GPS-Based Relative Navigation during the Separation Sequence of the PRISMA Formation

S. D’Amico1 and O. Montenbruck.2

German Aerospace Center (DLR), Münchner Str. 20, 82234 Wessling, Germany

R. Larsson3 and C. Chasset4

Swedish Space Corporation (SSC), Strandväg 86, P.O. Box 4207, Solna, Stockholm, Sweden

PRISMA is a Swedish-led micro-satellite mission that serves as a test platform for autonomous formation flying and rendezvous of spacecraft. It comprises two satellites which are launched together in a clamped configuration and separated in orbit after completion of all checkout operations. The challenge of the subsequent early operations phase is to maintain the formation safety and in particular to minimize the risk of collision using only a reduced subset of the overall guidance, navigation and control functionalities. While not specifically designed for safe mode operations, the PRISMA GPS-based relative navigation system is still considered the best source of relative orbit information during this mission phase. A comprehensive simulation of the separation sequence has been therefore conducted that demonstrates the robust operation of the GPS navigation system under the adverse conditions of the separation event and the subsequent non-nominal spacecraft attitude. While initially based on offline Simulink/C++ software simulations, the employed test approach makes use of the prototype flight software for the GPS navigation system and enables a seamless transition to real-time software simulations as well as hardware-in-the-loop simulations.

I. Introduction he PRISMA technology demonstration mission originates from an initiative of the Swedish National Space Board and the Swedish Space Corporation1. PRISMA comprises a fully maneuverable micro-satellite (MAIN)

as well as a smaller sub-satellite (TARGET) that will be released from MAIN after initial commissioning. The MAIN satellite is 3-axis stabilized and has full 3D delta-V maneuverability that is independent of the spacecraft’s attitude. The TARGET satellite has a simplified, yet 3-axis stabilizing, magnetic attitude control system and no orbit maneuver capability. The mission schedule foresees a launch in 2009 of the two spacecraft into a Low Earth Orbit (LEO) with a targeted lifetime of at least eight months. The PRISMA mission objective is to demonstrate in-flight technology experiments related to autonomous formation flying, homing and rendezvous scenarios, precision close range 3D proximity operations, soft and smooth final approach and recede maneuvers, as well as to test instruments and unit developments related to formation flying2,3. DLR’s German Space Operations Center (GSOC) provides various key contributions to the PRISMA mission in the area of GPS based navigation and autonomous formation flying (Fig. 1). These comprise a redundant set of Phoenix GPS receiver and antenna systems for both spacecraft, a GPS based navigation system software to support formation flying during all phases, dedicated experiments for relative and absolute orbit control as well as an on-ground automated Precise Orbit Determination (POD) for off-line verification purposes4-6.

T

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This paper analyses the behavior of the GPS-based navigation system during one of the most critical phases of the PRISMA technology demonstration mission, namely the separation of the two participating spacecraft and the acquisition of the first collision-free formation geometry. After the separation from the launcher the MAIN and TARGET spacecraft are clamped in a single combined unit. This configuration is held for a time frame of approximately 25 days during which early operations are performed aiming at the activation and health check of the

1 Scientist, Space Flight Technology Dept., simone.damico@dlr.de. 2 Scientist, Space Flight Technology Dept., oliver.montenbruck@dlr.de. 3 GNC Engineer, Space Vehicle Design Dept., robin.larsson@ssc.se. 4 GNC Engineer, Space Vehicle Design Dept., camille.chasset@ssc.se.

AIAA Guidance, Navigation and Control Conference and Exhibit18 - 21 August 2008, Honolulu, Hawaii

AIAA 2008-6661

Copyright © 2008 by German Aerospace Center (DLR). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

various spacecraft units. The GPS hardware on both spacecraft will be switched on and verified during this phase. Furthermore the Inter-Satellite-Link will be activated and will allow the transmission of GPS measurements from TARGET to MAIN for a zero-baseline verification of the GPS-based navigation system. Only afterwards TARGET will be released from MAIN on ground command by firing one of the two redundant wire cutters of the separation mechanism. The challenge of the subsequent early proximity operations phase is to maintain the formation safety and in particular minimize the risk of collision by making use of a reduced subset of the overall guidance, navigation and control functionalities available on the two spacecraft. Although the GPS system has not been designed specifically to support safe mode activities, it is currently considered the best candidate to support fault detection, isolation and recovery tasks during this formation flying configuration due to its inherent versatility and robustness.

