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A new constant false alarm rate (CFAR) target detector for synthetic aperture radar (SAR) images is developed. For each pixel under test, both the local probability density function (PDF) of the pixel and the clutter PDF in the reference window are estimated by the non-parametric density estimation. The target detector is defined as the mean square error (MSE) distance between the two PDFs. The CFAR detection in SAR images having multiplicative noise is achieved by adaptive kernel bandwidth proportional to the clutter level. In addition, for obtaining a threshold with respect to a given probability of false alarm (PFA), an unsupervised null distribution fitting method with outlier rejection is proposed. The effectiveness of the proposed target detector is demonstrated by the experiment result using the RADATSAT-2 SAR image.