The function of fringe search is to find the maximum amplitude of complex cross-correlation function and determine the
residual delay and delay rate with respective to correlator model. When the signals transmitted by deep space probes
have high SNR, the fringe search algorithm based on weighted least square estimation is very effective by tracking the
fringe phase without 2π ambiguities in the frequency and time domain respectively, but it is not suitable for very weak
signals when fringe phases include relatively large noises. According to VLBI data processing method for extra-galactic
radio sources, a robust 2D fringe search algorithm is proposed for radio interferometry of very weak downlink signals of
deep space probes. Compared with phase tracking fringe search algorithm, the proposed iterative process for searching
the maximum correlation amplitude is performed in the two dimensional delay and delay rate plane, which is insensitive
to large phase fluctuation in time and frequency domain, phase cycle ambiguities and phase outliers, so it is an optimal
algorithm and much more robust for very weak signals. It can be proved theoretically that the proposed algorithm is
equivalent to weighted least square estimation. Finally, fringe search for the VLBI observation of Mars Express is
presented by using a software program implementing the iterative algorithm.
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