The instantaneous frequency (IF) is a vital parameter for the analysis of non-stationary multicomponent signals, and plays an important role in space cone-shaped target recognition. For a cone-shaped target, IF estimation is not a trivial issue due to the proximity of the energy of the IF components, the intersections among different IF components, and the existence of noise. Compared with the general parameterized time-frequency (GPTF), the traditional Kalman filter can perform better when the energy of different signal components is close. Nevertheless, the traditional Kalman filter usually makes association mistakes at the intersections of IF components and is sensitive to the noise. In this paper, a novel IF estimation method based on modified Kalman filter (MKF) is proposed, in which the MKF is used to associate the intersecting IF trajectories obtained by the synchroextracting transform (SET). The core of MKF is the introduction of trajectory correction strategy in which a trajectory survival rate is defined to judge the occurrence of association mistakes. When the trajectory survival rate is below the predetermined threshold, it means that an association mistakes occurs, and then the new trajectories generated by the random sample consensus algorithm are used to correct the wrong associations timely. The trajectory correction strategy can effectively obviate the association mistakes caused by the intersections of IF components and the noise. The windowing technique is also used in the trajectory correction strategy to improve computational speed. The experimental results based on the electromagnetic computation data show that the proposed method is more robust and precise than the traditional Kalman filter. Moreover, the proposed method has great performance advantages compared with other methods (i.e., the multiridge detection, the ant colony optimization, and the GPTF methods) especially in the case of low signal noise ratio (SNR).
RANSAC algorithm for instantaneous frequency estimation and reconstruction of frequency-modulated undersampled signals
