Moving targets in SAR images cause phase modulation of the phase
history corresponding to the target. Depending on the motion, such
modulations cause SAR image distortions. A simple case is an
oscillating point reflector which causes sinusoidal phase
modulation. Such signals can be analyzed with time-frequency
techniques. The techniques reveal the time dependent Doppler frequency
corresponding to the target. Using both direct instantaneous frequency
estimates and quadratic time-frequency methods, we may estimate the
oscillation parameters. Examples are given from simulated and real
data. In the case of real data, the results agree well with ground
truth. The direct estimates are best for high signal-to-noise ratios
and single reflectors. In other cases the more sophisticated and
computationally intensive quadratic methods perform best.
Synthetic aperture radar (SAR) processors generally assume that the scene reflectors are stationary over the time of integration of the image. When this is not the case, various kinds of image distortions may occur, such as target displacement or smearing. In the present paper, oscillating targets are considered. It is shown that such targets are smeared in azimuth to an extent determined by the amplitude and frequency of the oscillation. The reason may be stated in terms of the slow-time Doppler shift of the target. The Doppler shift is not constant, but varies with aperture time. We show that time-frequency analysis provides useful tools to handle problems of this kind. The choice of analysis method is often difficult. Here, we compare several methods of the Cohen's class, and show good results with the data adaptive optimal kernel method. This method, being adaptive, dispenses with some of the trial-and-error often necessary with quadratic methods. We show data from a controlled experiment where oscillating reflectors were placed within a scene imaged by an airborne SAR system. The reflectors are smeared in azimuth. We estimate the amplitude and frequency of the oscillations from the time-frequency distributions.
Time-frequency analysis is useful for inverse synthetic aperture radar (ISAR) imaging of aircraft with general motion. For applications of ISAR images, quantifiable performance is preferrable. Such performance can be described in terms of effective resolution and dynamic range of an image, quantities that can be obtained from inpulse responses. The problem with this approach is that time-frequency ISAR impulse responses are signal dependent. Based on two representative test signals, four Cohen's class time-frequency methods are compared. The comparison uses estimated resolution and dynamic range from selected azimuth impulse responses. It is found that the adaptive optimal kernel estimator is best of the four tested. This method is less signal dependent than the other methods, and have reasonable dynamic range for radar imaging.
The key to successful ISAR imaging is frequency estimation, as the cross range position of scatteres on the target is determined from the differential Doppler shifts of the received radar signal. Many ISAR images are blurred when conventional processing is used. We show that such blurring can result because the full complexity of the target motion is not taken into account. A sufficiently general model shows that the Doppler shifts are time dependent. We give an example using a quadratic time-frequency method on radar data of an aircraft. Irregular motion is detected, and sharp images are formed in the case where the conventional ISAR processor gave a blurred image. The complexity of the target motion was verified using motion reference data.