Detection of small target in sea clutter via multiscale directional Lyapunov exponents

Purpose This study aims to provide a new method of multiscale directional Lyapunov exponents (MSDLE) calculated based on the state space reconstruction for the nonstationary time series, which can be applied to detect the small target covered by sea clutter. Design/methodology/approach Reconstructed state space is divided into non-overlapping submatrices whose columns are equal to a predetermined scale. The authors compute eigenvalues and eigenvectors of the covariance matrix of each submatrix and extract the principal components sigma(ip) and their corresponding eigenvectors. Then, the angles psi(ip) of eigenvectors between two successive submatrices were calculated. The curves of (sigma(ip), psi(ip)) reflect the nonlinear dynamics both in kinetic and directional and form a spectrum with multiscale. The fluctuations of (sigma(ip), psi(ip)), which are sensitive to the differences of backscatter between sea wave and target, are taken out as the features for the target detection. Findings The proposed method can reflect the local dynamics of sea clutter and the small target within sea clutter is easily detected. The test on the ice multiparameter imaging X-ban radar data and the comparison to K distribution based method illustrate the effectiveness of the proposed method. Originality/value The detection of a small target in sea clutter is a compelling issue, as the conventional statistical models cannot well describe the sea clutter on a larger timescale, and the methods based on statistics usually require the stationary sea clutter. It has been proven that sea clutter is nonlinear, nonstationary or cyclostationary and chaotic. The new method of MSDLE proposed in the paper can effectively and efficiently detect the small target covered by sea clutter, which can be also introduced and applied to military, aerospace and maritime fields.