Analysis of Decentralized Estimation Filters for Formation Flying Spacecraft

Abstract

Future formation flying missions are being planned for fleets of spacecraft in MEO, GEO, and beyond where relative navigation using GPS will either be impossible or insufficient. To perform fleet estimation for these scenarios, local ranging devices on each vehicle are being considered to replace or augment the available GPS measurements. A previous paper presented several approaches for distributing the computational load of the estimation process across the vehicles in the fleet. This paper extends the previous work to present a more detailed investigation of the covariances for the different distributed estimation algorithms. This enables an analysis of the transient effects as the ranging measurements are added to the estimator, which extends the previous steady-state comparison. This transient covariance analysis more clearly shows the effect of ignoring errors in the ranging measurements that result when the location of the target vehicle is also not well known. These results provide further insight on the relative performance of these filters and identifies the Schmidt covariance correction (SCC), the essence of the Schmidt Kalman Filter, as being responsible for better performance of Schmidt Kalman Filter compared to other decentralized filters.

Distributed Orbit Determination for Global Navigation Satellite System with Inter-Satellite Link

“…For the distributed navigation algorithms, several techniques including the iterative cascade extended Kalman filter (ICEKF), increased measurement covariance EKF (IMCEKF), and Schmidt-Kalman Filter (SKF) are discussed by Schmidt, Park, and Ferguson [ 11 , 12 , 13 ]. The ICEKF is employed to processes a large number of space-borne GPS measurement data and a small quantity of ISL measurement data for low-Earth orbit formation flying satellites.…”

Distributed Orbit Determination for Global Navigation Satellite System with Inter-Satellite Link

“…The simulation for Galileo system showed that URE is on the level of decimeters [10], which is better than that of GPS. For the distributed navigation algorithms, several techniques including iterative cascade extended Kalman filter (ICEKF), increased measurement covariance EKF (IMCEKF), and Schmidt-Kalman Filter (SKF) are discussed by Schmidt, Park and Ferguson [11][12][13]. The ICEKF is employed to processes a large number of space-borne GPS measurement data and a small quantity of ISL measurement data for low-Earth orbit formation flying satellites.…”

“…In the equation 11, the array of state parameters of GAS ( ) g t X is known, only the state vector of i th satellite is unknown. The reference ground coordinate is hence introduced into the satellite state by equation (11), this overcomes the lack of the datum mark in data processing while only ISL measurements are utilized. The current linearized measurement equation which is similar to equation (8) becomes:…”

Lightweight infrared sensing for relative navigation of quadrotors

“…In particular, by adding the communicated position estimates of the leader to the relative position estimates from the follower in x and y as x meas = x rel +x leader y meas = y rel +ŷ leader the follower can directly use x meas and y meas in its filter. Additionally, as detailed in [18], the uncertainty in these position estimates can be accurately accounted for by adding the component of the covariance matrix of the leader that lies in the direction of the camera sensor to the uncertainty of the relative measurements.…”