Fractal properties of autoregressive spectrum and its application on weak target detection in sea clutter background

This study concerns the fractal properties of sea clutter in the power spectrum domain. To overcome the deficiencies of Fourier transform analysis, the power spectrum of the sea clutter is obtained by autoregressive (AR) spectrum estimation. The AR model is a linear predictive model, which estimates the power spectrum of sea clutter form its autocorrelation matrix and has a higher frequency resolution than Fourier analysis. This study concentrates on analysing the fractal property of the power spectrum based on AR spectral estimation and its application on weak target detection. First, fractional Brownian motion is taken as an example to prove the fractal property of the power spectrum. Then, real measured X-band data is used to verify the fractal property of the power spectrum of sea clutter. Finally, a novel detection method based on AR Hurst exponent is proposed and the factors influencing the fractal properties of power spectrum are analysed. The results show that the Hurst exponent of AR spectrum is effective for weak target detection in sea clutter background. Compared with the existing fractal method and the traditional constant false alarm rate (CFAR) method, the proposed method has a better detection performance.