Behavior of the LMS algorithm with hyperbolic secant cost

This paper presents a new least mean square (LMS) algorithm with defining hyperbolic secant cost function. Then, the detailed analysis is conducted to reveal the behavior of the proposed algorithm. The transient analysis is conducted based on a Taylor expansion approach and energy conservation (EC)...

Full description

Saved in:
Bibliographic Details
Published inJournal of the Franklin Institute Vol. 357; no. 3; pp. 1943 - 1960
Main Authors Lu, Lu, Chen, Lihui, Zheng, Zongsheng, Yu, Yi, Yang, Xiaomin
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.02.2020
Elsevier Science Ltd
Subjects
Online AccessGet full text
ISSN0016-0032
1879-2693
0016-0032
DOI10.1016/j.jfranklin.2019.12.040

Cover

Abstract This paper presents a new least mean square (LMS) algorithm with defining hyperbolic secant cost function. Then, the detailed analysis is conducted to reveal the behavior of the proposed algorithm. The transient analysis is conducted based on a Taylor expansion approach and energy conservation (EC) relation expression. Following the results of transient state analysis of excess means square-error (EMSE), we achieve the steady-state EMSE and mean-square deviation (MSD) expressions of the proposed algorithm. Moreover, the sufficient condition for the stability convergence is given. Simulation results validate the theoretical analyses and demonstrate the enhanced performance of the proposed algorithm as compared with conventional LMS algorithm in the presence of white Gaussian noise (WGN) and uniform noise.
AbstractList This paper presents a new least mean square (LMS) algorithm with defining hyperbolic secant cost function. Then, the detailed analysis is conducted to reveal the behavior of the proposed algorithm. The transient analysis is conducted based on a Taylor expansion approach and energy conservation (EC) relation expression. Following the results of transient state analysis of excess means square-error (EMSE), we achieve the steady-state EMSE and mean-square deviation (MSD) expressions of the proposed algorithm. Moreover, the sufficient condition for the stability convergence is given. Simulation results validate the theoretical analyses and demonstrate the enhanced performance of the proposed algorithm as compared with conventional LMS algorithm in the presence of white Gaussian noise (WGN) and uniform noise.
Author Zheng, Zongsheng
Chen, Lihui
Lu, Lu
Yu, Yi
Yang, Xiaomin
Author_xml – sequence: 1
  givenname: Lu
  orcidid: 0000-0002-6077-0977
  surname: Lu
  fullname: Lu, Lu
  email: lulu19900303@126.com
  organization: School of Electronics and Information Engineering, Sichuan University, Chengdu, Sichuan 610065, China
– sequence: 2
  givenname: Lihui
  orcidid: 0000-0002-0948-1600
  surname: Chen
  fullname: Chen, Lihui
  email: lihuichen@126.com
  organization: School of Electronics and Information Engineering, Sichuan University, Chengdu, Sichuan 610065, China
– sequence: 3
  givenname: Zongsheng
  orcidid: 0000-0002-4198-5788
  surname: Zheng
  fullname: Zheng, Zongsheng
  email: bk20095185@my.swjtu.edu.cn
  organization: School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031, China
– sequence: 4
  givenname: Yi
  orcidid: 0000-0003-3790-0945
  surname: Yu
  fullname: Yu, Yi
  email: yuyi_xyuan@163.com
  organization: School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, China
– sequence: 5
  givenname: Xiaomin
  orcidid: 0000-0002-1094-3841
  surname: Yang
  fullname: Yang, Xiaomin
  email: arielyang@scu.edu.cn
  organization: School of Electronics and Information Engineering, Sichuan University, Chengdu, Sichuan 610065, China
