Vision-Based Relative State Estimation Using the Unscented Kalman Filter

A new approach for spacecraft absolute attitude estimation based on the unscented Kalman filter (UKF) is extended to relative attitude estimation and navigation. This approach for nonlinear systems has faster convergence than the approach based on the standard extended Kalman filter (EKF) even with inaccurate initial conditions in attitude estimation and navigation problems. The filter formulation employs measurements obtained from a vision sensor to provide multiple line(-) of(-) sight vectors from the spacecraft to another spacecraft. The line-of-sight measurements are coupled with gyro measurements and dynamic models in an UKF to determine relative attitude, position and gyro biases. A vector of generalized Rodrigues parameters is used to represent the local error-quaternion between two spacecraft. A multiplicative quaternion-error approach is derived from the local error-quaternion, which guarantees the maintenance of quaternion unit constraint in the filter. The scenario for bounded relative motion is selected to verify this extended application of the UKF. Simulation results show that the UKF is more robust than the EKF under realistic initial attitude and navigation error conditions.

[1]  M. Shuster.  A survey of attitude representation , 1993 .

[2]  Rudolph van der Merwe,et al.  The unscented Kalman filter for nonlinear estimation , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).

[3]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[4]  Malcolm D. Shuster.  Survey of attitude representations , 1993 .

[5]  Nasser Kehtarnavaz,et al.  A vision-based DSP embedded navigation sensor , 2002 .

[6]  Son-Goo Kim,et al.  Kalman filtering for relative spacecraft attitude and position estimation , 2005 .

[7]  E. J. Lefferts,et al.  Kalman Filtering for Spacecraft Attitude Estimation , 1982 .

[8]  F. Markley,et al.  Unscented Filtering for Spacecraft Attitude Estimation , 2003 .

[9]  M. Shuster,et al.  Three-axis attitude determination from vector observations , 1981 .

[10]  E. Glenn Lightsey,et al.  GPS/INS Kalman filter design for spacecraft operating in the proximity of the international space station , 2003 .

[11]  M. C. VanDyke,et al.  UNSCENTED KALMAN FILTERING FOR SPACECRAFT ATTITUDE STATE AND PARAMETER ESTIMATION , 2004 .

[12]  Robert Grover Brown,et al.  Introduction to random signals and applied Kalman filtering : with MATLAB exercises and solutions , 1996 .

[13]  John L. Junkins,et al.  " Vision-Based Navigation for Rendezvous , Docking and Proximity Operation " , 1999 .

[14]  H.F. Durrant-Whyte,et al.  A new approach for filtering nonlinear systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[15]  S. A. Banani,et al.  A New Version of Unscented Kalman Filter , 2007 .

[16]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[17]  Jong-Hwan Kim,et al.  Unscented Filtering in a Unit Quaternion Space for Spacecraft Attitude Estimation , 2007, 2007 IEEE International Symposium on Industrial Electronics.

[18]  J. Junkins,et al.  Stereographic Orientation Parameters for Attitude Dynamics: A Generalization of the Rodrigues Parameters , 1996 .

[19]  John L. Crassidis,et al.  Attitude estimation for large field-of-view sensors , 2006 .

[20]  J. Junkins,et al.  Analytical Mechanics of Space Systems , 2003 .