After a description of the GPS-based relative navigation system, the paper provides an overview of the simulation scenario and addresses the verification of the on-board navigation software during the separation sequence of the PRISMA formation

Figure 1. GPS-based relative navigation of the PRISMA satellites.

II. The PRISMA Navigation System

A. GPS Hardware Architecture The GPS receivers to be flown on PRISMA are 12 channel single-frequency Phoenix receivers based on a

commercial-off-the-shelf hardware platform7. The receivers have been qualified for use in LEO by a series of thermal-vacuum, vibration, and total ionization dose tests. Phoenix offers Coarse/Acquisition (C/A) code and carrier tracking with a noise level of 0.4 m and 0.5 mm, respectively at a representative carrier-to-noise ratio of 45 dBHz. The receivers support aiding with a priori trajectory information to allow a rapid acquisition of GPS signals under highly dynamic conditions. Upon tracking, Phoenix outputs a One-Pulse-per-Second (1PPS) signal and aligns the message time tags to integer GPS seconds which supports onboard clock synchronization and facilitates differential measurement processing, respectively.

The physical architecture of the Phoenix GPS system is identical on MAIN and TARGET. For redundancy, two Phoenix GPS receivers are available, which are connected to two GPS antennas with opposite field of view via a coaxial switch. The dual antenna system provides increased flexibility for handling non-zenith pointing attitudes and antennas may be selected by ground command. Only one receiver will be active at any time (Fig. 2).

Each GPS receiver is connected to its own low-noise amplifier (LNA) and provides 5 V DC for its operation via the R/F input. Compared to a single LNA placed between the antenna and the coaxial switch, this configuration avoids the need for an external LNA power supply and DC blocks. Furthermore, the adopted design reduces the risk of single-point failures. The use of a passive antenna, finally, allows the insertion of a band-pass or notch-filter prior to the coaxial switch and LNAs, if adverse out-of-band R/F signals should be encountered during interference tests.

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Figure 2. Redundant Phoenix GPS receiver system of MAIN and TARGET spacecraft.

B. Navigation Filter Design One of the main challenges of the PRISMA formation flying is the realization of an on-board navigation system

for all mission phases which is robust and accurate even for various spacecraft orientations and frequent thruster firing for orbit control. The goal of the absolute and relative orbit determination is to achieve an accuracy of 2 m and 0.1 m, respectively (3D, r.m.s.) and to provide continuous position and velocity data of the participating spacecraft at a 1 Hz rate for guidance and control purposes as well as for the PRISMA payload.

As detailed in 5, an extended Kalman Filter processes pseudo-range and carrier-phase measurement data issued by the local Phoenix GPS receiver on MAIN and sent via an Inter Satellite Link (ISL) from the remote Phoenix GPS receiver on TARGET. In contrast to earlier approaches that separate the GPS-based navigation into the independent reconstruction of absolute and relative states, a single reduced-dynamic Kalman filter for the absolute states of both spacecraft has been adopted for PRISMA.

Two different types of measurements are processed by the filter: undifferenced GRAPHIC measurements of the individual spacecraft as well as single-difference carrier-phase measurements. The GRoup and PHase Iono-spheric Correction (GRAPHIC) denotes a ionosphere-free linear combination of pseudo-range and carrier-phase data. It enables an absolute orbit determination of each individual spacecraft with a representative accuracy of about 1-2m, whenever a sufficient number of GPS satellites is tracked. The single-difference carrier-phase measurements in contrast can only be formed for commonly observed GPS satellites but exhibit a much lower noise level and thus provide the relative orbit with much higher accuracy. Both data types are subject to ambiguities related to the nature of carrier phase measurements. Channel specific ambiguities must therefore be estimated as part of the navigation filter. However, no effort is made to fix double-difference ambiguities to integer values. In view of residual modeling uncertainties (caused, for example, by a limited knowledge of the TARGET attitude and antenna position) the benefits of ambiguity fixing cannot be materialized in the PRISMA real-time navigation filter.

