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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收藏 640KB PDF 举报 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
978-1-5386-6119-2/18/$31.00 ©2018 IEEE
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