비선형 자세 공간에서 UKF로 구현한 선박 위치 추적

Abstract

In this study, Lie group theory was used for implementing the unscented Kalman filter (UKF). The UKF was used to track an unmanned surface vehicle (USV) by using radar measurements and the data recorded by the automatic identification system. The attitude of the USV was represented using unit quaternions constituting a Lie group called the 3-sphere space (S³). The increment and difference in the attitudes in S³ constitute a Lie algebra. The correspondence between the Lie group component and the Lie algebra component was used by the exponential and logarithm functions of the UKF. Simulation studies verify that the Lie group based UKF results in better convergence property in Kalman gain, measurement innovation, and covariance, as well as better tracking accuracy than the traditional UKF.