Analyzing the Unscented Kalman Filter Robustness for Orbit Determination through Global Positioning System Signals

The nonlinear unscented Kalman filter (UKF) is evaluated for the satellite orbit determination problem, using Global Positioning System (GPS) measurements. The assessment is based on the robustness of the filter. The main subjects for the evaluation are convergence speed and dynamical model complexity. Such assessment is based on comparing the UKF results with the extended Kalman filter (EKF) results for the solution of the same problem. Based on the analysis of such criteria, the advantages and drawbacks of the implementations are presented. In this orbit determination problem, the focus is to analyze UKF convergence behavior using different sampling rates for the GPS signals, where scattering of measurements will be taken into account. A second aim is to evaluate how the dynamical model complexity affects the performance of the estimators in such adverse situation. After solving the real-time satellite orbit determination problem using actual GPS measurements, through EKF and UKF algorithms, the results obtained are compared in computational terms such as complexity, convergence, and accuracy.

[1]  H. K. Kuga,et al.  Non Linear Sigma Point Kalman Filter Applied to Orbit Determination Using GPS Measurements , 2009 .

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

[3]  Oliver Montenbruck,et al.  Satellite Orbits: Models, Methods and Applications , 2000 .

[4]  Paula Cristiane Pinto Mesquita Pardal,et al.  A Discussion Related to Orbit Determination Using Nonlinear Sigma Point Kalman Filter , 2009 .

[5]  Halil Ersin Soken,et al.  REKF and RUKF development for pico satellite attitude estimation in the presence of measurement faults , 2011, Proceedings of 5th International Conference on Recent Advances in Space Technologies - RAST2011.

[6]  Xiaoji Niu,et al.  Performance Comparison of the Extended and the Unscented Kalman Filter for Integrated GPS and MEMS-Based Inertial Systems , 2005 .

[7]  Richard A. Brown,et al.  Introduction to random signals and applied kalman filtering (3rd ed , 2012 .

[8]  Paula Cristiane Pinto Mesquita Pardal,et al.  ROBUSTNESS ASSESSMENT BETWEEN SIGMA POINT AND EXTENDED KALMAN FILTER FOR ORBIT DETERMINATION , 2011 .

[9]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[10]  W. M. Kaula.  Theory of satellite geodesy , 1966 .

[11]  Paula Cristiane Pinto Mesquita Pardal,et al.  Comparing the Extended and the Sigma Point Kalman Filters for Orbit Determination Modeling Using GPS Measurements , 2010 .

[12]  Rudolph van der Merwe,et al.  Sigma-point kalman filters for probabilistic inference in dynamic state-space models , 2004 .

[13]  R. Grover Brown,et al.  A Kalman Filter Approach to Precision GPS Geodesy , 1983 .

[14]  Helio Koiti Kuga,et al.  Single frequency GPS measurements in real-time artificial satellite , 2003 .

[15]  Peter S. Maybeck,et al.  Stochastic Models, Estimation And Control , 2012 .