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The time-frequency analysis of nonstationary multicomponent linear frequency modulation (LFM) signals is still a challenging task due to their cross-term interferences. In this paper, a novel signal-dependent adaptive compact kernel based time-frequency distribution (CKD) named regional adaptive CKD (RACKD) is proposed. The proposed RACKD firstly represents the signal in the Doppler-lag (ν , τ) ambiguity domain, and then applies a signal-dependent regional compact kernel to filter the cross-term interferences, with preserving the auto-terms in the ambiguity domain. By automatically selecting the auto-terms' distribution area which represents the signals in the ambiguity domain, the parameters of the newly designed signal-dependent regional compact kernel can be adaptively set according to the signals to be processed. The proposed RACKD shows a more stable performance in the ability of cross-term rejection and component energy of signals concentration around their respective instantaneous frequency, compared to several existing state-of-the-art methods. Both simulation results and experimental results based on sea-truth data have validated the improved performance of the proposed method. For the simulated signal composed of one weak and two strong LFM components with crossing frequency, the proposed RACKD shows up to 2.6% gain as compared to the signal-dependent multidirectional distribution (MDD) approach. [ABSTRACT FROM AUTHOR]