This paper presents relative navigation using intermittent laser-based measurement data for spacecraft flying formation that consist of two spacecrafts; namely, chief and deputy spacecrafts. The measurement data consists of the relative distance measured by a femtosecond laser, and the relative angles between the two spacecrafts. The filtering algorithms used for the relative navigation are the extended Kalman filter (EKF), unscented Kalman filter (UKF), and least squares recursive filter (LSRF). Numerical simulations reveal that the relative navigation performances of the EKF- and UKF-based relative navigation algorithms decrease in accuracy as the measurement outage period increases. However, the relative navigation performance of the UKF-based algorithm is 95 % more accurate than that of the EKF-based algorithm when the measurement outage period is 80 sec. Although the relative navigation performance of the LSRF-based relative navigation algorithm is 94 % and 370 % less accurate than those of the EKF- and UKF-based navigation algorithms, respectively, when the measurement outage period is 5 sec; the navigation error varies within a range of 4 %, even though the measurement outage period is increased. The results of this study can be applied to the design of a relative navigation strategy using the developed algorithms with laser-based measurements for spacecraft formation flying.

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.