as drag perturbations. Ballistic properties of the satellites were modeled with assumed values of the cross-section A=1.3 m2, mass m=154.4 kg, and drag coefficient CD=2.5 for MAIN and A=0.38 m2, m=42.5 kg, CD=2.25 for TARGET. Table 1 Simulated MAIN and TARGET spacecraft orbits Osculating Elements (EME2000) 2nd July 2006, 00:00:00 GPS Time

Semi-major axis (a)

Value [m, deg] MAIN

TARGET

7087297.67733179

7087297.55686634

0.00145908

0.00145443

Inclination (i)

98.18466676

98.18528613

Long. of ascend. node (Ω)

189.8908602

189.8913845

Arg. of perigee (ω)

0.0

1.097451382

Mean anomaly (M)

0.0

-1.093323794

Eccentricity (e)

The GPS constellation is modeled based on the actual GPS almanac for week 1381, which is propagated to the scenario time within the signal simulator. The antenna diagram corresponds to a Sensor Systems S67-1575-141 antenna without ground plane as used on PRISMA, which has earlier been calibrated in outdoor tests by DLR. To study the influence of key error sources, ionospheric path delays and broadcast ephemeris errors have been considered in the test. The “spacecraft ionosphere model” (which implements the Lear mapping function [15]) and a constant total electron content (TEC) of 10·1016 electrons/m2 (=10 TECU) have been selected for the simulation of ionospheric effects. The impact of broadcast ephemeris and clock errors on the navigation solution has been modeled by considering constant offsets between the modeled GPS spacecraft position and the one described by the GPS navigation message. These offsets affect the simulated trajectory but are not included in the broadcast ephemeris message issued by the simulator. The offsets are constant in time and applied only to the radial satellite position. No tangential and normal offsets have been configured since this would not provide added realism to the simulation. In an effort to mimic a realistic Signal in Space Range Error (SISRE), the applied offsets are based on uniformly distributed random numbers with zero mean and a

NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)

standard deviation of 1.5 m. For comparison, the performance of the current GPS constellation and ground segment achieves a representative SISRE of 1.0 to 1.5 m including both ephemeris and clock errors [16]. The orientation of the MAIN and TARGET spacecraft is such that the spacecraft body-fixed axes (x, y, z) are aligned with the co-moving orbital frame defined by the radial, along-track and cross-track directions (R, T, N). This attitude configuration ensures a zenith pointing of the GPS antennas in use on the formation flying spacecraft and guarantees that the FFRF antennas on MAIN and TARGET are pointing to one another during the simulation. In an attempt to increase the realism of the overall test scenario, attitude determination errors are added to the MAIN and TARGET true attitude profile. Representative attitude errors are extracted from previous simulation runs performed on a dedicated test-bench at the Swedish Space Corporation. Typically the error distribution is characterized by ca. 0.1° mean and 0.3° standard deviation on TARGET and ca. 0.0° mean and 0.005° standard deviation on MAIN. The actually estimated attitude is then fed to the GPS- and FFRF-based relative navigation processes in order to reproduce as close as possible the conditions met during flight.

Fig. 6 Relative orbital motion of MAIN with respect to TARGET mapped in the radial (top), along-track (middle) and cross-track (bottom) directions. 5. Test Results and Discussion This section summarizes the GPS- and FFRF-based relative navigation performance obtained during the aforementioned test campaign. The MAIN and TARGET Phoenix-S GPS receivers were directly connected to the signal simulator via a low noise amplifier (LNA). The native messages generated by the receivers have been logged and used post-facto as input to the POD process and to the prototype R/T PRISMA onboard software. Table 2 PRISMA GPS- and FFRF-based relative navigation accuracy. Real-time and post-facto relative navigation positions are compared against each other and against the true trajectory. The upper-right part shows component-wise mean and standard deviations, the lower-left portion of the table shows 3D r.m.s. figures. True Trajectory

