# DOA estimation of moving, radiating source in the near-field with nonuniform Doppler shifting

I am trying to estimate the DOA of a radiating source using two passive sensors.

In the case of a stationary source, I find the lag $$k$$ of the maximum in the sample cross-covariance sequence $$E \lbrace x(t) y(t-k) \rbrace$$ between both Signals $$x(t)$$ and $$y(t)$$ and relate this delay to the DOA using a trigonometric relation.

Now I have the problem of a moving source which causes both time signals to be stretched or compressed on the time axis depending on whether the source is moving towards or away from the sensor. Furthermore, the source is close to the sensors. Therefore, $$x(t)$$ can be compressed and $$y(t)$$ stretched or any other combination. This causes the correlation of both Signals to become smaller.

Question: How do I estimate the DOA using both time series in the presence of nonuniform stretching/squeezing?

• you really need a third sensor for the near passive problem. – user28715 Jun 17 '19 at 12:03
• Can you explain why? – Crenguta Jun 17 '19 at 13:14
• you are measuring a curved wavefront. it’s just the geometry – user28715 Jun 17 '19 at 13:25