Overall, a total of 49 parameters are estimated in the navigation filter5. These comprise the position/velocity vector, empirical accelerations, drag coefficient and clock offset as well as a total of 12 GRAPHIC bias parameters for each of the two spacecraft. In addition, the filter state is augmented by a 3-parameter Delta-v vector to enable the estimation of impulsive velocity increments after maneuvers.

The inherent robustness of the symmetric filter design originates from the fact that common GPS satellites visibility is not a prerequisite to reconstruct the relative state. Even in the case of spacecraft with completely different attitude, the relative state can be determined by simply differencing absolute estimates exclusively based on GRAPHIC data types. The unified filter design simplifies the initialization and the maneuver handling procedures, and, consequently, improves the flexibility of the navigation system and its reliability during the formation flying experiments.

A Runge-Kutta fourth order integrator with Richardson extrapolation and Hermite interpolation allows the pro-vision of continuous position and velocity data at a 1 Hz rate and gives the possibility to efficiently cover the GPS

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data gaps caused by the tumbling of the TARGET spacecraft during the early Sun acquisition phase. Moreover the PRISMA GPS system is able to incorporate orbit control maneuvers in the navigation process. This feature enables not only the absorption of the velocity variations imparted to MAIN and TARGET by the separation mechanism but also their estimation via the Kalman filter state.

C. Navigation Software Architecture The PRISMA onboard software (OBS) architecture consists of a layered structure with a Basic Software (BSW)

level and an Application Software (ASW) level communicating with each other through dedicated message queues. While the BSW includes basic applications, device drivers and I/O-utilities, the ASW encapsulates all top-level applications like spacecraft navigation, control, telecommand and telemetry. The GPS-based navigation system is split into three modules located in different OBS levels and running at different sample rates4,5 (Fig. 3).

The GPS interface (GIF) is part of the BSW, runs at 1 s sample time and is directly fed with GPS messages is-sued by the Phoenix GPS receivers on-board MAIN and TARGET. GIF handles GPS raw data formats and ephemerides, and performs data sampling as well as coarse editing prior to the GPS-based orbit determination. The GPS-based Orbit Determination (GOD) and GPS-based Orbit Prediction (GOP) are embedded in the ASW layer as part of the ORB core (30 s sample time) and the GNC core (1 s sample time), respectively.

GOD implements an extended Kalman filter to process GRAPHIC observables as well as single difference car-rier phase measurements from MAIN and TARGET. Attitude data from both spacecraft are applied to correct for the GPS receivers antenna offset with respect to the spacecraft center of mass. Furthermore, a history of maneuver data is provided to GOD and taken into account in the orbit determination task. GOD performs a numerical orbit propagation which is invoked after the measurement update and provides orbit coefficients for interpolation to GOP for both spacecraft.

The GOP module interpolates the orbit coefficients provided by GOD and finally supplies the various GNC core functions as well as the PRISMA payload with continuous position and velocity data of MAIN and TARGET. Due to the different data rates of the GPS-based navigation modules, orbit maneuver data have to be taken into account in both GOD and GOP. In particular at each GNC step, the GOP task accounts for maneuvers which have not been considered by GOD in the last orbit determination/prediction process.

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D. Development and Validation Concept The PRISMA Onboard Software (OBSW) development at the Swedish Space Corporation (SSC) makes use of

the Model Based Design (MBD) approach and is completely based on Matlab/Simulink9. The MBD method raises the abstraction level for the system development and is especially suited to efficiently handle complex systems like e.g. the ones required to implement formation flying missions. The adoption of this development strategy can be compared to previous steps which have been taken in the history of software programming languages, like for example from assembler to C/C++, switching from a lower abstraction level language to a higher one. MBD can be seen as a natural step in this evolution chain, where emphasis is given to system engineering instead of focusing on software engineering.

