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We address the problem of detecting slow moving targets from a moving radar system using space-time adaptive processing (STAP) techniques. Optimum interference rejection is known to require the estimation and the subsequent inversion of an interference-plus-noise covariance matrix. To reduce the number of training samples involved in the estimation and the computational cost inherent to the inversion, many suboptimum STAP techniques have been proposed. Earlier attempts at unifying these techniques had a limited scope. In this paper, we propose a new canonical framework that unifies all of the STAP methods we are aware of. This framework can also be generalized to include the estimation of the covariance matrix and the compensation of the range dependence; it applies to monostatic and bistatic configurations. We also propose a new decomposition of the CSNR performance metric that can be used to understand the performance degradation specifically due to the use of a suboptimum method.