基于库普曼-卡尔曼滤波的海面目标检测方法
Marine Target Detection Based on Koopman-Kalman Filter
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摘要: 海面目标检测受海杂波影响严重,海杂波具有非线性、非平稳、非高斯等特性,使得现有基于统计分布、特征提取、深度学习等技术的检测方法在动态海杂波环境下依然面临挑战。从海杂波时空特性分析出发,提出了基于库普曼算子理论与卡尔曼滤波方法相结合的海杂波预测模型,并构建了海杂波背景下的目标检测方法。首先,该方法通过构造时空二维海杂波的Hankel矩阵形式,将海杂波矩阵映射到高维空间;随后,利用动态模式分解方法对升维后的海杂波矩阵进行线性化建模,挖掘海杂波内在时空非线性动力规律,并通过库普曼模态和库普曼特征值建立海杂波线性演化模型;其次,将海杂波线性演化模型转化为状态空间方程形式,进而与卡尔曼滤波方法结合,实现对海杂波时空二维序列的短时预测;最后,将预测绝对值误差作为检测统计量,构建形成库普曼-卡尔曼滤波检测器,在虚警概率一定的情况下设置检测门限,判决目标有无。所提方法将海面目标检测问题转化为对海杂波时空序列的预测问题,检测过程无需迭代训练和先验知识,而且对于短时目标检测具有一定优势。基于实测数据的实验结果表明,该方法在目标出现时长仅为10 ms的短时条件下,检测性能优于现有对比方法,为海面目标检测提供了一种潜在的新途径。Abstract: 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.
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