GPS POD

-

R [mm] 0.17 ± 0.71 T [mm] -1.34 ± 1.85 N [mm] 0.52 ± 1.77

True Trajectory

R/T GPS

-

R [mm] T [mm] N [mm] R [mm] T [mm] N [mm]

-1.36 ± 4.41 0.00 ± 4.47 2.65 ± 2.96 -1.21 ± 4.54 -1.34 ± 3.98 3.18 ± 2.04

GPS POD

3D [mm]

3.03

R/T GPS

3D [mm]

7.60

3D [mm]

7.30

-

R/T FFRF

3D [cm]

5.10

3D [cm]

5.06

3D [cm] 5.30

R/T FFRF R [cm] 0.15 ± 2.01 T [cm] 3.39 ± 2.59 N [cm] -0.22 ± 1.93 R [cm] 0.17 ± 2.00 T [cm] 3.26 ± 2.64 N [cm] -0.17 ± 1.99 R [cm] 0.29 ± 2.14 T [cm] 3.39 ± 2.76 N [cm] -0.49 ± 2.04 -

As shown in Table 2, the POD relative navigation accuracy observed during the complete data-arc amounts to 3.03 mm (3D, r.m.s.), POD results obtained at CNES provides similar accuracy. The R/T GPS onboard software is accurate to 7.6 mm (3D, r.m.s.), while the R/T FFRF onboard processing gives 5.10 cm (3D, r.m.s.) accuracy. The R/T navigation accuracy has been computed using data from the steady state phase of the filter, excluding the initial convergence phase of ca. 30 min. Cross-comparison figures are also listed in table 2, where all navigation products are compared to one another for completeness. GPS-based POD and R/T GPS relative navigation results differ statistically by 7.30 mm (3D, r.m.s.), mainly because of the integer ambiguity fixing feature which is only implemented in the POD FRNS software. On the other end the R/T FFRF relative navigation errors are shown to be one order of magnitude larger than in the NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)

