As a target moves in the cross-range (azimuth) direction, it rotates relative to a radar. Over a limited observation interval, target points at different azimuths have different range rates that are approximately constant with time. The discrete Fourier transform can be used to construct multi- pulse filters that are matched to the different constant- frequency Doppler components. Maneuvers and other unpredictable effects introduce time varying range rates that defocus the target image on a range-Doppler map. Representations of instantaneous frequency vs. time attempt to reduce blurring by accurate portrayal of time-varying Doppler shifts. An alternative, ideal receiver (correlation) approach to adaptive ISAR focusing is considered here. The predicted delay history of each target point is corrected so as to maintain focus when the corresponding reference function is correlated with echo data. Proposed delay and/or target rotation corrections can be evaluated by comparing test images. For a delay-and-sum synthetic beam former, the nth test image is formed by adding delay-corrected samples of the nth echo to an image that has been sequentially constructed with previous echoes. Image bandwidth can be used as a focus measure for selecting the test image with the best delay/rotation correction. The final image is sequentially constructed from the best test images. The resulting image- based tracker can incorporate a dynamic model as in Kalman filtering and is similar to time warp compensation in speech classifiers.
Richard A. Altes, Richard A. Altes,
"Adaptive ISAR focusing of distributed time-varying targets", Proc. SPIE 3462, Radar Processing, Technology, and Applications III, (14 October 1998); doi: 10.1117/12.326761; https://doi.org/10.1117/12.326761