Synthetic Aperture Radar (SAR)

1. Synthetic Aperture Radar (SAR)

2. Ground Region We took a small sample of a SAR image to use as test data

3. Flight Simulation • Realistic Parameters • Beam angle • Beam squint • Platform velocity • Platform altitude • Pulse duration • Ground pixel resolution • Sampling frequency • Number of samples • Carrier frequency • Transmit/Receive switching delay

4. Beam Shape • One of the sub-functions we wrote calculates the beam pattern for any horizontal and vertical beam angle

5. ROI Closure • All of the ground points that affect the data points which give information about the ROI

6. ROI Closure • Union of intersections of the beam pattern and a radius for which ground pixel reflections are being sampled

7. Data from ground pixel Each ground pixel affects a certain set of data points Figure 3 shows nulls in the data sets that are due to nulls in the beam pattern

8. Closure for a data point Each data point represents a sample taken at a certain time, so each data point collects reflectivity data from ground pixels in an area that is roughly the shape of the beam pattern Data Point Corresponding Ground Pixels

9. FHF • The data gathered is a linear combination of different ground reflectivities • F is a matrix that explains the mixing going on in the data • Each column holds data for a ground pixel • Each row is a different data sample mixed with information about the ground pixel it relates to • d=Fg+n • FHd=FHFg

10. SAR Possibilities • Optimum ML change detection: • d1 = F1 g + n1 d2 = F2 (g + δ) + n2 • Can obtain both g and the change δ in closed form. • GMTI: Incorporate moving targets into signal model. Can estimate target position, direction, and velocity vector. • Motion compensation: • Allow for errors in both data d and regressors F using weighted total least-squares techniques. • Estimate SAR trajectory using known strong targets of opportunity.

11. SAR Possibilities • Ground elevation estimation. • Extend to bistatic SAR. • Extend to continuous wave signaling (will improve rank of F ).

12. Future Work • Imposing Block Structure • If the structure of FHF could be made to be Toeplitz, or have a block diagonal structure with small diagonal blocks, then inversion of FHF would be easy. • Signal Design • Design the signal waveform to make FHF have a structure that is easily invertible. This may require transmitting a different pulse signal at each azimuth position. It may also require using pulse coded waveforms instead of chirps. • Antenna design • Suppose an antenna array is used. Then the array weights could be designed and made to vary with time in a fashion that imposes structure on FHF that makes it easy to invert.