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<front>
<journal-meta>
<journal-id journal-id-type="pmc">SV</journal-id>
<journal-id journal-id-type="nlm-ta">SV</journal-id>
<journal-id journal-id-type="publisher-id">SV</journal-id>
<journal-title-group>
<journal-title>Sound &#x0026; Vibration</journal-title>
</journal-title-group>
<issn pub-type="epub">2693-1443</issn>
<issn pub-type="ppub">1541-0161</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">15634</article-id>
<article-id pub-id-type="doi">10.32604/sv.2022.015634</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Dynamic Active Noise Control of Broadband Noise in Fighter Aircraft Pilot Helmet</article-title><alt-title alt-title-type="left-running-head">Dynamic Active Noise Control of Broadband Noise in Fighter Aircraft Pilot Helmet</alt-title><alt-title alt-title-type="right-running-head">Dynamic Active Noise Control of Broadband Noise in Fighter Aircraft Pilot Helmet</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Bharath</surname><given-names>Y. K.</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref><email>ykb@mcehassan.ac.in</email>
</contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Veena</surname><given-names>S.</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<aff id="aff-1"><label>1</label><institution>Malnad College of Engineering</institution>, <addr-line>Hassan, 573202</addr-line>, <country>India</country></aff>
<aff id="aff-2"><label>2</label><institution>National Aerospace Laboratories</institution>, <addr-line>Bengaluru, 560017</addr-line>, <country>India</country></aff>
</contrib-group><author-notes><corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Y. K. Bharath. Email: <email>ykb@mcehassan.ac.in</email></corresp></author-notes>
<pub-date date-type="collection" publication-format="electronic">
<year>2023</year></pub-date>
<pub-date date-type="pub" publication-format="electronic"><day>2</day>
<month>3</month>
<year>2023</year></pub-date>
<volume>56</volume>
<issue>4</issue>
<fpage>319</fpage>
<lpage>331</lpage>
<history>
<date date-type="received"><day>01</day><month>1</month><year>2021</year></date>
<date date-type="accepted"><day>18</day><month>3</month><year>2021</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2022 Bharath and Veena</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Bharath and Veena</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_SV_15634.pdf"></self-uri>
<abstract>
<p>This paper presents the development of a dynamic Active Noise Control (ANC) algorithm aimed towards reducing the broadband noise inside the helmet earcups of a fighter aircraft pilot helmet. The dynamic ANC involves a Variable Step-Size Griffiths (VSSG) FxLMS algorithm to attenuate noise entering directly through helmet, a LMS based adaptive noise canceller to attenuate noise entering through the pilot microphone, and energy detectors for failure protection and optimized battery power usage. The algorithms are implemented on Texas Instruments&#x2019; TMS320C6748 processor and are tested in a helmet ANC experimental setup.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Active noise control</kwd>
<kwd>Variable Step-Size Griffiths algorithm</kwd>
<kwd>FxLMS</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>The typical noise levels inside a fighter aircraft cockpit will be broadband and will be in the range from 95 to 105&#x2005;dB. This level of noise exceeds the OSHA requirement of 85 dBA, 8 h/day exposure criterion, which may affect the alertness of the pilot and prolonged exposure may result in hearing impairment. Increased rate of periodontal diseases and cardiovascular risks in aircrew members because of high cockpit noise demands the reduction of noise levels [<xref ref-type="bibr" rid="ref-1">1</xref>&#x2013;<xref ref-type="bibr" rid="ref-4">4</xref>]. Further, cockpit noise reaching the pilot&#x2019;s ear through radio communication channel affects the intelligibility of speech and makes the identification of caution signals difficult [<xref ref-type="bibr" rid="ref-5">5</xref>,<xref ref-type="bibr" rid="ref-6">6</xref>].</p>
<p>The primary objective of a pilot helmet is to provide safety. But, it also provides protection against certain amount of high frequency noise owing to passive noise attenuation achieved through its design and fitment [<xref ref-type="bibr" rid="ref-7">7</xref>]. However, considerable amount of low frequency noise will still penetrate the helmet and this can only be addressed with Active Noise Control (ANC) technique.</p>
