1 Generalized Matrix-Pencil Approach to Estimation of Complex Exponentials with Gapped Data

2025-04-30 0 0 358.47KB 5 页 10玖币

侵权投诉

Generalized Matrix-Pencil Approach to Estimation

of Complex Exponentials with Gapped Data

Jianping Wang and Alexander Yarovoy

Abstract—A generalized matrix-pencil approach is proposed

for the estimation of complex exponential components with seg-

mented signal samples, which is very efﬁcient and provides super-

resolution estimations. It is applicable to the signals sampled

segmentally with the same sampling frequency and direction of

arrival (DOA) estimation with distributed arrays within which

array elements are placed uniformly with the same inter-element

spacing.

Index Terms—Generalized Matrix Pencil Approach, Super-

resolution Estimation, Complex Exponential, Segmented Sam-

ples, Signal Estimation.

I. INTRODUCTION

Harmonic retrival problem is a general problem of estimat-

ing the frequencies and damping factors from the measure-

ments taken in time, space, etc. It is widely used in the ﬁeld

of radar, sonar, communication, radio astronomy, and so on.

In the literature, the estimation approaches of un-

damped/damped exponential components which are gener-

ally developed based on parametric models. The existing

approaches are typically rely on the analysis of state-space of

measurements and are implemented via space-searching tech-

nique or search-free strategies. The classical space-searching

approaches include MUltiple SIgnal Classiﬁcation (MUSIC),

the Amplitude and Phase EStimation method (APES) [1]

and the Iterative Adaptive Approach (IAA) [2] while typi-

cal search-free approaches contain the Estimation of Signal

Parameters via Rational Invariance Techniques (ESPRIT) al-

gorithm [3] and matrix pencil-type approaches [4]. All these

approaches have been extended to multidimensional cases for

various applications.

All the above approaches are developed for harmonic re-

trieval with continuously sampled data with a ﬁxed sampling

interval. However, in practice, due to sensor failure, interfer-

ence or noise effect, memory constraint, etc, gapped signals are

frequently acquired as a few separate segments. In such cases,

the aforementioned estimation methods are not applicable due

to the break of certain structures implicitly used. To tackle this

problem, several methods have been introduced for harmonic

retrieval with gapped data [5]–[18]. In [7], the generalized

APES (GAPES) method was introduced to deal with the

gapped data based on Fourier basis grid search. For more

general missing data pattern, missing-data APES (MAPES)

[8] was developed using the expectation maximization (EM)

algorithm [8]. Meanwhile, the missing-data IAA (MIAA) [9]

The authors are with the Faculty of Electrical Engineering, Mathematics and

Computer Science (EEMCS), Delft University of Technology, Delft, 2628CD

the Netherlands e-mail: J.Wang-4@tudelft.nl, A.Yarovoy@tudelft.nl.

was introduced based on the IAA to estimate the harmonic

frequencies and the missing samples. Both MAPES and MIAA

are search-based methods but MIAA, as the author claimed,

is much faster than the MAPES. However, both methods have

difﬁculties in tackle damping harmonics estimation. On the

other hand, the weighted multiple invariance (WMI) approach

[14] was introduced based on a linear combination of the

rank-reduction criteria obtained shift-invariances of the signal

model. Using the MUSIC criterion, the WMI can in principle

get accurate estimation; however, the WMI based on poly-

nomial intersection is computationally very sensitive and not

stable. Moreover, similar to the MAPES, a Gaussian regression

method [16] is introduced for spectral estimation with missing

data based on the EM algorithm but it requires the power

spectral density sufﬁciently smooth.

In this paper, taking advantage of the search-free MPA,

we introduce the generalized MPA (GMPA) for estimating

harmonic components with gapped data. The proposed GMPA

exploits the shift-invariance of the signal space of the harmonic

components and utilize the singular value decomposition to

ﬁgure out the signal poles of the constructed Hankel-like ma-

trix. It is accurate and computational very efﬁcient. Although

the propper approach has been directly used for signal fusion

in [17], [18], rigorous analysis was missing. To ﬁll this gap,

a mathematical derivation is provided in this paper.

The remainder of the paper is organized as follows. In

section II, the generic signal model for harmonic retrieval

with gapped data is presented and section III introduces the

proposed generalized matrix pencil approach. After that, some

numerical simulations are shown in section IV to demonstrate

the performance of the proposed GMPA and comparisons with

the state-of-the-art methods. Finally, conclusions are drawn in

section V.

II. SIGNAL MODEL

Signal estimation of damped/undamped complex exponen-

tial components is a popular problem in signal processing.

The damped/undamped complex exponential signal can be

generally expressed as

s(t) =

n=1

αnexp [(βn+jωn)t](1)

where j=√−1is the unit of imaginary number. αn,βnand

ωnare the amplitude, damping factor and angular frequency

of the nth complex exponential component, respectively. For

the undamped exponential components, their damping factor

are zero in (1).

arXiv:2210.15270v1 [eess.SP] 27 Oct 2022

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

1GeneralizedMatrix-PencilApproachtoEstimationofComplexExponentialswithGappedDataJianpingWangandAlexanderYarovoyAbstractAgeneralizedmatrix-pencilapproachisproposedfortheestimationofcomplexexponentialcomponentswithseg-mentedsignalsamples,whichisveryefcientandprovidessuper-resolutionestimations.Itisa...

展开>> 收起<<

1 Generalized Matrix-Pencil Approach to Estimation of Complex Exponentials with Gapped Data.pdf

共5页,预览1页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

1 Generalized Matrix-Pencil Approach to Estimation of Complex Exponentials with Gapped Data

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: