Redundant adaptive robust tracking of active satellite and error evaluation

An approach to active target satellite tracking is presented. The kinematic models based on differential orbital elements and unbiased converted measurements are adopted to approximate the dynamic orbital relative tracking system, and then followed by the proposed redundant adaptive robust extended Kalman filter (RAREKF). The analysis of working status of robust filters shows that the innovation controlled switching scheme in AREKF fails under the unmodelled non-linear errors that exist all the time in orbital motions, and the loss of filtering optimality will be caused. So, a tunable redundancy factor and a novel compensation function are introduced into the RAREKF by extending the sufficient conditions of stable filtering. To evaluate the result of this tracking method, a meaningful error index is provided by consideration of the errors from both the model and the filter. The simulation shows the superiority of the RAREKF over the AREKF, uncoupled extended Kalman filter (EKF) and the usual EKF. By using the provided index, it also illustrates the lowest error level and best performance of the proposed tracking method in all the compared ones with different models and filters.

[1]  K. Alfriend,et al.  State Transition Matrix of Relative Motion for the Perturbed Noncircular Reference Orbit , 2003 .

[2]  K. Xiong,et al.  Adaptive robust extended Kalman filter for nonlinear stochastic systems , 2008 .

[3]  Y. Bar-Shalom,et al.  Unbiased converted measurements for tracking , 1998 .

[4]  K. Alfriend,et al.  Evaluation and Comparison of Relative Motion Theories , 2005 .

[5]  Mark L. Psiaki,et al.  High-Altitude Satellite Relative Navigation Using Carrier-Phase Differential Global Positioning System Techniques , 2007 .

[6]  Penina Axelrad,et al.  Formation Design in Eccentric Orbits Using Linearized Equations of Relative Motion , 2006 .

[7]  Mark L. Psiaki,et al.  Modeling, Analysis, and Simulation of GPS Carrier Phase for Spacecraft Relative Navigation , 2005 .

[8]  John L. Junkins,et al.  Non-Gaussian error propagation in orbital mechanics , 1996 .

[9]  Thomas P. Yunck,et al.  Reduced-dynamic technique for precise orbit determination of low earth satellites , 1991 .

[10]  S. Kawase.  Intersatellite tracking methods for clustered geostationary satellites , 1990 .

[11]  Mark L. Psiaki,et al.  Autonomous Orbit Determination for Two Spacecraft from Relative Position Measurements , 1998 .

[12]  Hari B. Hablani,et al.  Autonomous Inertial Relative Navigation with Sight-Line-Stabilized Sensors for Spacecraft Rendezvous , 2009 .

[13]  B. T. Fang.  Satellite-to-Satellite Tracking Orbit Determination , 1979 .

[14]  Jang Gyu Lee,et al.  An Extended Robust H$_infty$Filter for Nonlinear Constrained Uncertain Systems , 2006, IEEE Transactions on Signal Processing.

[15]  Pini Gurfil,et al.  Cyclic Spacecraft Formations: Relative Motion Control Using Line-of-Sight Measurements Only , 2007 .

[16]  Chongzhao Han,et al.  Comments on "Unbiased converted measurements for tracking" , 2004 .

[17]  David K. Geller,et al.  Relative Angles-Only Navigation and Pose Estimation for Autonomous Orbital Rendezvous , 2006 .

[18]  Konrad Reif,et al.  Stochastic stability of the discrete-time extended Kalman filter , 1999, IEEE Trans. Autom. Control..

[19]  P. A. M. Abusali,et al.  Hybrid precise orbit determination strategy by global positioning system tracking , 2004 .

[20]  K. Preiss,et al.  Onboard orbit estimation with tracking and data relay satellite system data , 1981 .

[21]  J. Arrillaga,et al.  An adaptive Kalman filter for dynamic harmonic state estimation and harmonic injection tracking , 2005, IEEE Transactions on Power Delivery.