<p>A few ANC headsets discussed in [<xref ref-type="bibr" rid="ref-8">8</xref>&#x2013;<xref ref-type="bibr" rid="ref-16">16</xref>] perform satisfactorily in aircraft cabin environments and helicopters. But to address noise inside a fighter aircraft helmet, the ANC algorithm needs to be more specific and dynamic to handle high level of noise entering through multiple paths. The noise appearing in the helmet earcups is because of two components, one is the low frequency noise that enters through the helmet directly, referred to as Cockpit Noise Direct (CND) and the other one is the noise that enters through the pilot microphone via Audio Management Unit (AMU), denoted as Cockpit Noise through AMU (CNA). Currently existing Helmet ANC systems for fighter aircrafts focus only on CND [<xref ref-type="bibr" rid="ref-17">17</xref>&#x2013;<xref ref-type="bibr" rid="ref-19">19</xref>]. In this paper CNA is also addressed along with CND.</p>
<p>Although tremendous efforts have been made by the scientific community to develop a better ANC system using machine learning algorithms like genetic algorithm, fuzzy logic, artificial neural network, etc. [<xref ref-type="bibr" rid="ref-20">20</xref>&#x2013;<xref ref-type="bibr" rid="ref-25">25</xref>], the traditional adaptive algorithms have always proven to be more stable, computationally less intensive and quite attractive to be used in real-time applications. Generally, noises like CND is addressed using FxLMS based Feed Forward ANC (FFANC) algorithm [<xref ref-type="bibr" rid="ref-26">26</xref>]. But here, as the noise is broadband in nature, better tracking of ANC system is necessary with respect to the varying noise levels and characteristics of the aircraft noise. For this, various adaptive ANC algorithms are proposed [<xref ref-type="bibr" rid="ref-27">27</xref>&#x2013;<xref ref-type="bibr" rid="ref-32">32</xref>]. In this paper, a Variable Step Size Griffiths (VSSG) algorithm for FxLMS algorithm as described in [<xref ref-type="bibr" rid="ref-33">33</xref>] has been used to achieve a faster convergence with lower residual noise. VSSG algorithms and its variants [<xref ref-type="bibr" rid="ref-34">34</xref>,<xref ref-type="bibr" rid="ref-35">35</xref>] have been proven for improved performance of LMS and FxLMS algorithms [<xref ref-type="bibr" rid="ref-36">36</xref>,<xref ref-type="bibr" rid="ref-37">37</xref>]. The second noise component, CNA is mitigated using an LMS based adaptive noise canceller.</p>
<p>In a typical ANC system, ANC algorithm starts execution once the system is powered ON, irrespective of the presence/absence of noise. This leads to unnecessary power consumption affecting the battery life. To tackle this, reference signal energy is used in this paper for turning ANC ON. Additionally, one of the major failure condition in the ANC system is the occurrence of divergence, which leads to the pilot being exposed to a higher level noise and deteriorated communication signals. This is a major safety issue and has to be addressed effectively. Signal energy [<xref ref-type="bibr" rid="ref-38">38</xref>,<xref ref-type="bibr" rid="ref-39">39</xref>] based tracking algorithm is proposed in this paper to address this issue. The algorithms proposed are targeted to meet the real-time requirements (majorly, less computational complexity and lower power consumption) of an embedded application. Further, the implementation of the algorithms is carried out on a Texas Instruments TMS320C6748 floating point DSP processor and its performance is demonstrated in a helmet ANC experimental setup.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Dynamic ANC Algorithms</title>
<p><xref ref-type="fig" rid="fig-1">Fig. 1</xref> shows the block diagram schematic of helmet ANC system. As discussed, the two noise components, CND and CNA are addressed using FFANC and adaptive noise canceller respectively. The cockpit noise picked up by reference microphone is used as noise reference <inline-formula id="ieqn-27">
<mml:math id="mml-ieqn-27"><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> for both FFANC and adaptive noise canceller. FFANC is based on VSSG FxLMS algorithm and has two separate channels for each earcup. The generated antinoise is fed through the audio communication speakers present inside the earcups. Adaptive noise canceller is based on LMS and its output (filtered pilot microphone signal) is fed to the same speakers. The residual noise is captured using error microphones placed inside the earcups. The algorithms to facilitate the dynamic operation of ANC so as to handle the scenarios in aircraft noise are depicted in <xref ref-type="fig" rid="fig-2">Fig. 2</xref> and are discussed in following subsections.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Block diagram schematic of Helmet ANC system</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-1.tif"/>
</fig><fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Algorithms for Helmet ANC</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-2.tif"/>
</fig>
<sec id="s2_1">
<label>2.1</label>
<title>VSSG FxLMS Algorithm for CND</title>
<p>In Normalized FxLMS algorithm as shown in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>, proposed by Sen et al. [<xref ref-type="bibr" rid="ref-26">26</xref>], the transfer function path between the reference microphone and the speaker is referred to as primary path denoted by <inline-formula id="ieqn-28">
