This paper presents the derivation of Gauss-Newton filter in linear cases and an analysis of its properties. Based on the minimum variance theorem, the Gauss-Newton filter is constructed and derived, including its sta...This paper presents the derivation of Gauss-Newton filter in linear cases and an analysis of its properties. Based on the minimum variance theorem, the Gauss-Newton filter is constructed and derived, including its state transition equation, observation equation and filtering process. Then, the delicate relationship between the Gauss-Aitken filter and the Kalman filter is discussed and it is verified that without process noise the two filters are equivalent. Finally, some simulations are conducted. The result shows that the Gauss-Aitken filter is superior to the Kalman filter in some aspects.展开更多
In this paper, a new passive modified iterated extended Kalman filter （MIEKF） using the combined set of beatings and frequency measurements in Earth Centered Inertial （ECI） coordinate is proposed. A new measuremen...In this paper, a new passive modified iterated extended Kalman filter （MIEKF） using the combined set of beatings and frequency measurements in Earth Centered Inertial （ECI） coordinate is proposed. A new measurement update equation of MIEKF is derived by modifying the objective function of the Gauss-Newton iteration. A new gain equation and iteration termination criteria are acquired by applying the property of the maximum likelihood estimate. The approximated second order linearized state propagation equation, Jacobian matrix of state transfer and measurement equations are derived in satellite two-body movement. The tracking performances of MIEKF, iterated extended Kalman filter （IEKF） and extended Kalman filter （EKF） are compared via Monte Carlo simulations through simulated data from STK8.1. Simulation results indicate that the proposed MIEKF is possible to passively track low earth circular orbit satellite by a high earth orbit satellite, and has higher tracking precision than the IEKF and EKF.展开更多
文摘This paper presents the derivation of Gauss-Newton filter in linear cases and an analysis of its properties. Based on the minimum variance theorem, the Gauss-Newton filter is constructed and derived, including its state transition equation, observation equation and filtering process. Then, the delicate relationship between the Gauss-Aitken filter and the Kalman filter is discussed and it is verified that without process noise the two filters are equivalent. Finally, some simulations are conducted. The result shows that the Gauss-Aitken filter is superior to the Kalman filter in some aspects.
基金partly supported by the National Natural Science Foundation of China(No.61104196)the China Specialized Research Fund for the Doctoral Program of Higher Education(No.200802881017)+1 种基金Nanjing University of Science and Technology Research Funding(No.2010ZYTS051)the 'Zijin star' Research Funding(No.AB41381)
文摘In this paper, a new passive modified iterated extended Kalman filter （MIEKF） using the combined set of beatings and frequency measurements in Earth Centered Inertial （ECI） coordinate is proposed. A new measurement update equation of MIEKF is derived by modifying the objective function of the Gauss-Newton iteration. A new gain equation and iteration termination criteria are acquired by applying the property of the maximum likelihood estimate. The approximated second order linearized state propagation equation, Jacobian matrix of state transfer and measurement equations are derived in satellite two-body movement. The tracking performances of MIEKF, iterated extended Kalman filter （IEKF） and extended Kalman filter （EKF） are compared via Monte Carlo simulations through simulated data from STK8.1. Simulation results indicate that the proposed MIEKF is possible to passively track low earth circular orbit satellite by a high earth orbit satellite, and has higher tracking precision than the IEKF and EKF.
