Unscented Kalman filter and its nonlinear application for tracking a moving target

The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 40 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. To overcome these limitations, this paper proposes the unscented Kalman filter (UKF). And the algorithms of the FEKF, SEKF and UKF are given. Furthermore, the state models and measurement models of a target are set up. For comparison purpose, the three algorithms is simulated for the target tracking, and the algorithm performance is analyzed and compared by the simulation results of FEKF, SEKF and UKF. Numerical results demonstrate that FEKF and UKF give almost identical results while the estimates of SEKF are clearly worse. The UKF is easier to implement, avoiding Jacobian and Hessian matrices computation.