<mml:math id="mml-ieqn-28"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>. The path between speaker and error microphone is referred to as secondary path denoted by <inline-formula id="ieqn-29">
<mml:math id="mml-ieqn-29"><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>, which is normally estimated offline (with random noise additive technique using LMS algorithm). <inline-formula id="ieqn-30">
<mml:math id="mml-ieqn-30"><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is the noise picked up by the reference microphone and <inline-formula id="ieqn-31">
<mml:math id="mml-ieqn-31"><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is the noise inside the earcup.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>FFANC using FxLMS algorithm</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-3.tif"/>
</fig>
<p>To estimate <inline-formula id="ieqn-32">
<mml:math id="mml-ieqn-32"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>, an adaptive FIR filter <inline-formula id="ieqn-33">
<mml:math id="mml-ieqn-33"><mml:msub><mml:mi>W</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> having <inline-formula id="ieqn-34">
<mml:math id="mml-ieqn-34"><mml:mtext>&#x00A0;</mml:mtext><mml:mi>L</mml:mi></mml:math>
</inline-formula> number of taps is used. Its coefficients are adjusted using,<disp-formula id="eqn-1"><label>(1)</label>
<mml:math id="mml-eqn-1" display="block"><mml:msub><mml:mi>W</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>&#x03BC;</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;</mml:mtext><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math>
</disp-formula>where,</p>
<p><inline-formula id="ieqn-35">
<mml:math id="mml-ieqn-35"><mml:msub><mml:mi>W</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>-main path filter.</p>
<p><inline-formula id="ieqn-36">
<mml:math id="mml-ieqn-36"><mml:mi>e</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>-residual noise at the loudspeaker point.</p>
<p><inline-formula id="ieqn-37">
<mml:math id="mml-ieqn-37"><mml:msub><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>-residual noise picked by error microphone.</p>
<p>In FxLMS algorithm, the input <inline-formula id="ieqn-38">
<mml:math id="mml-ieqn-38"><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is filtered using the secondary path estimate <inline-formula id="ieqn-39">
<mml:math id="mml-ieqn-39"><mml:msub><mml:mrow><mml:mover><mml:mi>S</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> having <inline-formula id="ieqn-40">
<mml:math id="mml-ieqn-40"><mml:mi>M</mml:mi></mml:math>
</inline-formula> number of taps, given by,<disp-formula id="eqn-2"><label>(2)</label>
<mml:math id="mml-eqn-2" display="block"><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">k</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>S</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>To compensate the large fluctuations in power levels of <inline-formula id="ieqn-41">
<mml:math id="mml-ieqn-41"><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>, the step size is normalized using,<disp-formula id="eqn-3"><label>(3)</label>
<mml:math id="mml-eqn-3" display="block"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">&#x03BC;</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03BC;</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>L</mml:mi><mml:mo>+</mml:mo><mml:mi>M</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-4"><label>(4)</label>
<mml:math id="mml-eqn-4" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math>
</disp-formula></p>
<p><inline-formula id="ieqn-42">
<mml:math id="mml-ieqn-42"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is the signal power. <inline-formula id="ieqn-43">
<mml:math id="mml-ieqn-43"><mml:mtext>&#x00A0;</mml:mtext><mml:mn>0</mml:mn><mml:mo>&#x003C;</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>
</inline-formula>&#x003C; 1 is known as the forgetting factor and should be small for fast varying signals.</p>
<p>Finally, the antinoise is computed using,<disp-formula id="eqn-5"><label>(5)</label>
<mml:math id="mml-eqn-5" display="block"><mml:mrow><mml:mi mathvariant="normal">y</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">k</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">L</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>This signal is fed to the speakers to cancel the acoustic noise. In LMS/FxLMS ANC algorithms, the convergence speed and final residual noise level depends on the step size <inline-formula id="ieqn-44">
<mml:math id="mml-ieqn-44"><mml:mi>&#x03BC;</mml:mi></mml:math>
</inline-formula>. Large values of <inline-formula id="ieqn-45">
<mml:math id="mml-ieqn-45"><mml:mi>&#x03BC;</mml:mi></mml:math>
</inline-formula> gives faster convergence but with higher residual noise. Smaller values of <inline-formula id="ieqn-46">
