摘要
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.
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.