BookMark eNqNkMtOwzAQRS1UJNrCN2CJdYJfTeIFi1LxkopYAGvLcRzikNrFdov697gqYsEGNjMa6Z470pmAkXVWA3COUY4RLi77vG-9tO-DsTlBmOeY5IihIzDGVckzUnA6AmOUohlClJyASQh9OkuM0Bjwa93JrXEeuhbGTsPl4zOUw5vzJnYr-Jkm7HZr7Ws3GAWDVtJGqFyIp-C4lUPQZ997Cl5vb14W99ny6e5hMV9mijIaMy4JkVqWrED1bMZ0jRWtqpY2pKGY1rSSlDe4kXVNmFQtphg3rCjxrJC8ShydgotD79q7j40OUfRu4216KQgtOUKIsSqlrg4p5V0IXrdCmSijcTZ6aQaBkdjbEr34sSX2tgQmItlKfPmLX3uzkn73D3J-IHWSsDXai6CMtko3xmsVRePMnx1fEWaLMQ
CitedBy_id crossref_primary_10_1016_j_sigpro_2022_108626
crossref_primary_10_1080_00207217_2020_1870742
crossref_primary_10_1109_TCSII_2022_3168990
crossref_primary_10_3390_app14031218
crossref_primary_10_1016_j_dsp_2024_104396
crossref_primary_10_1109_TCSII_2021_3113465
crossref_primary_10_1007_s11276_021_02754_4
crossref_primary_10_1109_TCSII_2020_3032089
crossref_primary_10_1016_j_jfranklin_2024_107071
crossref_primary_10_1109_TII_2022_3153835
crossref_primary_10_1016_j_dsp_2022_103609
crossref_primary_10_1080_00207721_2024_2409850
crossref_primary_10_1007_s11760_024_03557_8
crossref_primary_10_3390_sym16101375
crossref_primary_10_1371_journal_pone_0258155
crossref_primary_10_1109_TCSII_2022_3200523
crossref_primary_10_1016_j_jfranklin_2022_07_012
crossref_primary_10_1016_j_apacoust_2023_109528
crossref_primary_10_1007_s11276_025_03916_4
crossref_primary_10_1007_s00034_022_02247_5
crossref_primary_10_1109_TCSII_2021_3106348
Cites_doi 10.1109/TSP.2014.2333559
10.1109/78.752610
10.1016/j.jfranklin.2018.10.019
10.1109/TSP.2017.2768024
10.1049/el.2009.2582
10.1016/j.sigpro.2010.03.025
10.1109/97.863150
10.1016/j.sigpro.2016.05.005
10.1016/j.sigpro.2017.06.005
10.1016/j.dsp.2008.11.006
10.1016/j.bspc.2019.01.021
10.1186/s13634-018-0581-5
10.1016/j.compeleceng.2013.11.025
10.1016/j.jsv.2015.11.029
10.1109/TSP.2005.849213
10.1016/j.sigpro.2017.05.009
10.1109/TIT.1958.1057444
10.1109/ACCESS.2017.2722464
10.1109/LSP.2012.2204435
10.1109/LSP.2014.2319308
10.1016/j.sigpro.2016.12.020
10.1155/S1110865701000348
ContentType Journal Article
Copyright 2019 The Franklin Institute
Copyright Elsevier Science Ltd. Feb 2020
Copyright_xml – notice: 2019 The Franklin Institute
– notice: Copyright Elsevier Science Ltd. Feb 2020
DBID AAYXX
CITATION
7TB
8FD
FR3
KR7
DOI 10.1016/j.jfranklin.2019.12.040
DatabaseName CrossRef
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
Civil Engineering Abstracts
DatabaseTitle CrossRef
Civil Engineering Abstracts
Engineering Research Database
Technology Research Database
Mechanical & Transportation Engineering Abstracts
DatabaseTitleList
Civil Engineering Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1879-2693
0016-0032
EndPage 1960
ExternalDocumentID 10_1016_j_jfranklin_2019_12_040
S0016003219309536
GrantInformation_xml – fundername: China Scholarship Council
  grantid: 201807000035
  funderid: https://doi.org/10.13039/501100004543
– fundername: China Postdoctoral Science Foundation
  grantid: 2018M640916
  funderid: https://doi.org/10.13039/501100002858
GroupedDBID --K
--M
-DZ
-~X
.~1
0R~
1B1
1RT
1~.
1~5
29L
4.4
41~
457
4G.
5GY
5VS
6TJ
7-5
71M
8P~
9JN
9JO
AAAKF
AAAKG
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AARIN
AAXUO
AAYFN
ABAOU
ABBOA
ABEFU
ABFRF
ABJNI
ABMAC
ABTAH
ABUCO
ABXDB
ABYKQ
ACAZW
ACCUC
ACDAQ
ACGFO
ACGFS
ACIWK
ACNCT
ACNNM
ACRLP
ACZNC
ADEZE
ADGUI
ADJOM
ADMUD
ADTZH
AEBSH
AECPX
AEFWE
AEKER
AETEA
AFDAS
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AHZHX
AIALX
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
APLSM
ARUGR
AXJTR
BJAXD
BKOJK
BLXMC
CS3
D1Z
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FA8
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
GBOLZ
HAMUX
HMJ
HVGLF
HZ~
H~9
IHE
J1W
JJJVA
KOM
LY7
M26
M41
MHUIS
MO0
MVM
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
SCC
SDF
SDG
SES
SET
SEW
SME
SPC
SPCBC
SSB
SSD
SST
SSV
