Note that knowledge of is used to compensate the phase error introduced to by the channel estimates.
In Fig. 7, we plot the absolute difference between the rotation number obtained with the 2-dimensional approach and the analytic one, namely | ρ 2 D − ρ |, whereas in Fig. 8, we plot the error when using the phase-reduction hypothesis, namely | ρ 1 D − ρ |.
Meanwhile, by using the zero Doppler bin data, the phase error estimation can behave independently of position errors.
Then, by using the zero Doppler bin data, the phase error estimation can be performed well independent of position errors.
The first correct delay needs to be estimated using long-term integration so that the phase error will be sufficiently small to resolve 2π ambiguity.
This generates regions of interest which we use to estimate the phase errors.
Then, the weighted covariance matrix is obtained, and the eigenvector corresponding to the largest eigenvalue is used to correct the phase errors roughly.
In addition, the vibration signatures can be used to compensate the phase errors in SAR returns to eliminate the image blur [3, 4].
Because the proposed solution does not use hard decisions, the phase errors of the erroneous channel estimates are not amplified, and their influence on the overall algorithm performance is smaller than in the DD algorithm.
In this second approach, our aim is to improve the computational efficiency of the phase error estimation procedure by first determining regions of interest (ROI) for potential motion using a fast procedure and then performing phase error estimation only in these regions.
