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Attentions have been focused on the moving target detection in a high-resolution sea clutter. This study commences with a proposal of median-based estimator to estimate the power spectrum of high-resolution sea clutter by the time series observed in adjacent range cells and time intervals. The estimator provides a robust estimation when just a few aberrant time series happen in observation. Based on the estimator, a block-adaptive clutter suppression filter (BACSF) is designed to suppress the clutter prior to the pulse integration. Then, the residual clutter, the output of the BACSF, is modelled as spherically invariant random vector. Upon applying an adaptive normalised matched filter (ANMF) to the residual clutter, a residual clutter's ANMF detector is derived. Moreover, in high-resolution radar background, considering that the approximately stationary intervals of sea clutter and residual clutter are much shorter than the coherent processing interval, another heuristic block-ANMF detector is proposed. It can integrate more pulses and can achieve better performance than the ANMF detector does. This study concludes with the experiments of simulated target against the real sea clutter. The experimental results demonstrate that, when target's Doppler frequency is beyond strong clutter region, the ANMF detector and block-ANMF detector perform better in the residual clutter than in the clutter.