The detection of weak, ground-moving targets can be improved through effective utilization of additional target signal energy collected over an extended dwell time. The signal model used in conventional radar processing limits integration of signal energy over an extended dwell. Two solutions that consider the complexity of the extended-dwell signal model and effectively combine signal energy collected over a long dwell are presented. The first solution is a single-channel algorithm that provides an estimate of the optimal detector to maximize output signal-to-interference-plus-noise ratio for the extended dwell time signal. Rather than searching for the optimal detector in an intractably large filter bank that contains all combinations of phase components, the single-channel algorithm projects dictionary entries against the data to estimate the signal’s linear and nonlinear phase components sequentially with small, phase-specific dictionaries in a multistage process. When used as the detector, the signal model formed from the estimated phase components yields near optimal performance for a wide range of target parameters for dwell times up to four seconds. In comparison, conventional radar processing methods are limited to an integration time of approximately 100 milliseconds. The second solution is a multichannel, multistage algorithm based on element-space pre-Doppler space-time-adaptive processing with two modifications that make it suitable for detection of weak targets whose energy is collected over an extended dwell time. The multichannel solution detects targets with lower radial velocities at significantly lower signal-to-noise ratios (SNRs) than conventional radar processing methods. The decrease in required input SNR for the multichannel solution as compared to conventional methods nearly doubles the detection range for a typical target of interest. Future related research includes extension of these concepts to other radar applications and investigation of algorithm performance for the multiple-target scenario.