Pulse-Doppler radar has been successfully applied to surveillance and tracking of both moving and stationary targets. For efficient processing of radar returns, delay-Doppler plane is discretized and FFT techniques are employed to compute matched filter output on this discrete grid. However, for targets whose delay-Doppler values do not coincide with the computation grid, the detection performance degrades considerably. Especially for detecting strong and closely spaced targets this causes miss detections and false alarms. Although compressive sensing based techniques provide sparse and high resolution results at sub-Nyquist sampling rates, straightforward application of these techniques is significantly more sensitive to the off-grid problem. Here a novel and OMP based sparse reconstruction technique with parameter perturbation, named as PPOMP, is proposed for robust delay-Doppler radar processing even under the off-grid case. In the proposed technique, the selected dictionary parameters are perturbed towards directions to decrease the orthogonal residual norm. A new performance metric based on Kull-back-Leibler Divergence (KLD) is proposed to better characterize the error between actual and reconstructed parameter spaces. © 2014 IEEE.