Multivariate bootstrapped relative positioning of spacecraft using GPS L1/Galileo E1 signals

https://doi.org/10.1016/j.asr.2010.10.001Get rights and content

Abstract

GNSS-based precise relative positioning between spacecraft normally requires dual frequency observations, whereas attitude determination of the spacecraft, mainly due to the stronger model given by the a priori knowledge of the length and geometry of the baselines, can be performed precisely using only single frequency observations. When the Galileo signals will come available, the number of observations at the L1 frequency will increase as we will have a GPS and Galileo multi-constellation. Moreover the L1 observations of the Galileo system and modernized GPS are more precise than legacy GPS and this, combined with the increased number of observations, will result in a stronger model for single frequency relative positioning. In this contribution we will develop an even stronger model by combining the attitude determination problem with relative positioning. The attitude determination problem will be solved by the recently developed Multivariate Constrained (MC-) LAMBDA method. We will do this for each spacecraft and use the outcome for an ambiguity constrained solution on the baseline between the spacecraft. In this way the solution for the unconstrained baseline is bootstrapped from the MC-LAMBDA solutions of each spacecraft in what is called: multivariate bootstrapped relative positioning. The developed approach will be compared in simulations with relative positioning using a single antenna at each spacecraft (standard LAMBDA) and a vectorial bootstrapping approach. In the simulations we will analyze single epoch, single frequency success rates as the most challenging application. The difference in performance for the approaches for single epoch solutions, is a good indication of the strength of the underlying models. As the multivariate bootstrapping approach has a stronger model by applying information on the geometry of the constrained baselines, for applications with large observation noise and limited number of observations this will result in a better performance compared to the vectorial bootstrapping approach. Compared with standard LAMBDA, it can reach a 59% higher success rate for ambiguity resolution. The higher success rate on the unconstrained baseline between the platforms comes without extra computational load as the constrained baseline(s) problem has to be solved for attitude determination and this information can be applied for relative positioning.

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

References (54)

  • G. Giorgi et al.

    Testing a new multivariate GNSS carrier phase attitude determination method for remote sensing platforms

    Adv. Space Res., Special issue: GNSS Remote Sensing: New Roles and Progresses

    (2010)
  • Buist, P.J. The baseline constrained LAMBDA method for single epoch, single frequency attitude determination...
  • Buist, P.J., Kumagai, S., Ito, T., Hama, K., Mitani, K. Development of the integrated navigation unit; combining a GPS...
  • Buist, P.J., Kumagai, S., Hama, K. Flight Experience of the integrated navigation unit; combining GPS attitude...
  • Buist, P.J., Kumagai, S., Kasahara, M., Ijichi, K., Hama, K., Nakamura, S. Flight experience of single and dual...
  • P.J. Buist et al.

    GPS-based attitude determination in different attitude modes: experimenting with a GPS receiver and a star sensor onboard the SERVIS-1 satellite

  • Buist, P.J., Teunissen, P.J.G., Giorgi, G., Verhagen, S. Instantaneous multi-baseline ambiguity resolution with...
  • P.J. Buist et al.

    Multiplatform instantaneous GNSS ambiguity resolution for triple- and quadruple-antenna configurations with constraints

    Int. J. Navig. Observ.

    (2009)
  • Buist, P.J., Teunissen, P.J.G., Giorgi, G., Verhagen, S. Instantaneous GNSS-based kinematic relative positioning and...
  • P.J. Buist et al.

    A vectorial bootstrapping approach for integrated GNSS-based relative positioning and attitude determination of spacecraft

    Acta Astronautica

    (2010)
  • Buist, P.J, Verhagen, S., Hashimoto, T., Sawai, S., Sakai, S., Bando, N., Shimizu, S., GPS experiment on the...
  • Cohen, C.E. Attitude determination. Parkinson, B.W., Spilker, J.J. (Eds.), Global Positioning System: Theory and...
  • Cohen, C.E., Parkinson, B.W. Integer Ambiguity resolution of the GPS carrier for spacecraft attitude determination, In:...
  • Duncan, S.M., Hodgart, M.S., Unwin, M.J., Hebden, R., In-orbit results from a space-borne GPS attitude experiment. In:...
  • T. Ebinuma et al.

