Radar offers unique advantages over other sensors for the detection of humans, such as remote operation during virtually all weather and lighting conditions, increased range, and better coverage. Many current radar-based human detection systems employ some type of Fourier analysis, such as Doppler processing. However, in many environments, the signal-to-noise ratio (SNR) of human returns is quite low. Furthermore, Fourier-based techniques assume a linear variation in target phase over the aperture, whereas human targets have a highly nonlinear phase history. The resulting phase mismatch causes significant SNR loss in the detector itself. In this work, human target modeling is used to derive a more accurate non-linear approximation to the true target phase history. Two algorithms are proposed: a parameter estimation-based optimized non-linear phase (ONLP) detector, and a dictionary search-based enhanced optimized non-linear phase (EnONLP) detector. The ONLP algorithm optimizes the likelihood ratio over the unknown model parameters to derive a more accurate approximation to the expected human return. The EnONLP algorithm stores expected target signatures generated for each possible combination of model parameters in a dictionary, and then applies Orthogonal Matching Pursuit (OMP) to determine the optimal linear combination of dictionary entries that comprises the measured radar data. Thus, unlike the ONLP, the EnONLP algorithm also has the capability of detecting the presence of multiple human targets. Cramer-Rao bounds (CRB) on parameter estimates and receiver operating characteristics (ROC) curves are used to validate analytically the performance of both proposed methods to that of conventional, fully adaptive STAP. Finally, application of EnONLP to target characterization is illustrated.