SSW
SSZ
T5K
TN5
UHS
VOH
WH7
WUQ
XOL
XPP
ZCG
ZMT
ZY4
~02
~G-
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABWVN
ACLOT
ACRPL
ADNMO
ADXHL
AEIPS
AFJKZ
AGQPQ
AHPAA
AIIUN
ANKPU
APXCP
CITATION
EFKBS
~HD
7TB
8FD
AGCQF
FR3
KR7
ID FETCH-LOGICAL-c343t-9a22aea7460b554eb1c388f3d2d313b38a39d1dabb24acf1311d467156a98ea73
IEDL.DBID .~1
ISSN 0016-0032
IngestDate Sun Sep 07 03:34:28 EDT 2025
Wed Oct 01 05:23:35 EDT 2025
Thu Apr 24 22:54:19 EDT 2025
Fri Feb 23 02:48:08 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 3
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c343t-9a22aea7460b554eb1c388f3d2d313b38a39d1dabb24acf1311d467156a98ea73
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-4198-5788
0000-0002-0948-1600
0000-0002-6077-0977
0000-0003-3790-0945
0000-0002-1094-3841
PQID 2379000448
PQPubID 2045917
PageCount 18
ParticipantIDs proquest_journals_2379000448
crossref_citationtrail_10_1016_j_jfranklin_2019_12_040
crossref_primary_10_1016_j_jfranklin_2019_12_040
elsevier_sciencedirect_doi_10_1016_j_jfranklin_2019_12_040
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate February 2020
2020-02-00
20200201
PublicationDateYYYYMMDD 2020-02-01
PublicationDate_xml – month: 02
  year: 2020
  text: February 2020
PublicationDecade 2020
PublicationPlace Elmsford
PublicationPlace_xml – name: Elmsford
PublicationTitle Journal of the Franklin Institute
PublicationYear 2020
Publisher Elsevier Ltd
Elsevier Science Ltd
Publisher_xml – name: Elsevier Ltd
– name: Elsevier Science Ltd
References Arunkumar, Bhaskar (bib0008) 2019; 50
Price (bib0033) 1958; 4
Xiong, Wang, Chen (bib0019) 2019; 7
Liu, Yu, Li (bib0004) 2011; 217
Rusu, Cowan (bib0005) 2000; 7
Roopa, Narasimhan (bib0007) 2014; 40
Sayed (bib0028) 2003
Petrus (bib0030) 1999; 47
Das, Narwaria (bib0016) 2017; 64
Lu, Zhu, Yang, Zhou, Liu, Wu (bib0027) 2019
Boukis, Mandic, Constantinides (bib0015) 2009; 19
Xiong, Wang (bib0018) 2019; 356
Peng, Chen, Sun, Lin, Ser (bib0022) 2016; 140
Lu, Zhao (bib0032) 2016; 364
Naffouri, Sayed (bib0034) 2001; 2001
Khalifi, Mayyala, Iqbal, Zerguine, Abedmeraim (bib0012) 2017
Mansoor, Asad, Zerguine (bib0013) 2014
Li, Jiang, Shi, Han, Chen (bib0021) 2019
Chen, Xing, Liang, Zheng, Principe (bib0023) 2014; 21
Rusu, Cowan (bib0006) 2010; 90
Chen, Principe (bib0020) 2012; 19
Mengüç, Acır (bib0029) 2017; 66
Zhang, Zheng, Zhang, Han (bib0026) 2017; 5
Weng, Barner (bib0031) 2005; 53
Majhi, Panda, Mulgrew (bib0009) 2009; 45
Song, Park, Newcomb (bib0025) 2013; 60
Yu, Lu, Zheng, Wang, Zakharov, de Lamare (bib0003) 2019
Sayin, Vanli, Kozat (bib0017) 2014; 62
Wang, Wang, Xiong, Iu, Tse (bib0024) 2019
Wang, Zheng, Duan, Wang, Tse (bib0014) 2016; 128
Bershad, Eweda, Bermudez (bib0002) 2018; 142
Lu, Wang, Yang, Wu, Zhu (bib0001) 2019; 66
Zheng, Liu, Ming (bib0010) 2017; 134
Mengüç, Acır (bib0011) 2018; 66
Wang, Li, Bermudez, Han (bib0035) 2018; 2018
Lu (10.1016/j.jfranklin.2019.12.040_bib0032) 2016; 364
Majhi (10.1016/j.jfranklin.2019.12.040_bib0009) 2009; 45
Khalifi (10.1016/j.jfranklin.2019.12.040_bib0012) 2017
Das (10.1016/j.jfranklin.2019.12.040_bib0016) 2017; 64
Zheng (10.1016/j.jfranklin.2019.12.040_bib0010) 2017; 134
Mengüç (10.1016/j.jfranklin.2019.12.040_bib0029) 2017; 66
Roopa (10.1016/j.jfranklin.2019.12.040_bib0007) 2014; 40
Naffouri (10.1016/j.jfranklin.2019.12.040_bib0034) 2001; 2001
Xiong (10.1016/j.jfranklin.2019.12.040_bib0019) 2019; 7
Wang (10.1016/j.jfranklin.2019.12.040_bib0024) 2019
Weng (10.1016/j.jfranklin.2019.12.040_bib0031) 2005; 53
Rusu (10.1016/j.jfranklin.2019.12.040_bib0006) 2010; 90
Price (10.1016/j.jfranklin.2019.12.040_bib0033) 1958; 4
Peng (10.1016/j.jfranklin.2019.12.040_bib0022) 2016; 140
Chen (10.1016/j.jfranklin.2019.12.040_bib0023) 2014; 21
