Parameters estimation of linear frequency modulated signal using Kalman filter and its extended versions

The problem of linear frequency modulated (LFM) or chirp signal analysis is proposed in this paper. It is considered as an estimation theory problem in which the LFM parameters are underestimated in the presence of Gaussian noise. The proposed approach is based on the signal state-space model extraction and application of different versions of the Kalman filter. Since the state-space model of this problem is nonlinear, the standard Kalman filter cannot be utilized directly, so other versions of the Kalman filter should be used. The recently proposed, iterated extended Kalman filter (IEKF), unscented Kalman filter (UKF), and iterated unscented Kalman filter (IUKF) are suggested as solutions of the stated problem. Compared with the traditional Kalman filter methods, i.e., the Kalman filter based on the Tretter approximation and the extended Kalman filter (EKF), the proposed methods have advantages in estimation performance and convergence. Finally, the numerical simulations are given to show the capability of proposed methods.