As stated earlier, the PRISMA OBSW consists of two main layers, BSW and ASW respectively. The ASW consists of a number of application-cores (e.g., ORB, GNC, etc.) implementing guidance, navigation and control, thermal control, power control, payload control functionalities etc.. All these application-cores are executed through a real-time monotonic scheduler, i.e. they all have a specified sample time and their priority depends on the sample time: the smaller the sample time, the higher the priority.

Figure 4. Illustration of software development (top) and software validation (middle) environments at DLR and consequent integrated system level tests (bottom) at SSC. The functionalities of the Orbit Propagator, GPS Emulator and Flight Software are located in different hardware units during the development and validation phase and are indicated between quotes.

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The application cores are implemented as input/output functions. When the desired inputs and outputs of the application-cores have been specified, parallel software development is made easy. A dummy-core can always replace the real application core and the necessary services, as specified by the core-interface, and is prepared at the same time as the core-algorithms are being developed.

The DLR software contribution to the PRISMA OBSW has to be pictured in this frame and consists of specific application-cores within the ASW. The real-time navigation system development follows the same overall approach but makes extensive use of C/C++ modules to implement the computationally intensive core navigation functions. Use of Simulink is thus restricted to wrappers providing the abstract top level software and interface description. This enables a fully consistent validation of the flight software as a standalone unit at DLR prior to the system integration. As illustrated in Fig. 4, a step-wise approach is adopted for the validation of the navigation system.

In a first phase the flight software, wrapped through dedicated Simulink S-functions, is executed on a standard laptop PC (cf. Fig. 4, top) and stimulated by different sources of raw GPS data. The simplest simulations make use of emulated GPS measurements generated by the Phoenix EMulator (PEM) software. PEM allows a realistic modeling of measurements issued by a GPS receiver in LEO. More specifically, PEM emulates the output messages for raw measurements, navigation solutions and broadcast ephemerides generated by the Phoenix GPS receiver. PEM is driven by user provided trajectories and attitude profiles for the MAIN and TARGET spacecraft. The GPS constellation is described by a YUMA almanac and broadcast ephemeris errors are applied based on a specified Signal-In-Space-Range-Error (SISRE). Ionospheric path delays are furthermore accounted through a constant Vertical Total Electron Content (TEC) and a Lear mapping function.

In a second phase the flight software is validated in real-time through the inclusion of hardware in the loop. The offline software blocks in charge of numerical orbit propagation and Phoenix receiver emulation (cf. Fig. 4, top) are replaced by a 2x12 channels Spirent GSS7700 GPS signal simulator and two Phoenix GPS receivers (cf. Fig. 4, middle) fully representative of PRISMA flight units. The flight software is still integrated in a pure Matlab/Simulink environment with the introduction of dedicated S-functions for data reading/writing from/to serial ports of the host PC. This paper presents results from open-loop hardware-in-the-loop simulations only without the inclusion of orbit maneuvers.

The preliminary evaluation of the memory usage and computational load of the DLR’s flight software is per-formed on a LEON-3 microprocessor FPGA board which is representative of the MAIN spacecraft onboard computer. The CPU is based on a SPARC V8 processor, clocked at 24 Mhz, and is complemented by a GRFPU Floating Point Unit. All RAM blocks (cache and register-file memory) are Single Event Upset (SEU) protected. Real-Time-Workshop is used to automatically generate C-code out of the Matlab/Simulink tests previously executed on the host PC. The generated code is compiled and linked with the handwritten C++ flight software libraries (i.e., the S-function wrappers) using the RTEMS cross-compilation system (RCC).

III. Simulation of the PRISMA Separation Sequence A dedicated simulation scenario has been defined to assess the behavior of the GPS-based navigation system

during the separation sequence of the PRISMA formation. The scenario defines a specific timeline for the separation sequence and covers a representative set of PRISMA MAIN and TARGET ephemerides with their associated attitude. The simulation scenario is adopted in this paper to enable a preliminary testing of the navigation system during the separation phase of the formation. All simulations conducted so far have been confined to pure software simulations. The corresponding hardware-in-the-loop simulations are presently deferred to the integrated GNC software validation campaign.