Song (10.1016/j.jfranklin.2019.12.040_bib0025) 2013; 60
Sayed (10.1016/j.jfranklin.2019.12.040_bib0028) 2003
Lu (10.1016/j.jfranklin.2019.12.040_bib0001) 2019; 66
Arunkumar (10.1016/j.jfranklin.2019.12.040_bib0008) 2019; 50
Wang (10.1016/j.jfranklin.2019.12.040_bib0035) 2018; 2018
Sayin (10.1016/j.jfranklin.2019.12.040_bib0017) 2014; 62
Lu (10.1016/j.jfranklin.2019.12.040_bib0027) 2019
Rusu (10.1016/j.jfranklin.2019.12.040_bib0005) 2000; 7
Liu (10.1016/j.jfranklin.2019.12.040_bib0004) 2011; 217
Mengüç (10.1016/j.jfranklin.2019.12.040_bib0011) 2018; 66
Zhang (10.1016/j.jfranklin.2019.12.040_bib0026) 2017; 5
Boukis (10.1016/j.jfranklin.2019.12.040_bib0015) 2009; 19
Yu (10.1016/j.jfranklin.2019.12.040_bib0003) 2019
Xiong (10.1016/j.jfranklin.2019.12.040_bib0018) 2019; 356
Li (10.1016/j.jfranklin.2019.12.040_bib0021) 2019
Chen (10.1016/j.jfranklin.2019.12.040_bib0020) 2012; 19
Bershad (10.1016/j.jfranklin.2019.12.040_bib0002) 2018; 142
Wang (10.1016/j.jfranklin.2019.12.040_bib0014) 2016; 128
Petrus (10.1016/j.jfranklin.2019.12.040_bib0030) 1999; 47
Mansoor (10.1016/j.jfranklin.2019.12.040_bib0013) 2014
References_xml – volume: 4
  start-page: 69
  year: 1958
  end-page: 72
  ident: bib0033
  article-title: A useful theorem for nonlinear devices having Gaussian inputs
  publication-title: IEEE Trans. Inform. Theory
– volume: 40
  start-page: 1028
  year: 2014
  end-page: 1041
  ident: bib0007
  article-title: Transform domain variable step-size Griffiths least mean square adaptive algorithm and its applications
  publication-title: Comput. Electr. Eng.
– volume: 64
  start-page: 1529
  year: 2017
  end-page: 1539
  ident: bib0016
  article-title: Lorentzian based adaptive filters for impulsive noise environments
  publication-title: IEEE Trans. Circuits Syst. I
– volume: 140
  start-page: 116
  year: 2016
  end-page: 126
  ident: bib0022
  article-title: Constrained maximum correntropy adaptive filtering
  publication-title: Signal Process.
– volume: 60
  start-page: 442
  year: 2013
  end-page: 445
  ident: bib0025
  article-title: A normalized least mean squares algorithm with a step-size scaler against impulsive measurement noise
  publication-title: IEEE Trans. Circuits Syst. II
– year: 2003
  ident: bib0028
  publication-title: Fundamentals of Adaptive Filtering
– start-page: 1
  year: 2019
  end-page: 13
  ident: bib0024
  article-title: Logarithmic hyperbolic cosine adaptive filter and its performance analysis
  publication-title: IEEE Trans. Syst. Man Cybern.
– volume: 53
  start-page: 2588
  year: 2005
  end-page: 2594
  ident: bib0031
  article-title: Nonlinear system identification in impulsive environments
  publication-title: IEEE Trans. Signal Process.
– start-page: 1
  year: 2019
  end-page: 5
  ident: bib0021
  article-title: Blocked maximum correntropy criterion algorithm for cluster-sparse system identifications
  publication-title: IEEE Trans. Circuits Syst. II
– volume: 356
  start-page: 654
  year: 2019
  end-page: 674
  ident: bib0018
  article-title: Robust least mean logarithmic square adaptive filtering algorithms
  publication-title: J. Frankl. Inst.
– start-page: 1
  year: 2019
  end-page: 5
  ident: bib0003
  article-title: DCD-based recursive adaptive algorithms robust against impulsive noise
  publication-title: IEEE Trans. Circuits Syst. II
– start-page: 1
  year: 2019
  end-page: 9
  ident: bib0027
  article-title: Affine projection algorithm based high-order error power for partial discharge denoising in power cables
  publication-title: IEEE Trans. Instrum. Meas.
– volume: 45
  start-page: 334
  year: 2009
  end-page: 335
  ident: bib0009
  article-title: Robust identification using new Wilcoxon least mean square algorithm
  publication-title: Electron. Lett.
