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.