E. Reference Orbit Specification After the separation from the launcher MAIN and TARGET are clamped to each other forming the so called

COMBINE configuration. This configuration is held for a time frame of approximately 25 days after which TARGET will be released from MAIN via a time-tagged command.

The simulation covers a time interval of about 2 + 4 orbital revolutions before and after the separation, respectively. Reference trajectories for the MAIN and TARGET are obtained via numerical orbit propagation including the aspherical Earth gravity field through an expansion in spherical harmonics up to degree and order 16 and the Sun and Moon third body forces. Among the non-gravitational accelerations atmospheric drag and solar radiation pressure are modeled as attitude dependent forces.

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Table 1 lists the initial osculating orbital elements for the MAIN spacecraft. They represent a Sun-synchronous polar orbit with an ascending node near 6 PM (dusk-dawn orbit). In the COMBINE configuration TARGET is modeled with half a meter MAIN attitude dependent offset. Thus the initial Keplerian orbital elements of MAIN and TARGET are almost identical at start time.

Before separation, MAIN is turned from having TARGET ahead in along-track, to a separation attitude almost perpendicular to the orbital plane. As MAIN is moving towards the sun, relative to TARGET, there will be good lighting condition to document the event with the Digital Video System on MAIN. The separation of TARGET from MAIN is performed through a ground command by firing one of two redundant wire cutters. The event is modeled as an instantaneous velocity variation for the MAIN and TARGET spacecraft. An additional impulsive maneuver is performed by MAIN at 8919 s after separation to cancel out the along-track drift and consequently stop the increase of along-track separation from TARGET. Tab. 2 lists the size and time of the nominal velocity variations used to generate the MAIN and TARGET reference trajectory profile.

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Table 1 Initial osculating elements of MAIN spacecraft.

Epoch 10. June 2009, 11:44:50.0 GPS time Osculating Elements (EME2000) Value Semi-major axis (a) [m] 7078140 Eccentricity (e) [ ] 0.0 Inclination (i) [°] 98.187777 Long. of ascend. node (Ω)[°] 168.959524 Arg. of perigee (ω) [°] 309.998815 Mean anomaly (M) [°] 0.0

The resulting relative motion of the MAIN spacecraft with respect to TARGET is depicted in Fig. 5. It may be

recognized that the ejection of TARGET instantaneously changes the orbital planes of both spacecraft and results in a periodic cross-track separation of 45 m amplitude. At the same time, the along-track velocity change modifies the relative semi-major axis by 16 m, which results in mean along-track drift of about 150 m per revolution. When the drift is ultimately stopped by MAIN after 1½ orbits, the spacecraft are sufficiently well separated in along-track distance. Furthermore, a high level of passive collision avoidance is achieved through the adopted phasing of the relative eccentricity and inclination vectors6 after the drift stop maneuver. It results in an elliptic relative motion in cross-track and radial direction and ensures a minimum separation of about 30 m at all times. Potential uncertainties in the knowledge of the along-track separation that might be caused by thruster performance errors or differential drag will therefore have no impact on safety of the initial PRISMA formation.

Table 2 Instantaneous velocity variations on MAIN and TARGET during the separation sequence.

Time [s] MAIN Δv [m/s]

TARGET Δv [m/s]

11892 Radial 0.0000 0.0000 Along-track -0.0022 +0.0065 Cross-track +0.0123 -0.0369

20811 Radial 0.0000 0.0000 Along-track +0.0087 0.0000 Cross-track 0.0000 0.0000

F. Attitude and GPS antenna orientation Prior to the TARGET separation, PRISMA maintains a Sun/Zenith orientation. Here, the solar panels (-Y axis of

MAIN) face the Sun and the zenith angle of MAIN’s +X is minimized to ensure a good GPS visibility. Due to the choice of a dusk-dawn orbit, the spacecraft body axes remain roughly aligned with the radial, along-track and cross-track direction at all times. As shown in Fig. 6 and 7, the active GPS antennas on MAIN and TARGET deviate by less than 30° from the zenith direction in the COMBINE configuration before separation. This gives a good sky visibility during the initialization and check-out of the GPS system.

After release from MAIN, the TARGET spacecraft starts tumbling with angular velocities up to 2 deg/s around an axis normal to the separation direction. TARGET then starts acquiring the desired Sun pointing orientation. Once it has been reached (within less than half an orbit), the TARGET keeps on tumbling around the Sun direction with a rate of ∼7 rev/orbit. Indeed the TARGET attitude control is only based on magnetic control, and this low tumbling motion provides a gyroscopic stiffness and ensures the spacecraft safety in Sun Acquisition and Safe Mode7. The spacecraft stays in this mode for a few orbits before it switches to a Sun/Zenith reference attitude. Its attitude is unpredictable during this phase and a switch of the GPS antennas cannot be performed.

On the contrary the MAIN spacecraft attitude is under control. It is TARGET/Sun pointing, and performs half a rotation around the orbit normal within one hour after separation. As can be recognized from Fig. 6, a switch of the active GPS antenna on MAIN is performed half an hour after the separation to use the unit with better GPS constellation visibility (i.e. unit antenna vector with positive radial coordinate).

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G. GPS Measurements Simulation Simulated raw measurements (and navigation solutions) for both spacecraft have been generated by the PEM

software based on the orbit and attitude profiles described above and taking into account the known antenna offsets in the spacecraft body frame.

A YUMA almanac for 1 July 2006 (GPS week 1381) was used to define a constellation of 29 active GPS satellites. Broadcast ephemerides were simulated with a SISRE of 2 m (i.e. slightly higher than the presently achieved performance of 1-1.5 m) and a VTEC of 10 TECU was assumed in the modeling of ionospheric path delays.

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A realistic antenna gain profile for the PRISMA GPS antennas (Sensor Systems S67-1575-20) was adopted and measurements were generated for all visible GPS satellites within less than 85° about the boresight direction. Bandwidths of 0.08 Hz and 9 Hz were assumed for the delay locked loop and phase locked loop to replicate the variation of code and carrier phase noise with signal-to-noise ratio in the Phoenix receiver.

Table 3 Relevant GOD telecommands during simulation.

Initialization and dynamic model Spacecraft parameters Parameter Value Parameter Value Ctrl_Initialize 0 Aux_Area_MAIN [m2] 0.67 Ctrl_n_Grav 10 Aux_mass_MAIN [kg] 150.0 Ctrl_m_Grav 10 Aux_CD_MAIN 2.3 Ctrl_Sun 1 Aux_CR_MAIN 1.3 Ctrl_Moon 1 Aux_Area_TARGET [m2] 0.23 Ctrl_Drag 1 Aux_mass_TARGET [kg] 50.0 Ctrl_SolRad 1 Aux_CD_TARGET 2.1 Ctrl_stepsize [s] 62.0 Aux_CR_TARGET 1.4

Extended Kalman filter (MAIN and TARGET) Parameter Value Parameter Value filter_sigma_pos [m] 1000.0 filter_taR [s] 900.0 filter_sigma_vel [m/s] 1.0 filter_taT [s] 900.0 filter_sigma_CD [m/s] 1.0 filter_taN [s] 900.0 filter_sigma_aR [nm/s2] 100.0 filter_sigma_B [m] 0.05 filter_sigma_aT [nm/s2] 60.0 filter_sigma_cdt [m] 500.0 filter_sigma_aN [nm/s2] 60.0 filter_noise_cdt [m] 500.0 filter_tcdt [s] 100.0 filter_noise_aR [nm/s2] 4.0 filter_noise_aT [nm/s2] 10.0 filter_sigma_PR [m] 0.1 filter_noise_aN [nm/s2] 10.0 filter_sigma_CP [m] 0.001 Maneuver related (only for MAIN)

Parameter Value filter_sigma_dvR [frac] 0.10 filter_sigma_dvT [frac] 0.10 filter_sigma_dvN [frac] 0.10

H. Navigation Software Settings Tab. 3 lists the relevant telecommand parameters and the correspondent values used to control the execution of

the GPS-based Orbit Determination (GOD) software during the simulation. Apart from the force model parameters, the indicated values represent typical defaults.

