Multiaircraft formation identification for narrowband coherent radar in a long coherent integration time

In this paper, we first propose a novel multiaircraft formation (MAF) signal model for narrowband coherent radar in a long coherent integration time (LCIT). We then give a quantitative analysis on the phase order approximation of the MAF echoes according to the LCIT duration with a given set of target motion and radar system parameters. It is shown that these echoes in a certain LCIT can be well approximated by multiple chirp signals or multiple cubic phase signals for MAFs with rigid or nonrigid structures, respectively. Subsequently, we propose to apply third-order polynomial Fourier transform (PFT), to accurately estimate the MAF parameters, which include aircraft number and different order motion parameters for each aircraft. The performance of third-order PFT is compared with the existing third-order polynomial generalized Radon transform (GRT) in time-frequency domain. It is shown that the third-order PFT has higher parameter estimation resolution than the third-order polynomial GRT, as well as higher estimation accuracies with some additional computational complexity. Finally, some numerical experiments are provided to demonstrate the effectiveness of the proposed MAF model and the parameter estimation method by using simulation and real measured data.