– volume: 364
  start-page: 14
  year: 2016
  end-page: 29
  ident: bib0032
  article-title: Adaptive Volterra filter with continuous
  publication-title: J. Sound Vib.
– volume: 134
  start-page: 268
  year: 2017
  end-page: 274
  ident: bib0010
  article-title: Diffusion least mean square/fourth algorithm for distributed estimation
  publication-title: Signal Process.
– start-page: 812
  year: 2017
  end-page: 815
  ident: bib0012
  article-title: Adaptive algorithm based on a new hyperbolic sine cost function
  publication-title: Proceedings of the Asilomar Conference on Signals, Systems and Computers
– volume: 19
  start-page: 491
  year: 2012
  end-page: 494
  ident: bib0020
  article-title: Maximum correntropy estimation is a smoothed MAP estimation
  publication-title: IEEE Signal Process. Lett.
– volume: 50
  start-page: 1
  year: 2019
  end-page: 9
  ident: bib0008
  article-title: Heart rate estimation from photoplethysmography signal for wearable health monitoring devices
  publication-title: Biomed. Signal Process. Control
– volume: 7
  year: 2019
  ident: bib0019
  article-title: Robust normalized least mean absolute third algorithms
  publication-title: IEEE Access.
– volume: 19
  start-page: 201
  year: 2009
  end-page: 212
  ident: bib0015
  article-title: A class of stochastic gradient algorithms with exponentiated error cost functions
  publication-title: Digit. Signal Process.
– volume: 2018
  start-page: 58
  year: 2018
  ident: bib0035
  article-title: An adaptive combination constrained proportionate normalized maximum correntropy criterion algorithm for sparse channel estimations
  publication-title: EURASIP J. Adv. Signal Process.
– volume: 47
  start-page: 1129
  year: 1999
  end-page: 1133
  ident: bib0030
  article-title: Robust Huber adaptive filter
  publication-title: IEEE Trans. Signal Process.
– volume: 7
  start-page: 256
  year: 2000
  end-page: 258
  ident: bib0005
  article-title: The convex variable step-size (CVSS) algorithm
  publication-title: IEEE Signal Process. Lett.
– volume: 128
  start-page: 340
  year: 2016
  end-page: 349
  ident: bib0014
  article-title: A class of improved least sum of exponentials algorithms
  publication-title: Signal Process.
– volume: 142
  start-page: 27
  year: 2018
  end-page: 35
  ident: bib0002
  article-title: Stochastic analysis of soft limiters in the LMS algorithm for stationary white Gaussian inputs – a unified theory
  publication-title: Signal Process.
– volume: 66
  start-page: 438
  year: 2018
  end-page: 448
  ident: bib0011
  article-title: An augmented complex-valued least-mean kurtosis algorithm for the filtering of noncircular signals
  publication-title: IEEE Trans. Signal Process.
– volume: 217
  start-page: 7365
  year: 2011
  end-page: 7371
  ident: bib0004
  article-title: A nonparametric variable step-size NLMS algorithm for transversal filters
  publication-title: Appl. Math. Comput.
– volume: 66
  start-page: 1272
  year: 2019
  end-page: 1276
  ident: bib0001
  article-title: Recursive Geman–McClure estimator for implementing second-order Volterra filter
  publication-title: IEEE Trans. Circuits Syst. II
– volume: 5
  start-page: 14716
  year: 2017
  end-page: 14727
  ident: bib0026
  article-title: A family of robust M-shaped error weighted least mean square algorithms: performance analysis and echo cancellation application
  publication-title: IEEE Access.
– start-page: 900
  year: 2014
  end-page: 903
  ident: bib0013
  article-title: Stochastic gradient algorithm based on an improved higher order exponentiated error cost function
  publication-title: Proceedings of the Asilomar Conference on Signals, Systems and Computers
– volume: 21
  start-page: 880
  year: 2014
  end-page: 884
  ident: bib0023
  article-title: Steady-state mean-square error analysis for adaptive filtering under the maximum correntropy criterion
  publication-title: IEEE Signal Process. Lett.
– volume: 62
  start-page: 4411
  year: 2014
  end-page: 4424
  ident: bib0017
  article-title: A novel family of adaptive filtering algorithms based on the logarithmic cost
  publication-title: IEEE Trans. Signal Process.
– volume: 2001
  start-page: 192
  year: 2001
  end-page: 205
  ident: bib0034
  article-title: Adaptive filters with error nonlinearities: Mean-square analysis and optimum design
  publication-title: EURASIP J. Adv. Signal Process.
– volume: 90
  start-page: 2784
  year: 2010
  end-page: 2791
  ident: bib0006
  article-title: The exponentiated convex variable step-size (ECVSS) algorithm
  publication-title: Signal Process.