<mml:math id="mml-ieqn-46"><mml:mi>&#x03BC;</mml:mi></mml:math>
</inline-formula> results in lower residual noise but with slower convergence. However, ANC is expected to have better tracking, i.e., to have faster convergence with least residual noise possible. With a fixed &#x03BC;, any one of the objective is achievable. To have both advantages, Variable Step-Size Griffiths (VSSG) algorithm for FxLMS algorithm proposed by Narasimhan et al. [<xref ref-type="bibr" rid="ref-33">33</xref>] is used. This allows to have a larger step size in the beginning and a smaller step-size towards the convergence.</p>
<p>This algorithm is based on Griffiths&#x2019; cross correlation coefficient between reference noise <inline-formula id="ieqn-47">
<mml:math id="mml-ieqn-47"><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> and error <inline-formula id="ieqn-48">
<mml:math id="mml-ieqn-48"><mml:msub><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> and is estimated by,<disp-formula id="eqn-6"><label>(6)</label>
<mml:math id="mml-eqn-6" display="block"><mml:msub><mml:mi>G</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>G</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math>
</disp-formula></p>
<p>The step-size is updated using,<disp-formula id="eqn-7"><label>(7)</label>
<mml:math id="mml-eqn-7" display="block"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03BC;</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>&#x03BC;</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03C3;</mml:mi></mml:mrow></mml:mrow><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>y</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mn>2</mml:mn></mml:msup></mml:math>
</disp-formula></p>
<p>A higher value of <inline-formula id="ieqn-49">
<mml:math id="mml-ieqn-49"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03C3;</mml:mi></mml:mrow></mml:mrow></mml:math>
</inline-formula> enables the step-size to track the changes in the residual noise at a faster rate for non-stationary signals. <inline-formula id="ieqn-50">
<mml:math id="mml-ieqn-50"><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> determines the cutoff frequency. Therefore, the new adaptation rule for the weight coefficients of FxLMS algorithm is given by,<disp-formula id="eqn-8"><label>(8)</label>
<mml:math id="mml-eqn-8" display="block"><mml:msub><mml:mi>W</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>&#x2026;</mml:mo><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math>
</disp-formula></p>
<p>Here, the weight vector adaptation gradient <inline-formula id="ieqn-51">
<mml:math id="mml-ieqn-51"><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is computed using,<disp-formula id="eqn-9"><label>(9)</label>
<mml:math id="mml-eqn-9" display="block"><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>L</mml:mi><mml:mo>+</mml:mo><mml:mi>M</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>y</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo stretchy="false">]</mml:mo></mml:mstyle></mml:math>
</disp-formula></p>
<p>The noise free Griffiths&#x2019; cross correlation term <inline-formula id="ieqn-52">
<mml:math id="mml-ieqn-52"><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>G</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> used for computing gradient <inline-formula id="ieqn-53">
<mml:math id="mml-ieqn-53"><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>. The step-size <inline-formula id="ieqn-54">
<mml:math id="mml-ieqn-54"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03BC;</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow></mml:math>
</inline-formula> adaptation by VSSG FxLMS algorithm significantly enhances the convergence characteristics.</p>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Adaptive Noise Canceller for CNA</title>
<p>To address CNA, a LMS based adaptive noise canceller is used. The signal coming from Audio Management Unit (AMU) constitutes of ATC communication signals, warning signals, pilot speech and CNA. With the use of this adaptive noise canceller, CNA alone can be addressed without affecting other signals.</p>
<p>As shown in <xref ref-type="fig" rid="fig-4">Fig. 4</xref>, the path between reference mic and pilot mic, denoted as <inline-formula id="ieqn-55">
<mml:math id="mml-ieqn-55"><mml:mi>Q</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>, is identified using LMS algorithm. The weight updation of adaptive filter <inline-formula id="ieqn-56">
<mml:math id="mml-ieqn-56"><mml:mi>W</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> having <italic>L</italic> number of taps is done using,<disp-formula id="eqn-10"><label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:mi>W</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>W</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>&#x03BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mtext>&#x00A0;</mml:mtext><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mo>.</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math>
