Formation flying of satellites as well as proximity operations during rendezvous and docking require a precise knowledge of the relative state of the involved spacecraft. Traditionally, dedicated navigation processors have been used to dynamically model the absolute and relative motion in a Kalman filter using appropriate scalar or higher-dimensional measurements. Using Global Positioning System (GPS) receivers it is possible to implement a sensor that directly provides both its own absolute position as well as the relative position of a partner spacecraft without requiring an external navigation processor.
Concept and Implementation
A prototype implementation of such a relative navigation sensor has been performed based on the GPS Orion 12-channel L1 receiver. It employs two individual receivers that exchange their raw pseudorange, carrier phase, and Doppler measurements via a dedicated serial data link. Subsequent to computing its own position and velocity, each receiver processes the differential range and phase after receiving the partner's data set to obtain the relative state vector. The differential processing allows for a high degree of common error cancellation over baselines of typically less than 10 km, which effectively eliminates the impact of broadcast ephemeris errors, ionospheric errors, and GPS satellite clock errors. By smoothing the differential pseudoranges with differential carrier phase measurements, a pronounced reduction of the relative position noise level is achieved.
In view of the small relative velocity, time differences of the single-differenced carrier phases provide an excellent approximation of the instantaneous differential range-rate, which also allows a highly accurate determination of the intersatellite velocity vector. Results of hardware-in-the-loop tests using a GPS signal simulator demonstrate the high performance of the system. Compared to a rigorous dynamical filtering, the overall hardware and software requirements are considerably reduced at a tolerable loss in overall precision. The small size and power consumption of the prototype receiver pair enables their implementation on micro- or nanosatellite platforms with restricted onboard resources, that are commonly considered as candidates for formation flying missions with distributed payloads.
The Orion GPS receiver used for the relative navigation system represents a prototype design for a terrestrial receiver based on the Mitel (now Zarlink GP2000) chipset. For use on low Earth satellites and other space applications numerous modifications and enhancements have been made to the original firmware. These include fixes related to the implicit assumption of a low speed vehicle in the Doppler prediction, the navigation and the time tagging error of the raw measurements. Aside from these fixes, multiple extensions have been made to the command and telemetry interface of the receiver to allow convenient and flexible operation of the receiver via a remote data link and to adapt the receiver output to the available downlink capacity. To ensure a robust tracking and rapid signal acquisition under the conditions of a high-dynamics space vehicle an open-loop Doppler and visibility prediction algorithm based on a priori trajectory information has been added to the receiver code. Also, an active alignment of measurements epochs and navigations solutions to the integer second of GPS time has been implemented, which ensures synchronized measurements collected by independent receivers. To improve the overall navigation performance of the Orion receiver, integrated carrier phase measurements have been made available using a 3rd order phase lock loop (PLL) assisted by 2nd order frequency lock loop (FLL). The loop provides accurate tracking and stable acquisition over a wide range of dynamical conditions. Raw data accuracies obtained in signal simulator tests for normal signal strengths are better than 1 m for C/A code pseudoranges, 1 mm for L1 carrier phases and 10 cm/s for L1 Doppler measurements.
The kinematic relative navigation performance was evaluated for a set of formation flying spacecraft in polar orbits with a ten kilometer along track separation. Motion data based on a realistic trajectory model were generated on a Spirent STR4760 signal simulator and a constant total electron content yielding a vertical path delay of 3.2m was applied in the signal modeling. In addition, broadcast ephemeris errors of up to ten meters were intentionally added to each GPS satellite. The excellent accuracy of the kinematic intersatellite position and velocity solution confirms the high level of common error cancellation obtained in the relative navigation solution. Other than the absolute position, the relative position solution is essentially unaffected by both the broadcast ephemeris errors and the ionospheric refraction. An r.m.s. accuracy of 0.15 m is achieved in the along-track direction, while the accuracy of the radial component is slightly worse (0.3-0.5 m) in view of the less favorable vertical dilution of precision. The relative velocity vector of the target and chaser vehicle exhibits an r.m.s noise of 2-10 mm/s, which complies well with a 2.5 mm/s noise of the carrier based range rate measurements at the 1 s sampling interval and representative horizontal and vertical dilution of precision values.
This study was performed in cooperation with the Center for Space Research, University of Texas (UT/CSR).
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