– volume: 66
  start-page: 438
  year: 2017
  end-page: 448
  ident: bib0029
  article-title: An augmented complex-valued least-mean kurtosis algorithm for the filtering of noncircular signals
  publication-title: IEEE Trans. Signal Process.
– volume: 64
  start-page: 1529
  issue: 6
  year: 2017
  ident: 10.1016/j.jfranklin.2019.12.040_bib0016
  article-title: Lorentzian based adaptive filters for impulsive noise environments
  publication-title: IEEE Trans. Circuits Syst. I
– volume: 60
  start-page: 442
  issue: 7
  year: 2013
  ident: 10.1016/j.jfranklin.2019.12.040_bib0025
  article-title: A normalized least mean squares algorithm with a step-size scaler against impulsive measurement noise
  publication-title: IEEE Trans. Circuits Syst. II
– volume: 62
  start-page: 4411
  issue: 17
  year: 2014
  ident: 10.1016/j.jfranklin.2019.12.040_bib0017
  article-title: A novel family of adaptive filtering algorithms based on the logarithmic cost
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2014.2333559
– volume: 47
  start-page: 1129
  issue: 4
  year: 1999
  ident: 10.1016/j.jfranklin.2019.12.040_bib0030
  article-title: Robust Huber adaptive filter
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/78.752610
– start-page: 900
  year: 2014
  ident: 10.1016/j.jfranklin.2019.12.040_bib0013
  article-title: Stochastic gradient algorithm based on an improved higher order exponentiated error cost function
– volume: 356
  start-page: 654
  issue: 1
  year: 2019
  ident: 10.1016/j.jfranklin.2019.12.040_bib0018
  article-title: Robust least mean logarithmic square adaptive filtering algorithms
  publication-title: J. Frankl. Inst.
  doi: 10.1016/j.jfranklin.2018.10.019
– volume: 66
  start-page: 438
  issue: 2
  year: 2017
  ident: 10.1016/j.jfranklin.2019.12.040_bib0029
  article-title: An augmented complex-valued least-mean kurtosis algorithm for the filtering of noncircular signals
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2017.2768024
– volume: 45
  start-page: 334
  issue: 6
  year: 2009
  ident: 10.1016/j.jfranklin.2019.12.040_bib0009
  article-title: Robust identification using new Wilcoxon least mean square algorithm
  publication-title: Electron. Lett.
  doi: 10.1049/el.2009.2582
– volume: 90
  start-page: 2784
  issue: 9
  year: 2010
  ident: 10.1016/j.jfranklin.2019.12.040_bib0006
  article-title: The exponentiated convex variable step-size (ECVSS) algorithm
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2010.03.025
– volume: 7
  start-page: 256
  issue: 9
  year: 2000
  ident: 10.1016/j.jfranklin.2019.12.040_bib0005
  article-title: The convex variable step-size (CVSS) algorithm
  publication-title: IEEE Signal Process. Lett.
  doi: 10.1109/97.863150
– volume: 128
  start-page: 340
  year: 2016
  ident: 10.1016/j.jfranklin.2019.12.040_bib0014
  article-title: A class of improved least sum of exponentials algorithms
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2016.05.005
– volume: 142
  start-page: 27
  year: 2018
  ident: 10.1016/j.jfranklin.2019.12.040_bib0002
  article-title: Stochastic analysis of soft limiters in the LMS algorithm for stationary white Gaussian inputs – a unified theory
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2017.06.005
– start-page: 812
  year: 2017
  ident: 10.1016/j.jfranklin.2019.12.040_bib0012
  article-title: Adaptive algorithm based on a new hyperbolic sine cost function
– volume: 7
  year: 2019
  ident: 10.1016/j.jfranklin.2019.12.040_bib0019
  article-title: Robust normalized least mean absolute third algorithms
  publication-title: IEEE Access.
– start-page: 1
  year: 2019
  ident: 10.1016/j.jfranklin.2019.12.040_bib0021
  article-title: Blocked maximum correntropy criterion algorithm for cluster-sparse system identifications
  publication-title: IEEE Trans. Circuits Syst. II
– start-page: 1
  year: 2019
  ident: 10.1016/j.jfranklin.2019.12.040_bib0027
  article-title: Affine projection algorithm based high-order error power for partial discharge denoising in power cables
  publication-title: IEEE Trans. Instrum. Meas.