</disp-formula></p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Adaptive noise canceller based on LMS algorithm</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-4.tif"/>
</fig>
<p>The step size is normalized using,</p>
<p><disp-formula id="eqn-11"><label>(11)</label>
<mml:math id="mml-eqn-11" display="block"><mml:msubsup><mml:mrow><mml:mi>&#x03BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mi>L</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-12"><label>(12)</label>
<mml:math id="mml-eqn-12" display="block"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>x</mml:mi><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math>
</disp-formula></p>
<p>Here, <inline-formula id="ieqn-57">
<mml:math id="mml-ieqn-57"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> is the signal power. To remove the noise form noisy AMU signal, the noise signal estimate <inline-formula id="ieqn-58">
<mml:math id="mml-ieqn-58"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is computed by,</p>
<p><disp-formula id="eqn-13"><label>(13)</label>
<mml:math id="mml-eqn-13" display="block"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">k</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mi>W</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-14"><label>(14)</label>
<mml:math id="mml-eqn-14" display="block"><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mo>+</mml:mo><mml:mi>A</mml:mi><mml:mi>M</mml:mi><mml:mi>U</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula></p>
<p>The noise free AMU signal <inline-formula id="ieqn-59">
<mml:math id="mml-ieqn-59"><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is an electrical signal, which is added to FFANC antinoise signals and fed to the speakers.</p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Energy Based Detectors for ANC Operation</title>
<p>To achieve battery efficiency, ANC unit has to be turned ON only when the engine starts running. To achieve this, an energy based detector is employed where the Short Term Energy (STE) of <inline-formula id="ieqn-60">
<mml:math id="mml-ieqn-60"><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is used to determine the presence and absence of noise inside the cockpit.</p>
<p>For this, the energy of reference noise <inline-formula id="ieqn-61">
<mml:math id="mml-ieqn-61"><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> is continuously computed using,<disp-formula id="eqn-15"><label>(15)</label>
<mml:math id="mml-eqn-15" display="block"><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>N</mml:mi></mml:mfrac></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mi>x</mml:mi><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mstyle></mml:math>
</disp-formula>where, <italic>N</italic> is the length of the circular buffer typically in the order of 1024.</p>
<p>The ANC unit is turned ON only if <inline-formula id="ieqn-62">
<mml:math id="mml-ieqn-62"><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math>
</inline-formula> crosses a threshold. If <inline-formula id="ieqn-63">
<mml:math id="mml-ieqn-63"><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math>
</inline-formula> goes below threshold, ANC unit is turned OFF. The threshold value is set based on the minimum signal power when engine is turned ON.</p>
<p>In any aircraft management application, detecting the condition of failure and its management is a major task. In the case of helmet ANC, the increase of noise inside the earcups due to divergence of ANC algorithm is considered as the major failure condition as this results in increased amount of noise and affects the intelligibility of communication signals. This is a catastrophic condition and has to be handled effectively by resetting ANC by cautiously detecting divergence.</p>
<p>For this, the ANC RESET factor <italic>R</italic> is computed as the gain in decibels,<disp-formula id="eqn-16"><label>(16)</label>
<mml:math id="mml-eqn-16" display="block"><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn><mml:mtext>&#x00A0;</mml:mtext><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</disp-formula>where,<disp-formula id="eqn-17"><label>(17)</label>
<mml:math id="mml-eqn-17" display="block"><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>N</mml:mi></mml:mfrac></mml:mrow><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mstyle></mml:math>
</disp-formula></p>
<p>If <italic>R</italic> crosses the <inline-formula id="ieqn-64">
<mml:math id="mml-ieqn-64"><mml:mn>3</mml:mn></mml:math>
</inline-formula> dB margin during ANC operation, the ANC RESET condition is invoked by resetting <inline-formula id="ieqn-65">
<mml:math id="mml-ieqn-65"><mml:msub><mml:mi>W</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:math>
