This presentation deals with estimation of the target sound Direction of Arrival (DoA) for a Hearing Aid System (HAS) which can connect to a wireless microphone worn by a target talker. In this setup, the HAS is "informed" about the almost noise-free content of the target sound via the wireless microphone and can use this information for the DoA estimation. Here, we propose an "informed" DoA estimator based on the Time Difference of Arrival (TDoA) of the target sound at two microphones mounted on the ears of the HAS user---one microphone on each ear. To estimate the TDoA and the DoA, we propose a maximum likelihood framework relying on the noise-free target sound and estimation of the ambient noise characteristics. We show how the proposed ML framework allows us to estimate the TDoA and the DoA jointly or consecutively. Further, to evaluate the likelihood function efficiently, we resort to an Inverse Discrete Fourier Transform (IDFT) technique. To study the performance of the proposed algorithms, we run simulations for various DoAs, Signal to Noise Ratios (SNRs), and distances in large crowd noise situations. In these situations, the proposed estimator improves the estimation performance markedly over a recently proposed "informed" TDoA-based DoA estimator.