Multivariate bootstrapped relative positioning of spacecraft using GPS L1/Galileo E1 signals
Introduction
In the near future a large number of new signals will come available from Galileo and modernized GPS. Signals will be broadcast at multiple frequencies. However, it is expected that due to the simple design and inherently lower cost, single frequency applications will remain important. In this contribution we will investigate a combined relative positioning and attitude determination approach in which the attitude solution is used to enhance the relative positioning. We will show that GNSS receivers onboard spacecraft using GPS and Galileo single frequency observations will benefit from the developed approach. As examples of potential applications for the combined approach, one should not only think of spacecraft. The approach can also be applied for relative positioning in aviation, for inshore and offshore vessels and other types of terrestrial vehicles. Therefore we will use the more general expression of platform for the vehicles discussed in this paper.
Section snippets
Global navigation satellite systems
In this contribution we will use the civil signals in the L1/E1 band with carrier frequency f1 = 1575.42 MHz for precise single frequency relative positioning. For GPS, the legacy L1C/A and the future L1C signals are in this band, whereas for Galileo there will be the E1A, E1B and E1C signals. The specifications of these signals are shown in Table 1. First we will discuss these signals in terms of modulations, chip and symbol rates in more detail. In the table also transmit bandwidths and nominal
Model
The Multivariate Constrained method was applied on baselines at a single platform in Teunissen (2007) and Giorgi et al., in press, Giorgi et al., 2010. In this contribution we will apply the method on the baselines at each platform and, in a next step, use the outcome for an ambiguity constrained solution on the baseline between the platforms. In the developed approach, the configuration of receiver/antennas can be seen as a kinematic network. The network consists of multiple baselines at each
Software simulation setup
Table 4 summarizes the conditions of the simulations used to investigate the performance of the proposed integrated approaches: vectorial and multivariate bootstrapped relative positioning. Utilizing the VISUAL software (Verhagen, 2006), based on the location of the receivers and an actual GNSS constellation, the design matrices of the model are calculated. The 150 m distance between the platforms is the inter-satellite distance as will be used in the Proba-3 mission from the European Space
Future work
The theory for a multivariate bootstrapped relative positioning was developed in this contribution, and the performance of the approach was tested using simulated data. The performance has to be evaluated further with realistic noise values for code and carrier observation on moving vehicles including the effects of multipath. Therefore we plan to test the approach using data collected in hardware-in-the-loop simulations (Buist et al., 2010a, Buist et al., 2010b) and orbital data collected at
Conclusion
GNSS-based precise relative positioning between spacecraft normally requires dual frequency observations, whereas attitude determination of the spacecraft can be performed precisely using only single frequency observations. When the Galileo signals will come available besides GPS, the number of observations at the L1 (or E1 as is the designation in the Galileo system) frequency will increase. Moreover the L1 observations of the Galileo system and modernized GPS are more precise than legacy GPS
Acknowledgements
The MicroNed-MISAT framework are kindly thanked for their support. Professor Teunissen is the recipient of an Australian Research Council Federation Fellowship (project number FF0883188). This work has also been done in the context of the Australian Space Research Program project: SAR Formation Flying. The research of Sandra Verhagen is supported by the Dutch Technology Foundation STW, applied science division of NWO and the Technology Program of the Ministry of Economic Affairs. All this
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