Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPSdenied environments. Starlight...Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPSdenied environments. Starlight refraction compensates for the significant along-track position error that occurs from only using gravity gradients and benefits from integration in terms of improved accuracy in radial and cross-track position estimates. The between-epoch differencing of gravity gradients is employed to eliminate slowly varying measurement biases and noise near the orbit revolution frequency. The refraction angle measurements are directly used and its Jacobian matrix derived from an implicit observation equation. An information fusion filter based on a sequential extended Kalman filter is developed for the orbit determination. Truth-model simulations are used to test the performance of the algorithm, and the effects of differencing intervals and orbital heights are analyzed. A semi-simulation study using actual gravity gradient data from the Gravity field and steady-state Ocean Circulation Explorer（GOCE） combined with simulated starlight refraction measurements is further conducted, and a three-dimensional position accuracy of better than 100 m is achieved.展开更多
Compared with a conventional unscented Kalman filter(UKF),the recently proposed marginalized unscented Kalman filter(MUKF)uses a partially sampling strategy to achieve similar filter accuracy with fewer sigma points,d...Compared with a conventional unscented Kalman filter(UKF),the recently proposed marginalized unscented Kalman filter(MUKF)uses a partially sampling strategy to achieve similar filter accuracy with fewer sigma points,demonstrating its powerful ability to deal with state estimation with mixed linearity and nonlinearity.However,the hypothesis that the accuracy of MUKF is equivalent to that of UKF is not true for all systems.In this paper,it is proved that when the state equation is expressed as a differential equation,the accuracy of MUKF is equivalent to that of UKF only when the propagations of the states to be sampled and the states not to be sampled in MUKF are independent of each other.The above condition corresponds to a common problem in engineering,which is a system with measurement biases.Through theoretical proof and numerical simulation,it is verified in this paper that for the systems with measurement biases,the differences of the computed means and covariances in filtering recursions between MUKF and UKF are restricted to the same order infinitesimal as the square of the scaling parameter.To sum up,this paper evaluates the accuracy of MUKF,providing references for engineers to choose MUKF or UKF in different systems.展开更多
基金supported by the National Natural Science Foundation of China (No.11002008)funded in part by Ministry of Science and Technology of China (No.2014CB845303)
文摘Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPSdenied environments. Starlight refraction compensates for the significant along-track position error that occurs from only using gravity gradients and benefits from integration in terms of improved accuracy in radial and cross-track position estimates. The between-epoch differencing of gravity gradients is employed to eliminate slowly varying measurement biases and noise near the orbit revolution frequency. The refraction angle measurements are directly used and its Jacobian matrix derived from an implicit observation equation. An information fusion filter based on a sequential extended Kalman filter is developed for the orbit determination. Truth-model simulations are used to test the performance of the algorithm, and the effects of differencing intervals and orbital heights are analyzed. A semi-simulation study using actual gravity gradient data from the Gravity field and steady-state Ocean Circulation Explorer（GOCE） combined with simulated starlight refraction measurements is further conducted, and a three-dimensional position accuracy of better than 100 m is achieved.
基金supported in part by the National Natural Science Foundation of China under Grant U21B6001 and in part by the Beijing Nova Program under Grant Z201100006820102.
文摘Compared with a conventional unscented Kalman filter(UKF),the recently proposed marginalized unscented Kalman filter(MUKF)uses a partially sampling strategy to achieve similar filter accuracy with fewer sigma points,demonstrating its powerful ability to deal with state estimation with mixed linearity and nonlinearity.However,the hypothesis that the accuracy of MUKF is equivalent to that of UKF is not true for all systems.In this paper,it is proved that when the state equation is expressed as a differential equation,the accuracy of MUKF is equivalent to that of UKF only when the propagations of the states to be sampled and the states not to be sampled in MUKF are independent of each other.The above condition corresponds to a common problem in engineering,which is a system with measurement biases.Through theoretical proof and numerical simulation,it is verified in this paper that for the systems with measurement biases,the differences of the computed means and covariances in filtering recursions between MUKF and UKF are restricted to the same order infinitesimal as the square of the scaling parameter.To sum up,this paper evaluates the accuracy of MUKF,providing references for engineers to choose MUKF or UKF in different systems.
