Relative Navigation for 
Formation Flying Spacecraft Using 
Carrier-Phase Differential GPS

Faculty Contact: Jonathan How

Student Contact: Franz Busse


This page presents hardware-in-the-loop results that experimentally demonstrate precise relative navigation for true formation flying spacecraft applications (see). The approach is based on carrier-phase 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 in-plane elliptical motion of three slave vehicles (starting at the "o" positions) around a reference vehicle (marked by "+"). 

The 1km in-plane 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), In-Track (I), and Cross-Track (C) directions). 

Simulations start with large errors (~2-5m) 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 on-line 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!

Table 1 gives the root-mean-square of these means and standard deviations of the errors across the fleet's three solutions. 
Position (cm)
Velocity (mm/s)
Mean
Std
Mean
Std
Radial 
0.25 
0.45
0.032
0.156 
In-track
1.06 
0.66
0.001
0.275
Cross-track
0.16 
0.29
0.017
0.107
Table 2 shows a list of results for different formations that were compiled in the same way. First, it is clear that for the close formations (1km or less), the performance is better than the target precision (performance approaches the noise floor as determined in the error analysis). As expected, the position accuracy degrades for the long separation formations. Velocity is good in all cases and has a low mean value, which is very important for the formation control. 
Position (cm)
Velocity (mm/s)
Mean
Std
Mean
Std
100m in-track
0.93
0.46
0.01
0.32
1km in-plane
0.83
0.82
0.04
0.33
1km out-plane
1.03
0.54 
0.04
0.34
10km in-track 
5.76
1.92
0.07
0.40
10km in-track
2.83
1.55
0.04
0.54 

Papers:

  1. Philip Ferguson, Franz Busse, and Jonathan How, "Navigation Performance Predictions for the Orion Formation Flying Mission" Presented at the International Symposium on Formation Flying: Missions and Technologies, October 2002
  2. Franz Busse and Jonathan How, "Demonstration of Adaptive Extended Kalman Filter for Low Earth Orbit Formation Estimation Using CDGPS", Institute of Navigation GPS Meeting, September 2002
  3. Franz Busse and Jonathan How, "Real-time Experimental Demonstration of Precise Decentralized Relative Navigation for Formation Flying Spacecraft", AIAA Guidance, Navigation, and Control Conference, August 2002

Connections to:

November 29, 2002