DOA estimation with known waveforms in the presence of unknown time delays and Doppler shifts.

•A DOA estimation method for known waveform sources with different unknown time delays and Doppler shifts is proposed.•A Toeplitz dominant rule is developed to perform initial estimates for nonlinear least squares (NLS) with a reduced dimension.•The proposed method proposed method outperforms some existing algorithms and achieves CRB at high SNR and with a large number of snapshots.