This study presents a precise relative navigation algorithm using both laser and Global Positioning System (GPS) measurements in real time. The measurement model of the navigation algorithm between two spacecraft is comprised of relative distances measured by laser instruments and single differences of GPS pseudo-range measurements in spherical coordinates. Based on the measurement model, the Extended Kalman Filter (EKF) is applied to smooth the pseudo-range measurements and to obtain the relative navigation solution. While the navigation algorithm using only laser measurements might become inaccurate because of the limited accuracy of spacecraft attitude estimation when the distance between spacecraft is rather large, the proposed approach is able to provide an accurate solution even in such cases by employing the smoothed GPS pseudo-range measurements. Numerical simulations demonstrate that the errors of the proposed algorithm are reduced by more than about 12% compared to those of an algorithm using only laser measurements, as the accuracy of angular measurements is greater than 0.001° at relative distances greater than 30 km.

1. INTRODUCTION
 2. METHODOLOGY
  2.1 Relative Navigation Algorithm in SphericalCoordinates
  2.2 Laser-based Navigation Algorithm with ModifiedMeasurement Model Employing GPS Pseudo-rangeMeasurements
 3.RESULT AND ANALYSIS
  3.1 Relative Navigation Results in Large-scale FormationFlying
  3.2 Analyses for Navigation Strategy
 4.CONCLUSION
 ACKNOWLEDGMENTS
 REFERENCES

• Kwangwon Lee(Astrodynamics & Control Laboratory, Department of Astronomy, Yonsei University, Seoul 03722, Korea)
• Hyungjik Oh(Astrodynamics & Control Laboratory, Department of Astronomy, Yonsei University, Seoul 03722, Korea)
• Han-Earl Park(Korea Astronomy and Space Science Institute, Daejeon 34055, Korea)
• Sang-Young Park(Astrodynamics & Control Laboratory, Department of Astronomy, Yonsei University, Seoul 03722, Korea) Corresponding Author
• Chandeok Park(Astrodynamics & Control Laboratory, Department of Astronomy, Yonsei University, Seoul 03722, Korea)