– volume: 19
  start-page: 201
  issue: 2
  year: 2009
  ident: 10.1016/j.jfranklin.2019.12.040_bib0015
  article-title: A class of stochastic gradient algorithms with exponentiated error cost functions
  publication-title: Digit. Signal Process.
  doi: 10.1016/j.dsp.2008.11.006
– volume: 50
  start-page: 1
  year: 2019
  ident: 10.1016/j.jfranklin.2019.12.040_bib0008
  article-title: Heart rate estimation from photoplethysmography signal for wearable health monitoring devices
  publication-title: Biomed. Signal Process. Control
  doi: 10.1016/j.bspc.2019.01.021
– year: 2003
  ident: 10.1016/j.jfranklin.2019.12.040_bib0028
– volume: 2018
  start-page: 58
  issue: 1
  year: 2018
  ident: 10.1016/j.jfranklin.2019.12.040_bib0035
  article-title: An adaptive combination constrained proportionate normalized maximum correntropy criterion algorithm for sparse channel estimations
  publication-title: EURASIP J. Adv. Signal Process.
  doi: 10.1186/s13634-018-0581-5
– volume: 40
  start-page: 1028
  issue: 4
  year: 2014
  ident: 10.1016/j.jfranklin.2019.12.040_bib0007
  article-title: Transform domain variable step-size Griffiths least mean square adaptive algorithm and its applications
  publication-title: Comput. Electr. Eng.
  doi: 10.1016/j.compeleceng.2013.11.025
– volume: 364
  start-page: 14
  year: 2016
  ident: 10.1016/j.jfranklin.2019.12.040_bib0032
  article-title: Adaptive Volterra filter with continuous lp-norm using a logarithmic cost for nonlinear active noise control
  publication-title: J. Sound Vib.
  doi: 10.1016/j.jsv.2015.11.029
– volume: 53
  start-page: 2588
  issue: 7
  year: 2005
  ident: 10.1016/j.jfranklin.2019.12.040_bib0031
  article-title: Nonlinear system identification in impulsive environments
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2005.849213
– volume: 66
  start-page: 1272
  issue: 7
  year: 2019
  ident: 10.1016/j.jfranklin.2019.12.040_bib0001
  article-title: Recursive Geman–McClure estimator for implementing second-order Volterra filter
  publication-title: IEEE Trans. Circuits Syst. II
– volume: 66
  start-page: 438
  issue: 2
  year: 2018
  ident: 10.1016/j.jfranklin.2019.12.040_bib0011
  article-title: An augmented complex-valued least-mean kurtosis algorithm for the filtering of noncircular signals
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2017.2768024
– volume: 140
  start-page: 116
  year: 2016
  ident: 10.1016/j.jfranklin.2019.12.040_bib0022
  article-title: Constrained maximum correntropy adaptive filtering
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2017.05.009
– volume: 4
  start-page: 69
  issue: 2
  year: 1958
  ident: 10.1016/j.jfranklin.2019.12.040_bib0033
  article-title: A useful theorem for nonlinear devices having Gaussian inputs
  publication-title: IEEE Trans. Inform. Theory
  doi: 10.1109/TIT.1958.1057444
– volume: 5
  start-page: 14716
  year: 2017
  ident: 10.1016/j.jfranklin.2019.12.040_bib0026
  article-title: A family of robust M-shaped error weighted least mean square algorithms: performance analysis and echo cancellation application
  publication-title: IEEE Access.
  doi: 10.1109/ACCESS.2017.2722464
– volume: 19
  start-page: 491
  issue: 8
  year: 2012
  ident: 10.1016/j.jfranklin.2019.12.040_bib0020
  article-title: Maximum correntropy estimation is a smoothed MAP estimation
  publication-title: IEEE Signal Process. Lett.
  doi: 10.1109/LSP.2012.2204435
– volume: 21
  start-page: 880
  issue: 7
  year: 2014
  ident: 10.1016/j.jfranklin.2019.12.040_bib0023
  article-title: Steady-state mean-square error analysis for adaptive filtering under the maximum correntropy criterion
  publication-title: IEEE Signal Process. Lett.
  doi: 10.1109/LSP.2014.2319308
– start-page: 1
  year: 2019
  ident: 10.1016/j.jfranklin.2019.12.040_bib0003
  article-title: DCD-based recursive adaptive algorithms robust against impulsive noise
  publication-title: IEEE Trans. Circuits Syst. II
– start-page: 1
  year: 2019
  ident: 10.1016/j.jfranklin.2019.12.040_bib0024
  article-title: Logarithmic hyperbolic cosine adaptive filter and its performance analysis
  publication-title: IEEE Trans. Syst. Man Cybern.
– volume: 134
  start-page: 268
  year: 2017
  ident: 10.1016/j.jfranklin.2019.12.040_bib0010
  article-title: Diffusion least mean square/fourth algorithm for distributed estimation
  publication-title: Signal Process.
  doi: 10.1016/j.sigpro.2016.12.020
– volume: 217
  start-page: 7365
  issue: 17
  year: 2011
  ident: 10.1016/j.jfranklin.2019.12.040_bib0004
  article-title: A nonparametric variable step-size NLMS algorithm for transversal filters
  publication-title: Appl. Math. Comput.
