This paper proposes a novel approach for the Direction-Of-Arrival (DOA) estimation of non-stationary signals. The proposed technique assumes signals characterized by Instantaneous Frequency (IF) laws and exploits IF estimates for improved DOA estimation. The focus is on achieving resolved and accurate DOA estimates for weak and closely spaced sources which demonstrate highly nonlinear and closely spaced time-varying IF signatures. The DOA estimation of a particular source is achieved by demodulation or stationarization of its signature and separating it from those of other sources. The source separation relies on the narrowband property of the demodulated signature and leads to improved Signal-to-Noise Ratio (SNR). The effectiveness of the proposed technique, in providing robust DOA estimation, is verified by simulation results.