Relative Navigation for 
This page presents hardwareintheloop results that experimentally
demonstrate precise relative navigation for true formation flying spacecraft
applications (see). The approach is based on carrierphase
differential GPS (CDGPS), which is an ideal navigation sensor for these
missions because it provides a direct measure of the relative positions
and velocities of the vehicles in the fleet. In preparation for Orion,
a planned microsatellite formation flying mission, four modified GPS receivers
were used in the NASA GSFC Formation Flying
Testbed to demonstrate relative navigation. The results in this paper
show unprecedented levels of accuracy (~2cm position and <0.5mm/s velocity)
which validate the use of a decentralized estimation architecture and
offer high confidence in the success of Orion.
Our estimation approach uses decentralized filters that offer the benefits of improved robustness & reconfigurability and because the processing effort is highly distributed, it should scale well to larger fleets. Fortunately, as shown in the papers, this application lends itself well to a decentralized filter. The primary goal of the work was to demonstrate that, even though the decentralized estimation approach is an approximation, it can still meet the target relative navigation goals. 

Figure shows the inplane elliptical motion
of three slave vehicles (starting at the "o" positions) around a reference
vehicle (marked by "+"). The 1km inplane ellipse (passive aperture) was the baseline relative motion for this study. One vehicle follows the reference orbit. The other three vehicles moved about the master vehicle in an evenly spaced ellipse, staying within the orbital plane. The elliptical path in the local frame was 1km x 2km. 
The figures below show the position errors for the three relative solutions (shown as projections of the error into the Radial (R), InTrack (I), and CrossTrack (C) directions).  

Simulations start with large errors (~25m) that result from the initial carrier phase bias errors. However, these biases are observable over time, and the position solution quickly converges. After the initial convergence, the biases on new measurements coming online are predicted from the current state estimate, but the results show that this initialization process does not disturb the position estimates. To quantify the performance, the standard deviation and mean of the error was computed over the last half of the simulation in each dimension (see Table 1). As shown, the position error has a mean of 0.2  1.1cm, and a standard deviation of 0.3  0.7cm. 

The plot shows the corresponding velocity
errors that have a mean of 0.03mm/s and a standard deviation of ~0.3mm/s.


A zoomed in plot of the position errors shows
some correlation in the final solutions. However, note the scale of these errors! 