GPS-based relative orbit determination (both POD and R/T). Evidently these results indicate that the GPS-based POD can be used to characterize the behavior of the FFRF sensor which will be flown for the first time on the PRISMA mission. Despite the promising results, the achievable GPS-based navigation accuracy in the real mission will be constrained by the limited knowledge of the MAIN and TARGET antenna offset vectors, of the phase center location as well as possible multipath effects from the spacecraft structure. Furthermore the FFRF instrument calibration campaigns will be characterized by pronounced attitude maneuvers where the GPS antennas will not be zenith-pointing. Such conditions will necessarily cause a degradation of the relative navigation accuracy due to the poor GPS constellation visibility and to the reduction of common visible GPS satellites from MAIN and TARGET. CONCLUSION AND WAY FORWARD The PRISMA FFRF sensor performance will be characterized using GPS POD solutions that will be regarded as true reference data. Since the FFRF sensor expected accuracy is down to the 1 cm range, the challenge is to obtain reference measurements reaching about one millimeter accuracy. According to the preliminary reference scenario presented in this paper the achievement of such an accurate relative orbit reconstruction using GPS is possible. Despite the very encouraging results, it is important to evaluate whether GPS POD is able to meet these requirements in various formation flying/proximity operations configurations. In fact FFRF data will be specifically collected for performance analysis and calibration purposes during dedicated campaigns where the GPS operations are more challenging. Tests will have to be performed in a more representative environment at the Swedish Space Corporation premises and the possibility to take into account multi-path effects will be considered. This joint effort may lead to some new flight scenario definition in order to optimize the characterization of the achievable GPS POD accuracy. ACKNOWLEDGEMENT PRISMA is a Swedish space mission realized under the lead of Swedish Space Corporation (SSC). International contributions to the PRISMA mission and avionics include the FFRF sensor provided by CNES, France and CDTI, Spain, the GPS navigation system provided by DLR, Germany, and the Vision Based Sensor by DTU, Denmark. REFERENCES [1] Tien, J.Y.; Purcell, G.H.; Amaro, L.R.; Young, L.E.; Mimi Aung; Srinivasan, J.M.; Archer, E.D.; Vozoff, A.M.; Yong Chong; “Technology validation of the autonomous formation flying sensor for precision formation flying”; Aerospace Conference, 2003. Proceedings. 2003 IEEE Volume 1, Issue , March 8-15, 2003 Page(s): 1 - 140 vol.1. Digital Object Identifier 10.1109/AERO.2003.1235048 [2] J. Harr, M. Delpech, T. Grelier, D. Seguela, S. Persson, "The FFIORD Experiment - CNES' RF Metrology Validation and Formation Flying Demonstration on PRISMA," Proceedings of the 3rd International Symposium on Formation Flying, Missions and Technology, ESA/ESTEC, April 23-25, 2008, ESA SP-654, Noordwijk, The Netherlands. [3] Persson S., Jakobsson B., Gill E.; “PRISMA – Demonstration Mission for Advanced Rendezvous and Formation Flying Technologies and Sensors”; IAC-05-B56B07; 56th IAC, Fukuoka, Japan, 2005. [4] Persson S., Bodin P., Gill E., Harr J., and Jorgensen J.; “PRISMA–an autonomous formation flying mission”; ESA Small Satellite Systems and Services Symposium (4S), Sardinia, Italy, September 2006. [5] Montenbruck, O., Nortier, B., Mostert, S., “A Miniature GPS Receiver for Precise Orbit Determination of the SUNSAT2004 Micro-Satellite”; ION National Technical Meeting, 26-28 Jan. 2004, San Diego, California, 2004 [6] Markgraf M., Montenbruck O., Metzger S.; “Radiation Testing of Commercial-off-the-Shelf GPS Technology for use on LEO Satellites”; 2nd ESA Workshop on Satellite Navigation User Equipment Technologies, NAVITEC'2004, 8-10 Dec. 2004, Noordwijk, The Netherlands (2004). [7] Montenbruck O.; Phoenix-S/-XNS Performance Validation; DLR/GSOC GTN-TST-0120; Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen (2007). [8] D’Amico S., Gill E., Garcia M., Montenbruck O.; “GPS-Based Real-Time Navigation for the PRISMA Formation Flying Mission“; NAVITEC’2006, Noordwijk, 11-13 December 2006. [9] Misra, P., Enge, P.; Global Positioning System (GPS): Signals, Measurements & Performance; Ganga-Jamuna Press, 2nd ed. 2006 [10] Yunck T.P.; “Orbit Determination”; in: Parkinson B.W., Spilker J.J. (eds.); Global Positioning System: Theory and Applications. AIAA Publications, Washington DC, 1996 [11] Montenbruck, O., van Helleputte, T., Kroes, R., Gill, E.; “Reduced Dynamic Orbit Determination using GPS Code and Phase Measurements”; Aerospace Science and Technology 9/3; 261-271, 2005 [12] Montenbruck O., Yoon Y., Ardaens J.-S., Ulrich D.; “In-Flight Performance Assessment of the Single Frequency MosaicGNSS Receiver for Satellite Navigation”; 7th International ESA Conference on Guidance, Navigation and Control Systems; 2-5 June 2008, Tralee, Ireland (2008). [13] Kroes R., Montenbruck O., Bertiger W., Visser P.; “Precise GRACE baseline determination using GPS”; GPS Solutions 9:21-31 (2005). DOI 10.1007/s10291-004-0123-5 [14] Montenbruck O., Kahle R., D'Amico S., Ardaens J.-S.; “Navigation and Control of the TanDEM-X Formation”; Journal of the Astronautical Sciences; in press. [15] Lear, W. M., “GPS Navigation for Low-Earth Orbiting Vehicle”s, NASA 87-FM-2, JSC-32031, rev. 1, Lyndon B. Johnson Space Center, Houston, Texas (1987). [16] Warren, D.L.M., Raquet, J.F., “Broadcast vs precise GPS ephemerides: a historical perspective”, GPS Solutions 7, 151–156, 2003 NAVITEC’2008, 10-12 December 2008, Noordwijk (2008)