基于核密度估计的海杂波分布建模：显著提升目标检测性能

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本文主要探讨了海杂波分布建模的一种创新方法，即核密度估计（Kernel Density Estimation, KDE）在海洋目标检测中的应用。海洋表面漂浮目标的探测过程中，准确理解海杂波的分布至关重要，因为它直接影响到决策区域的划定。传统参数模型在面对海洋状况的波动时往往无法提供足够的精确性，因此，研究人员提出了一个无需先验知识的非参数化建模框架。核心内容包括以下几个方面： 1. **核密度估计原理**：核密度估计是一种统计学方法，通过将数据点周围邻域的密度加权平均来估计总体的概率密度函数。这种方法的优势在于其灵活性，能适应各种复杂的数据分布形态，无需假设数据符合特定的数学分布。 2. **内核函数的选择**：作者探讨了三种常用的核函数——高斯分布、伽马分布和威布尔分布。每种核函数都有其特定的特性，选择哪种取决于数据的特性以及在海杂波分布中的适用性。通过选择合适的核函数，能够更准确地捕捉海杂波的空间依赖关系。 3. **最优带宽确定**：优化带宽是核密度估计中的关键步骤，它决定了核函数的宽度，从而影响估计结果的精度。作者针对每种核函数推导出了闭式最优带宽方程，这是优化建模过程中的重要进展，有助于减小模型误差。 4. **快速迭代带宽选择算法**：由于核函数方程的复杂性，设计了一种快速迭代算法来求解最优带宽。这种算法旨在提高计算效率，使得在实际应用中能够快速而有效地执行模型构建。 5. **实验结果与比较**：通过对比实验，新方法显示出显著的优势，相比于传统方法，能减少海杂波建模误差大约两个数量级，同时在保持低误报率的情况下，提高了目标检测概率，高达36%。这表明该方法在实际目标检测任务中具有更高的精度和可靠性。总结来说，这篇文章在海洋工程领域引入了核密度估计技术来解决海杂波分布建模问题，其优势在于其适应性和优化的带宽选择策略。这种方法有望在实际海洋目标检测系统中发挥重要作用，提升决策的准确性和效率。

Sea Clutter Distribution Modeling: A Kernel

Density Estimation Approach

Hongkuan Zhou, Yuzhou Li, and Tao Jiang

School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, China

{hongkuanzhou, yuzhouli, taojiang}@hust.edu.cn

Abstract—An accurate sea clutter distribution is crucial for

decision region determination when detecting sea-surface ﬂoating

targets. However, traditional parametric models possibly have

a considerable gap to the realistic distribution of sea clutters

due to the volatile sea states. In this paper, we develop a

kernel density estimation based framework to model the sea

clutter distributions without requiring any prior knowledge. In

this framework, we jointly consider two embedded fundamental

problems, the selection of a proper kernel density function

and the determination of its corresponding optimal bandwidth.

Regarding these two problems, we adopt the Gaussian, Gamma,

and Weibull distributions as the kernel functions, and derive the

closed-form optimal bandwidth equations for them. To deal with

the highly complicated equations for the three kernels, we further

design a fast iterative bandwidth selection algorithm to solve

them. Experimental results show that, compared with existing

methods, our proposed approach can signiﬁcantly decrease the

error incurred by sea clutter modeling (about two orders of mag-

nitude reduction) and improve the target detection probability

(up to 36% in low false alarm rate cases).

I. INTRODUCTION

An important application for marine surveillance radar is to

detect sea-surface small ﬂoating targets such as buoys, human

divers, and small boats [1]. When detecting, the received target

signals at the radar are buried in the strong returned signals

reﬂected by the sea surface, referred to as sea clutters [2], [3].

It is known that better detection performance is achieved if

prior knowledge of sea clutters’ distribution can be acquired,

since by this a proper detection threshold can be determined

at the detector [4]–[6]. Therefore, an important question that

arises is how to accurately model the distribution of sea clutters

in the ﬂuctuating sea state for small target detection.

By adopting various parametric models [7]–[10], there have

been extensive works attempting to characterize the distribu-

tion of sea clutters to obtain better detection performance.

In [7], the authors utilized the Gauss distribution to model

the amplitude of the sea clutter at a low-resolution radar.

With an increase in radar’s spatial resolution, the amplitude

distribution of the sea clutters was further extended from the

Gaussian to compound-Gaussian probability density functions

(PDFs) in [8] for small target detection. Gao et al. in [9]

This work was supported in part by the National Science Foundation of

China with Grant Numbers 61601192, 61631015, 61831013, and 61729101,

the Young Elite Scientists Sponsorship Program by CAST with Grant Number

2017QNRC001, the State Key Laboratory of Integrated Services Networks

(Xidian University) with Grant Number ISN19-09, and the Fundamental Re-

search Funds for the Central Universities with Grant Numbers 2016YXMS298

and 2015ZDTD012.

adopted the generalized Gamma distribution to describe the

statistical behaviors of sea clutters, and provided a parameter

estimation scheme by taking both of estimation precision and

applicable conditions into consideration. In [10], the authors

adopted the Weibull model in the constant false alarm rate

(CFAR) detector for radar detection and evaluated the involved

parameter optimization problem.

To summarize, the distributions of sea clutters adopted

in [7]–[10] for target detection are generally established as

parametric models. However, considering the two following

defects of the parametric models, a considerable gap possibly

exists between the ﬁtted and realistic distribution of sea clut-

ters. Firstly, the parametric models can hardly depict the spiky

components in sea clutters, which is produced when the high-

resolution radar works at a low grazing angle or under dynamic

sea states [11]. Secondly, as the distribution of sea clutters

usually varies with different detection environments, assuming

a ﬁxed parametric model for it cannot guarantee satisfactory

ﬁtting performance in the varying detection environments and

thus degrades the detection performance.

Following these insights, the distribution of sea clutters

should be characterized by sufﬁciently analyzing the collected

data instead of assuming a parametric model. Inspired by

this, the kernel density estimation (KDE), a non-parametric

approach for estimating the PDF of a random variable, can be

adopted to reveal the distribution of the collected sea clutters.

Different from the methods in [7]–[10], the KDE method uti-

lizes smooth kernel functions to ﬁt the realistic distribution of

the observed data without making any assumption on it, which

can effectively reﬂect the information of the spiky components

and ﬂexibly adapt to the varying detection environments.

When applying the KDE method, it is of utmost importance

to determine two key parameters, namely the kernel function

and the bandwidth [12]. In [13], the Gaussian kernel and some

traditional bandwidth selectors such as the plug-in were adopt-

ed in the KDE method, which show good ﬁtting performance

on random sequence samples. However, few works have

ever studied how the KDE method works in the sea-surface

target detection. In addition, whether there are other kernel

functions that can achieve better ﬁtting performance than the

Gaussian kernel or not is still unclear. Furthermore, it is also

quite challenging to derive the optimal bandwidth for other

specialized kernels by the traditionally complicated bandwidth

selection methods such as the plug-in technique [13]. These

challenges impose restrictions on the application of KDE

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