An Algorithm For Estimating Rotation Speed From Projections
A synthetic aperture radar (SAR) is a microwave radar system mounted on a moving platform, such as an aircraft or a satellite, to image strips or pitches of terrain. It can also be used as ground-based radar to image orbiting objects. It has been shown that the formulation of the SAR is equivalent to the backprojection method commonly used in the computer-aided tomography (CAT). More specifically, if a chirp signal is transmitted by the radar, the demodulated returned signal at each angle approximates a piece of the onedimensional Fourier transform of the central projection of the object at the corresponding angle. According to the Fourier-slice theorem, this in turn equals to a slice of the threedimension Fourier transform of the imaged object. Hence, in order to accurately reconstruct the object, it is important to first know the relative position of the antenna and the object at every transmitting/receiving time instance. Equivalently, in the scenario of a rotating object, we are interested in estimating the angular velocity. In this paper, we present a new algorithm for estimating the rotation speed of an point source which is orbiting around a fixed axis. There are three phasles in our algorithm. In the first phase, the preprocessing step, we use a priori information to obtain a range of possible rotation speeds. Accordingly, we can reconstruct images using different rotation speeds in the second phase. In the third phase. We compute the variance of the distribution of each of the reconstructed point source. Presumably, the ideally reconstructed image would have smallest variance, while all the other images will have larger variances due to the non-linear effects induced during the reconstruction phase. We have applied this algorithm to a number of simulated data and satisfactory results are obtained. With this algorithm, we can estimate the rotation speed with error less than 2% in more than 85% of the cases. The average estimation error is less than 0.5%, and the largest error is only 5.7%.