We develop an adjustable Kalman smoother (AKS) for local mean estimation of sea clutter, where the sea clutter has a spatially correlated K-distribution, and the spatial correlation is modeled by a first order autoregressive (AR) process. For this model, the Wiener filter is the optimal linear estimator of the clutter mean and the AKS is an adaptive, computationally efficient implementation of the Wiener filter. The AR(1) model is parameterized by four parameters which are estimated (adjusted) adaptively from the data. Performance of the detector employing the AKS for local mean estimation is compared to the cell-averaging constant false alarm rate (CA-CFAR) detector, the fixed-CFAR detector that uses the global clutter mean, and the ideal-CFAR detector that has knowledge of the local clutter mean. The AKS-based detector significantly outperforms CACFAR detectors of various lengths as well as the fixed-CFAR detector, and approaches the performance of the ideal-CFAR detector for longer correlation ranges.