Doppler Coefficient Estimation for Synthetic Aperture Radar Using Sub-Aperture Interferogram
4. Simulations
We use ERS SAR as the simulation system, the parameters were the same as previous case, except that moving target speed, target heading, and sub-aperture size.
For convenience, we reference equation (8) to rewritten (6) as a type chirp signal form
We assume that a moving target heading is 161°, moving speed vary from 0.1m/sec to 30m/sec and the sub-aperture size is 39.90574m. We can to estimate the coefficient of
and
by follow the procedure of sub-aperture interferometry method described in section III. The relational frequency rate f
2 and estimate result of
is display in Figure.3, we can find the estimate results agree very well with the truth coefficient. The frequency f
1 and estimated results
of
is display in Figure.4. To observed the variation of Figure.4, we find when that f
1DY is larger than 2
p then
is deviant. Which is caused by the original signal is wrapped by 2
p , and
therefore the limit of interferometric approach is that the absolute value of 2f
2DY
2 and f
1DY have to be smaller than 2
p. In addition, we can obtain the minimum velocity of moving targets is restricted within the resolution of phase of SAR.
In last, we summarize, the estimation procedure consists of six steps:
Step 1: Select a appropriate sub-aperture size and then segment recorded data to a finite number of subsets with the same size.
Step 2: transform {
Ðg(y)} into {
fj(y)} by equation (10).
Step 3: evaluate the phase difference by equation (12).
Step 4: use equation (13) to estimate
;
Step 5: Once
is available, follow equation (16) to obtain {
(y)} ;
Step 6: evaluate the phase difference between{
fj(y) and {
(y)} , to obtain
;
5. Conclusion
In this paper, we have developed an algorithm for estimate the coefficients of chirp signal. Through some analysis, we proved the relation of a phase difference of a series subsets' interferometric signals with the coefficients of chirp signal. In this algorithm, the coefficients
and
are contrary to the sub-aperture size
DY . So sub-aperture sizes selection is a trade-off between the target velocity and noise.
We finally applied the algorithm to estimate the target speed of a simulation data of ERS SAR signals. Computer simulation results agree very well with the theoretical performance derived. And we find that the cost of computation is fewer and only need a small amount of samples of the data compare to some other methods.
Current, this algorithm is confined to use the principle value of the phase function, so to overcome this restriction, it could be to estimate the higher-speed's target and support a lower SNR of a signal.
Refferences
- J. Patrick Fitch, "Synthetic Aperture Radar," New York : Springer-Verlag , 1988.
- R.K. Raney, "Synthetic aperture imaging radar and moving target," IEEE Trans. Aerospace and Electronic Systems, Vol. AES-7, pp. 499-505, 1971.
- Soumekh Mehrdad, "Fourier array imaging," Englewood Cliffs, N.J : PTR Prentice-Hall, c1994.
- Slocumb, B.J.; Kitchen, J., "A polynomial phase parameter estimation-phase unwrapping algorithm," ICASSP-94: IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 129 -132, 1994.
- Besson, O.; Ghogho, N.; Swami, A., "Parameter estimation for random amplitude chirp signals ," IEEE Transactions on Signal Processing, vol. 47, pp 3208 -3219,1999.
- Jong-Sen Lee, Karl W. Hoppel, "Intensity and phase statistics of multilook polarimetric and interferometric SAR imagery", IEEE Transactions on Geoscience and Remote Sensing v 32 n 5 p 1017-1027, Sept 1994.
Azimuth position(meter)
Figure.1. The histories of some interferometric signals phase from the original signal
Azimuth position(meter)
Figure.2. The histories of some interferometric signals phase from the dechirped signal
Velocity(m/sec)
Figure.3. The frequency rate f2 and estamate results .
f2: solid line, " * ":
Velocity(m/sec)
Figure.4. The frequency f1 and estimate result .
f1: solid line, " * ":
