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Adaptive detection of signals embedded in non-Gaussian clutter is an important challenge for radar engineers. We present an analysis of sea clutter nonstationarity with respect to clutter covariance matrix estimation and its impact on the constant false alarm rate (CFAR) property of the normalized adaptive matched filter (NAMF). Three covariance matrix estimators, e.g., the sample covariance matrix (SCM), the normalized sample covariance matrix (NSCM), and the approximate maximum likelihood (AML) estimators, have been investigated. The impact of nonstationarity, which emerges in the statistical analysis of the clutter data, is measured in terms of probability of false alarm and probability of detection. Performance analysis is presented using both simulated data and measured sea clutter data recorded by two different X-band radars, namely, the Fynmeet radar and the IPIX radar.