鲁棒子空间跟踪算法：应对脉冲噪声环境

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本篇研究论文标题为"脉冲噪声环境中基于鲁棒性的子空间跟踪算法"，发表在《数字信号处理》(Digital Signal Processing)杂志的62卷(2017年)，第168-175页。该研究由金峰和田爽两位作者完成，分别来自深圳大学的天线与传播实验室以及大连理工大学电子信息技术与电气工程学院。文章的核心内容聚焦于在脉冲噪声环境下提高子空间跟踪算法的鲁棒性。脉冲噪声是一种常见且具有破坏性的干扰，它对信号处理系统的性能有显著影响。传统的子空间跟踪算法可能在面对这种突发、异常的数据点时表现不佳，因为它们容易受到噪声或异常值的影响。为了增强算法的稳健性，研究者引入了最大克伦特罗普准则(MCC)。克伦特罗普熵是一种非高斯分布的数据拟合度量，它能够有效处理噪声中的异常值，从而体现出良好的抗干扰能力。通过将MCC作为投影近似子空间跟踪(PAST)算法的成本函数，作者提出了MCC-PAST算法。这种新方法利用MCC的特性来处理和过滤掉脉冲噪声，使得子空间的估计更加准确和稳定。此外，考虑到实际应用场景中子空间可能会快速变化，文中还引入了可变遗忘因子，以动态调整算法对历史数据的依赖程度，进一步提高了算法的实时性和适应性。这种变量遗忘因子的设计允许算法在保持对先前知识的记忆的同时，能够灵活地适应环境变化。这篇论文提供了一种在脉冲噪声环境下有效的子空间跟踪策略，它结合了最大克伦特罗普准则的鲁棒性与投影近似子空间跟踪的灵活性，为处理含有脉冲噪声的信号处理问题提供了新的解决方案。对于从事信号处理、鲁棒控制或者抗噪声技术领域的研究人员和工程师来说，这篇文章具有重要的理论价值和实际应用参考意义。

Digital Signal Processing 62 (2017) 168–175

Contents lists available at ScienceDirect

Digital Signal Processing

www.elsevier.com/locate/dsp

A robust correntropy based subspace tracking algorithm in impulsive

noise environments

Jin-feng Zhang

a,b

, Tian-shuang Qiu

b,∗

Shenzhen Key Laboratory of Antennas and Propagation, Shenzhen University, Shenzhen, 518060, China

Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China

a r t i c l e i n f o a b s t r a c t

Article history:

Available

online 8 December 2016

Keywords:

Impulsive

noise

Maximum

correntropy criterion

Projection

approximation subspace tracking

Variable

forgetting factor

The maximum correntropy criterion (MCC) demonstrates the inherent robustness to outliers in adaptive

ﬁltering. By employing the MCC based cost function in projection approximation subspace tracking (PAST)

algorithm, the MCC-PAST algorithm is deduced and utilized for the subspace tracking under impulsive

noise environments. To handle the fast varying subspaces circumstances, the variable forgetting factor

(VFF) technique is developed and incorporated into the MCC-PAST algorithm. To assess the robustness

of the proposed MCC-PAST with VFF algorithm, SαS processes are employed to comprehensively model

different scenarios of impulsive noises. The simulation results show the proposed MCC-PAST algorithm

with VFF performs better than the other two PAST algorithms developed for subspace tracking in

impulsive noise environments, namely, the robust PAST algorithm and the robust Kalman ﬁlter based

algorithm with variable number of measurements (KFVNM), especially when the noise is extremely

impulsive or the GSNR (generalized signal to noise ratio) is relatively low.

1. Introduction

As an important branch of subspace-based methods, subspace

tracking, which aims to derive a selected subset of eigenvectors of

a Hermitian matrix, has been developed as a valuable tool in array

signal processing in the few past decades [1–3]. One very eﬃcient

subspace tracking algorithm is the project approximation subspace

tracking (PAST) approach [3]. By employing the recursive least-

squares

(RLS) techniques, the PAST algorithm recursively estimates

the signal subspace by minimizing the least square errors between

the observation and a “projection approximation” obtained from

previously estimated subspace.

Unfortunately,

the conventional PAST method has two distinct

shortcomings. First, the RLS technique is vulnerable to impulsive

noise in nature. In fact, in some scenarios, sudden bursts or spikes,

which are either man-made or occurred naturally, are exhibited at

the array outputs. In such cases, the performance of the PAST al-

gorithm

will be degraded substantially. The second defect of the

conventional PAST algorithms is also traced back to the RLS tech-

nique.

That is, the RLS algorithm with a constant forgetting factor

(FF) is not suitable for tracking fast varying subspaces. In fact, both

Corresponding author.

E-mail

address: qiutsh@dlut.edu.c (T.-s. Qiu).

of the drawbacks of the conventional PAST algorithm have been

studied. In [4], Chan derived a robust subspace tracking method

by incorporating the M-estimate technique in robust statistics into

PAST algorithm to suppress the adverse effects of the impulsive

noise. As for the limitation of the tracking capability, in [5], an ex-

tension

of the Kalman ﬁlter-based algorithm with variable number

of measurements (KFVNM) is developed to handle the tracking of

the fast varying subspaces. That is, when the subspace substan-

tially

varies, a small number of measurements is employed in the

algorithm so that the estimation bias introduced by remote and

unrelated measurements will be small. On the other hand, if the

subspace is slowly varying, a large number of measurements is

used to reduce the estimation variance. In addition, to deal with

the impulsive noise, the M-estimation technique in robust statis-

tics

is also incorporated into the KFVNM algorithm. The superior

performance of the robust KFVNM algorithm for tracking fast vary-

ing

subspaces in impulsive noise environments has been showed

by the simulation results [5].

However,

as we noticed, the robust KFVNM algorithm suffers

from two limitations. First, the computation complexity may in-

crease

considerably since a relative large number of the past mea-

surements

need to be utilized for the estimation of the signal

subspace when the signal subspace varies slowly at the tth time

instant. Second, in the robust KFVNM algorithm, when one impulse

is detected at the tth time instant, the corresponding measurement

http://dx.doi.org/10.1016/j.dsp.2016.11.011

1051-2004/

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