– volume: 2001
  start-page: 192
  issue: 4
  year: 2001
  ident: 10.1016/j.jfranklin.2019.12.040_bib0034
  article-title: Adaptive filters with error nonlinearities: Mean-square analysis and optimum design
  publication-title: EURASIP J. Adv. Signal Process.
  doi: 10.1155/S1110865701000348
SSID ssj0017100
Score 2.3809702
Snippet This paper presents a new least mean square (LMS) algorithm with defining hyperbolic secant cost function. Then, the detailed analysis is conducted to reveal...
SourceID proquest
crossref
elsevier
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 1943
SubjectTerms Algorithms
Computer simulation
Cost analysis
Cost function
Energy conservation
Error analysis
Hyperbolic functions
Mean square errors
Noise
Performance enhancement
Random noise
Stability analysis
Taylor series
Transient analysis
Title Behavior of the LMS algorithm with hyperbolic secant cost
URI https://dx.doi.org/10.1016/j.jfranklin.2019.12.040
https://www.proquest.com/docview/2379000448
Volume 357
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Baden-Württemberg Complete Freedom Collection (Elsevier)
  customDbUrl:
  eissn: 1879-2693
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0017100
  issn: 0016-0032
  databaseCode: GBLVA
  dateStart: 20110101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Elsevier ScienceDirect
  customDbUrl:
  eissn: 1879-2693
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0017100
  issn: 0016-0032
  databaseCode: .~1
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Elsevier ScienceDirect
  customDbUrl:
  eissn: 1879-2693
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0017100
  issn: 0016-0032
  databaseCode: AIKHN
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Elsevier ScienceDirect
  customDbUrl:
  eissn: 1879-2693
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0017100
  issn: 0016-0032
  databaseCode: ACRLP
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NT8JAEN0QvOjB-BlRJHvwWqE7S9v1RogEP-CiJNw2u21XIAik1Ku_3Z2yJWpMOHhtOk3zuvN2Zjr7hpCbluLC-AY8Flsn58xoL9Kce1GgufF1IJjGesdgGPRH_HHcHldItzwLg22Vjvs3nF6wtbvSdGg2V9MpnvH17W4N1uUARdNQdpvzEKcY3H5u2zx8VK_ZsLHNnO3dP3q8ZsZNRsceL1HUBbEK8vcO9Yuriw2od0QOXeRIO5uXOyaVdHFCDr7pCZ4S4dQOM7o01EZ29HnwQtX8bZlN88k7xZorndjEM9OoBkzXKeJK4-U6PyOj3v1rt--52QheDBxyTyjGVKpCHrS0jQgs48YQRQYSloAPGiIFIvETpTXjKjYoqpNYTrTZmhKRtYNzUl0sF-kFoWAgEKGGVLdjroNQtYVCkZYoTETMoVUjQYmHjJ1wOM6vmMuyQ2wmt0BKBFL6TFoga6S1NVxttDN2m9yVgMsfy0Baht9tXC8_kXSeuJYMQlH8to4u__PsK7LPMNMu-rXrpJpnH-m1DUdy3SjWW4PsdR6e-sMvxlTeow
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3PT8IwFG4QD-rB-DOiqD14nbC-sq3eDJGgAhch4da02yoQZGTMq3-77dYRMSYcvC57y_Kt73s_9voVobumoEy5ChwSaienREknkJQ6gSepcqXHiDT9jv7A647oy7g1rqB2uRfGjFVa7i84PWdre6Vh0Wwsp1Ozx9fV0Rq0y4ERTfN20C5tEd9UYPdf6zkP18jXFHSsS2d9-8aQ10zZo9HNkBfLG4OmDfJ3iPpF1nkE6hyhQ5s64sfi7Y5RJV6coIMfgoKniFm5wxQnCuvUDvf6b1jM35N0mk0-sGm64omuPFNp5IDxKjbA4jBZZWdo1HkatruOPRzBCYFC5jBBiIiFT72m1CmBptwQgkBBRCJwQUIggEVuJKQkVITKqOpEmhR1uSZYoO3gHFUXySK-QBgUeMyXEMtWSKXnixYTRqUl8CMWUmjWkFfiwUOrHG4OsJjzckRsxtdAcgMkdwnXQNZQc224LMQztps8lIDzjXXANcVvN66Xn4hbV1xxAj7L_1sHl_959i3a6w77Pd57HrxeoX1iyu58eLuOqln6GV_r3CSTN_na-wYJ2eA4
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Behavior+of+the+LMS+algorithm+with+hyperbolic+secant+cost&rft.jtitle=Journal+of+the+Franklin+Institute&rft.au=Lu%2C+Lu&rft.au=Chen%2C+Lihui&rft.au=Zheng%2C+Zongsheng&rft.au=Yu%2C+Yi&rft.date=2020-02-01&rft.issn=0016-0032&rft.volume=357&rft.issue=3&rft.spage=1943&rft.epage=1960&rft_id=info:doi/10.1016%2Fj.jfranklin.2019.12.040&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jfranklin_2019_12_040
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0016-0032&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0016-0032&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0016-0032&client=summon