A fast FRFT based detection algorithm of multiple moving targets in sea clutter

Abstract

On the basis of the detection and estimation model of multiple moving targets, a new algorithm based on wavelet packet transform (WPT) and fractional Fourier transform (FRFT) is proposed for weak moving targets detection in sea clutter. The multi-resolution property of WPT and the characteristic of good energy concentration on LFM signals in FRFT domain are combined together. At first, optimal wavelet tree is calculated using "minimum Shannon entropy" and threshold censored method is used to suppress sea clutter of different frequency bands. Then, take the absolute amplitude of signals after FRFT as test statistic and search for peaks in two dimensions with the threshold. Grading iterative method is used for parameter estimation with fast calculation speed and the shading problem between multiple targets is solved through "CLEAN" method. In the end, simulations with IPIX data indicate that the proposed algorithm has good performance of detecting low-observable moving targets in sea clutter.

Detection of low observable moving target in sea clutter via fractal characteristics in fractional Fourier transform domain

“…The kernel of FRFT is a chirp signal, as a result, if a LFM signal is projected onto a rotated frequency axis with a proper angle, the energy distribution will be highly concentrated with a impulse function. Within the observation time T, the received signal model of single moving target in the presence of sea clutter can be characterised as follows [20,24] x(t) = s(t) + w(t) = A exp j2pf 0 t + jpmt 2 + c(t) + n(t), |t| ≤ T…”

“…When the time series of sea clutter in FRFT domain Y p is considered as 'random walk' process, which should be satisfied with (20), the process under investigation is said to be a fractal process. Given a time series of sea clutter, we can obtain the fluctuation function log 2 F(m) in FRFT domain at different scales m. If the fractal characteristic of sea clutter in FRFT domain coincides with the theoretical model, log 2 F(m) will increase with log 2 (m) in a linear manner.…”

“…However, the results of [13] show that using this model the Hurst exponents of sea clutter and primary target are almost the same, which are very close to 1. Let us now consider Y p as an 'increment' process and then check whether it satisfies the condition (20). From Fig.…”

“…Also it will save a lot of time using the grading iterative method to search for the best transform order [20,24]. Since the fractal characteristics are estimated according to the fractal curves within the scale-invariant interval 2 5 -2 10 , it needs about 1000 samples to achieve the true real-time processing, which is about 1 s with 1000 Hz sampling frequency of IPIX radar.…”

“…Based on the above analysis, when sea clutter in FRFT domain is referred as fractal, the following conditions should be satisfied: (i) it should have the form of (20), which indicates the self-similarity property within the scale-invariant interval; and (ii) the FD should be bigger than its topological dimension with stability. Both of the two requirements are well satisfied using dataset_17 and dataset_31 with the results in Figs.…”