Long-time coherent integration detection of weak manoeuvring target via integration algorithm, improved axis rotation discrete chirp-Fourier transform

Range/Doppler migrations, which result from the integration time increasing and the target´s manoeuvring motion, will affect the coherent integration performance severely. To deal with range/Doppler migration, a novel coherent integration algorithm, improved axis rotation discrete chirp-Fourier transform (IAR-DCFT), is proposed. IAR-DCFT could eliminate range migration via improved axis rotation transform, and realise the compensation of Doppler migration and coherent integration via discrete chirp-Fourier transform. IAR-DCFT may be regarded as tri-dimensional motion parameter filter banks, which is analogous to moving target detection that can be treated as Doppler filter banks, and estimate a target´s velocity, acceleration and jerk simultaneously. Then the derivations of maximum-likelihood estimator and likelihood ratio test detector show that IAR-DCFT is the optimal estimator and a detector. The performance of the optimal estimator is verified by comparing with Cramer-Rao lower bound. Subsequently, the detailed performance analyses of IAR-DCFT are provided, including coherent integration gain, coherent integration time, multi-target detection and computational complexity. Furthermore, the authors introduce the generalisation of IAR-DCFT, that is, multi-range-cell associated IAR-DCFT (MR-IAR-DCFT), which can be applied to detect a target with high-manoeuvring motion or used in a longer time integration case. Finally, some numerical experiments are given to verify the performance of IAR-DCFT and MR-IAR-DCFT.