    GPS receiver operations on the disaster monitoring constellation satellites

    J. Navig.

    (2005)
  • Giorgi, G., Teunissen, P.J.G., Verhagen, S., Buist, P.J. Integer ambiguity resolution with nonlinear geometrical...
  • Gomez, S.F.M.L., Lammers, M.L. Lessons learned from two years of on-orbit global positioning system experience on...
  • Hauschild, A., Montenbruck, O., GPS-based attitude determination for microsatellite. In: Proceedings of ION GNSS-2007,...
  • Hodgart, M.S., Purivigraipong, S. New approach to resolving instantaneous integer ambiguity resolution for spacecraft...
  • Interface Specification IS-GPS-800 Navstar GPS Space Segment/User Segment L1C Interfaces, Available at...
  • Julien, O., Alves, P., Cannon, M.E., Zhang, W. A tightly coupled GPS/GALILEO combination for improved ambiguity...
  • O. Julien et al.

    Triple frequency ambiguity resolution using GPS/GALILEO

    Eur. J. Navig.

    (2004)
  • Kim, D., Langely, R.B. GPS RTK-based attitude determination for the e-POP platform onboard the Canadian CASSIOPE...
  • Knight, D. A new method of instantaneous ambiguity resolution. ION-GPS-1994, Institute of Navigation, Colorado Springs,...
  • Krauss, P.A., Kühl, C., Mittnacht, M., Heim, J., Gottzein, E. Modernized spaceborne GNSS receivers. In: Proceedings of...
  • Kroes, R. Precise relative positioning of formation flying spacecraft using GPS, Ph.D. Thesis, Delft, The Netherlands,...
  • Kumagai, S., Ito, T., Toda, K., Iwata, T. Precision GPS receiver for the advanced land observing satellite (ALOS). In:...
  • Cited by (15)

    • Ambiguity resolution performance with GPS and BeiDou for LEO formation flying

      2014, Advances in Space Research
      Citation Excerpt :

      The aforementioned challenges, however, may not be overcome with a GPS-only receiver. The added value of using the observations from more than one GNSS has been confirmed in many performance studies, see e.g. (Buist et al., 2010; Cao et al., 2008; Chen et al., 2009; O’Keefe et al., 2009; Rizos, 2009; Verhagen, 2007; Verhagen et al., 2010). Here, it will be specifically investigated how the relative positioning performance of a formation of LEOs may improve if BeiDou is used, either on its own or combined with GPS.

    • Ps-LAMBDA: Ambiguity success rate evaluation software for interferometric applications

      2013, Computers and Geosciences
      Citation Excerpt :

      Another example is GNSS-based georeferencing as used in many remote sensing applications. The remote sensing platforms range from survey ships to airborne and Unmanned Airborne Vehicles (Everaerts, 2008; Rieke et al., 2011), and even spaceborne platforms (Buist et al., 2010; Kroes et al., 2005; Leung and Montenbruck, 2005; Huber et al., 2010; Nadarajah et al., in press). GNSS allows for precise positioning and attitude determination of the platforms, in real-time or in post-processing mode.

    • Precise line-of-sight vector estimation based on an inter-satellite radio frequency system

      2013, Advances in Space Research
      Citation Excerpt :

      This is especially valid for space applications where the signals can only reflect from the near surfaces at the vehicle itself. For a single epoch processing, multipath can be considered as Gaussian distribution and lumped into the thermal noise as the time-correlation property of the multipath is not relevant in single epoch (Buist et al, 2011). Given the different combinations of all parameters, ADOPLOS is shown in Fig. 8.

    View all citing articles on Scopus
    View full text