Normally the force model for the numerical orbit propagation considers the aspherical Earth gravity field through an expansion in spherical harmonics up to degree and order 20 based upon coefficients from the GGM01S gravity model. In order to improve the realism of the simulation the order and degree of the gravity field have been reduced to 10. This because the reference trajectory applies spherical harmonics up to degree and order 16 only. Furthermore, the Sun and Moon third body forces are computed based on analytical models for the Sun and Moon position. Non-gravitational accelerations are based on a modified Harris-Priester model for the computation of the atmospheric density and on a cylindrical shadow model for the solar radiation pressure. No attitude dependency of the drag, CD, and solar radiation pressure, CR coefficients is considered.

It has to be noted that GOD incorporates only maneuvers executed by the MAIN spacecraft in the navigation process. The inclusion and estimation of the maneuvers requires the a-priori knowledge of the equivalent impulsive velocity variations imparted to the MAIN spacecraft. The separation event of TARGET from MAIN represents the only occasion in the TARGET‘s operational life after orbit injection where an impulsive maneuver is applied to the

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spacecraft. This information is not provided to the navigation modules during the simulation, which take into account only the a-priori information listed in Table 4. The a-priori velocity variations values correspond to half of the velocity variations actually imparted to MAIN. For the current simulation, the velocity variations applied to TARGET during separation are much larger and are not known by the navigation filter.

An alternative approach would be to apply the foreseen differential velocity variations to the filter. This would provide a better a priori knowledge for the estimation of the relative motion, while increasing the uncertainty of the absolute orbit determination. Considering that it is more important to achieve accurate relative trajectory estimation right after separation than a good absolute MAIN trajectory, this approach should be preferred for the actual flight operations.

Table 4. A-priori impulsive maneuver information provided to GOD and GOP during the simulation.

Time [s] MAIN TARGET Δv [m/s] Δv [m/s]

11892 Radial 0.00000 n/a Along-track -0.00110 n/a Cross-track +0.00615 n/a

20811 Radial 0.00000 n/a Along-track +0.00435 n/a Cross-track 0.00000 n/a

IV. Results and Discussions The navigation filter is initialized at start time as soon as valid navigation solutions are provided by the GPS In-

terFace (GIF). No re-initialization of GOD is performed during the simulation. The pattern of the valid navigation solution flag (cf. Fig. 8) reflects the fact that numerous navigation solutions generated by the Phoenix GPS receiver onboard TARGET are not valid after separation. This is due to the poor visibility conditions (i.e. less than 4 satellites tracked at the same time) faced by the active GPS antenna on TARGET. In particular no GPS satellites are tracked by TARGET in several occasions (cf. Fig. 9).

Fig. 10 and 11 show the navigation accuracy during the simulation. GOP provides stable absolute and relative navigation solutions. The maximum relative navigation errors are reached shortly after separation and are shown to be within ±2 m for all RTN components. The absolute navigation error lies within ±20 m.

Finally Fig. 12 shows size and time of the impulsive maneuvers estimated by GOD. Two maneuvers are estimated during the separation sequence (i.e. at separation time and one orbital revolution later). At separation GOD estimates a total velocity variation imparted to MAIN that matches the sum of the individual velocity variations applied to MAIN and TARGET. Even if the a-priori knowledge of the delta-vs is affected by huge errors, the maneuver estimation is quite accurate and absorbs the velocity impulse applied to TARGET into the estimated MAIN velocity variation.

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Time since simulation start [h] Figure 9 Number of GPS satellites tracked by MAIN (top), by TARGET (middle) and

commonly visible (bottom) during the simulation of the separation sequence.

0 1 2 3 4 5 6 7 8 9 10-3

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Time since simulation start [h]

Figure 10 Relative position error (MAIN-TARGET), in radial, along-track and cross-track direction of the PRISMA real-time navigation filter during the simulation of the separation

American Institute of Aeronautics and Astronautics

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0 1 2 3 4 5 6 7 8 9 10-40

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Figure 11 Absolute position error (TARGET), in radial, along-track and cross-track

direction of the PRISMA real-time navigation filter during the simulation of the separation sequence.

