Optimal and Suboptimal Velocity Estimators for ArcSAR With Distributed Target

Two new methods of radial velocity estimation for distributed targets in arc-scanning synthetic aperture radar (ArcSAR) systems, namely, the maximum-likelihood estimator (MLE) and the suboptimal method based on the least squares estimation (LSE), are proposed, derived, and analyzed. To this end, we establish that $n$ scatterers of the distributed target are uniformly dispersed within the radar resolution cell of dimensions $a \times b$ and they move randomly at different velocities. Furthermore, the effect of the antenna pattern is considered to characterize the amplitude of the scattered signal. Thus, from the coherent integration of the scatters at each pulse repetition interval in radar scanning, $m$ data sequences are obtained as samples of the composite signal, which follows a multivariate normal distribution. From this, the covariance matrix, upon which the methods are based, is derived. Simulations have been carried out to compare the new methods with existing methods, namely, phase, energy, and correlation, as a function of the signal-to-noise ratio. Finally, the results show that the MLE and LSE methods outperform the conventional methods, providing a gain of more than 10 dB.