Marine Target Detection Based on Koopman-Kalman Filter

Marine target detection is severely affected by sea clutter， which poses the nonlinear， non-stationary， and non-Gaussian characteristics. Existing detectors， based on statistical models， feature extraction， and deep learning， encounter challenges in dynamic sea clutter environments. Thus， a sea clutter prediction model based on the Koopman-Kalman filter （KKF） is proposed herein， and a marine target detector is constructed under the prediction model. First， a Hankel-matrix form of the spatial and temporal sea clutter is constructed， thereby transforming the sea clutter matrix into a higher-dimensional space. Subsequently， dynamic mode decomposition （DMD） is employed to perform linear modeling on the augmented sea clutter matrix， uncovering the inherent spatio-temporal nonlinear dynamic patterns of the sea clutter. A linear evolution model for sea clutter is then established using Koopman modes and Koopman eigenvalues. This model is then converted into a state-space equation form， which can be integrated with the Kalman filter to achieve short-term prediction of spatial and temporal sea clutter sequences. Finally， the absolute prediction error is utilized as the detection statistic. Additionally， a detection threshold is set to determine whether a target exists for a certain false alarm rate， thereby constructing the KKF detector. The proposed detector can transform marine target detection into a problem of predicting the spatio-temporal evolution of sea clutter. The detection process requires neither iterative training nor prior knowledge， making it particularly advantageous for short-duration target detection. Experimental results on measured data show that the proposed detector outperforms existing comparative approaches for a short duration， in which the target presence lasts only 10 ms， offering a promising approach for marine target detection.