synthetic aperture radar (sar)

Synthetic Aperture Radar Synthetic Aperture Radar (SAR)(SAR)

Ground RegionGround Region

We took a small sample of a SAR image to use as test data

Flight SimulationFlight SimulationRealistic

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

Beam ShapeBeam ShapeOne of the sub-

functions we wrote calculates the beam pattern for any horizontal and vertical beam angle

ROI ClosureROI ClosureAll of the ground points that

affect the data points which give information about the ROI

ROI ClosureROI ClosureUnion of intersections of the

beam pattern and a radius for which ground pixel reflections are being sampled

Data from ground pixelData from ground pixelEach 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

Closure for a data pointClosure for a data pointEach 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 PointCorresponding Ground Pixels

FFHHFFThe 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+nFHd=FHFg

SAR Possibilities 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.

SAR Possibilities SAR Possibilities Ground elevation estimation.Extend to bistatic SAR.Extend to continuous wave signaling

(will improve rank of F ).

Future WorkFuture 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.