American Institute of Aeronautics and Astronautics

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0 1 2 3 4 5 6 7 8 9 10-0.010

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Figure 12 Estimated impulsive maneuvers on MAIN during the simulation of the separation sequence. The velocity variations are mapped into the RTN orbital frame centered on MAIN.

American Institute of Aeronautics and Astronautics

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V. Summary and Way Forward A simulation scenario has been specified for the GPS-based navigation functions during the separation sequence

of the PRISMA formation flying spacecraft. To this end, a representative orbit and attitude profile of the MAIN and TARGET spacecraft have been adopted. GPS-related characteristics have been described in terms of a GPS almanac and settings for a highly realistic GPS receiver emulator. The simulation scenario has been used to emulate the behavior of the navigation system during one of the most delicate phases of the PRISMA mission. Preliminary results show that the navigation system, in its current shape, is robust enough to handle the highly dynamic conditions and the poor sky visibility of the TARGET GPS antennas during Sun acquisition via magnetic attitude control. The shown high level of robustness stems from the specific navigation system design, which can process both un-differenced GRAPHIC data types and single difference carrier phase measurements.

Despite the promising results, further investigations have to be performed to remove some simplifications applied within the simulation scenario and verify the adopted assumptions. Multipath effects have been completely neglected and the partial shadowing of the MAIN structure on the TARGET GPS antenna has not been considered. The ISL has been assumed to work properly during the complete separation sequence. Furthermore no GPS antenna offsets for transmitting GPS antennas have been take into account. On top of that, the operation of the Phoenix GPS receivers has been assumed as nominal during the tumbling of the spacecraft. Contingency scenarios should be defined that could trigger the re-initialization of the GPS receivers and consequently the degradation of the navigation system behavior.

References 1S. Barabash, O. Norberg, J.-E. Wahlund, M. Ya-mauchi, S. Grahn, S. Persson, L. Blomberg; “Towards Low-cost Swedish

Planetary Missions”; 24th International Symposium on Space Technology and Science, Miyazaki, Japan, May 30-June 6, (2004). 2S. Persson, P. Bodin, E. Gill, J. Harr, J. Jörgensen; “PRISMA – AN AUTONOMOUS FORMATION FLYING MISSION”;

ESA Small Satellite Systems and Services Symposium (4S), Sardinia, Italy, 25-29 September (2006). 3Bodin P., Chasset C., Larsson R., Nilsson F., Note-born, R., Nylund M., Vretblad Ö., Veldman S., Persson S.; “Guidance,

Navigation, and Control Experiments on the PRISMA in-Orbit Test Bed”, IAC-07-C1.6.01, In: 58th International Astronautical Congress, Hyderabad, India (2007).

4Gill E., D’Amico S., Montenbruck O.; “Autonomous Formation Flying for the PRISMA Mission”; Journal of Spacecraft and Rockets 44/3: 671-681 (2007).

5D’Amico S., Gill E., Garcia-Fernandez M., Montenbruck O.; “GPS-based Real-time Navigation for the PRISMA Formation Flying Mission”; 3rd ESA Workshop on Satellite Navigation User Equipment Technologies, NAVITEC’2006, 11-13 December 2006, Noordwijk (2006).

6D'Amico S., Gill E., Montenbruck O..; “Relative Orbit Control Design for the PRISMA Formation Flying Mission”; AIAA Guidance, Navigation, and Control Conference, 21-24 Aug. 2006, Keystone, Colorado (2006).

7Montenbruck O., Markgraf M.; “User’s Manual for the Phoenix GPS Receiver”; DLR/GSOC; GTN-MAN-0120; Issue 1.7, 06 June (2006).

8Chasset C., Berge S., Bodin P., Jakobsson B.,; “3-Axis Magnetic Control with Multiple Attitude Profile Capabilities in the PRISMA Mission”, Space Technology, Vol. 26, Issue 3-4, pp 137-154 (2007).

9Edfors A.; “PRISMA ASW Subsystem Description”; Document ID: SSPH1000-S38; Version 1.0; Swedish Space Corporation, Solna (2005).