</inline-formula> and all related buffers.</p>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Simulation Results</title>
<p>For simulation of ANC algorithms, the cockpit noise of a Light Combat Aircraft (LCA) was recorded using M-Audio digital noise recorder. The recorded data consist of temporal noise during the takeoff, flight and landing conditions. The noise levels were recorded using a B&#x0026;K 2270 sound level meter, which showed that the noise levels vary between <inline-formula id="ieqn-66">
<mml:math id="mml-ieqn-66"><mml:mn>90</mml:mn><mml:mtext>&#xA0;</mml:mtext><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">B</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:mrow><mml:mspace width="negativethinmathspace" /><mml:mspace width="negativethinmathspace" /><mml:mo>&#x2212;</mml:mo><mml:mspace width="negativethinmathspace" /><mml:mspace width="negativethinmathspace" /><mml:mn>110</mml:mn><mml:mrow><mml:mtext>&#xA0;</mml:mtext><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">B</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:mrow></mml:math>
</inline-formula>. From the periodogram computed using MATLAB and one third octave spectrum computed using DATS analysis tool indicated that the noise spectrum was of broadband nature with significant contribution from low frequency components.</p>
<p>The algorithms discussed in <xref ref-type="sec" rid="s2">Section 2</xref> are simulated in MATLAB with parameters given in <xref ref-type="table" rid="table-1">Table 1</xref>. A practical impulse response of length 128 samples is used for VSSG-FXLMS and adaptive noise canceller. The comparison of ANC with and without VSSG can be seen in <xref ref-type="fig" rid="fig-5">Fig. 5</xref>.</p>
<table-wrap id="table-1"><label>Table 1</label>
<caption>
<title>Parameters used for ANC simulation</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Parameter</th>
<th align="left"><inline-formula id="ieqn-74">
<mml:math id="mml-ieqn-74"><mml:mi>&#x03BC;</mml:mi></mml:math>
</inline-formula></th>
<th align="left"><inline-formula id="ieqn-75">
<mml:math id="mml-ieqn-75"><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula></th>
<th align="left"><inline-formula id="ieqn-76">
<mml:math id="mml-ieqn-76"><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula></th>
<th align="left"><inline-formula id="ieqn-77">
<mml:math id="mml-ieqn-77"><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>
</inline-formula></th>
<th align="left"><inline-formula id="ieqn-78">
<mml:math id="mml-ieqn-78"><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mi>v</mml:mi></mml:msub></mml:math>
</inline-formula></th>
<th align="left"><inline-formula id="ieqn-79">
<mml:math id="mml-ieqn-79"><mml:mi>&#x03B1;</mml:mi></mml:math>
</inline-formula></th>
<th align="left"><inline-formula id="ieqn-80">
<mml:math id="mml-ieqn-80"><mml:mi>&#x03C3;</mml:mi></mml:math>
</inline-formula></th>
<th align="left"><inline-formula id="ieqn-81">
<mml:math id="mml-ieqn-81"><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula></th>
<th align="left"><inline-formula id="ieqn-82">
<mml:math id="mml-ieqn-82"><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Value</td>
<td align="left">0.1</td>
<td align="left">1</td>
<td align="left">0.02</td>
<td align="left">0.999</td>
<td align="left">0.999</td>
<td align="left">0.0001</td>
<td align="left">0.99</td>
<td align="left">0.1</td>
<td align="left">0.999</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>Comparison of ANC with and without VSSG</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-5.tif"/>
</fig>
<p>In <xref ref-type="table" rid="table-1">Table 1</xref>, <inline-formula id="ieqn-67">
<mml:math id="mml-ieqn-67"><mml:mi>&#x03BC;</mml:mi></mml:math>
</inline-formula> is the step size for ANC without VSSG. In ANC with VSSG, initially the step size is <inline-formula id="ieqn-68">
<mml:math id="mml-ieqn-68"><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>. Towards convergence, the step size keeps on decreasing and is stagnated to <inline-formula id="ieqn-69">
<mml:math id="mml-ieqn-69"><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula> to stop further reduction. In <xref ref-type="fig" rid="fig-5">Fig. 5</xref>, improved performance of ANC using VSSG-FXLMS can be observed with respect to convergence time and residual error.</p>

<p>A speech signal corrupted by fighter aircraft noise is considered for simulation of adaptive noise canceller. <xref ref-type="fig" rid="fig-6">Fig. 6</xref> shows the convergence of adaptive noise canceller.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>Convergence of adaptive noise remover</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-6.tif"/>
</fig>
<p><xref ref-type="fig" rid="fig-7">Fig. 7</xref> shows the simulation of algorithms for battery saving and system failure management, which are included to control ANC algorithm. It can bee observed that whenever ANC diverges, the main path filter coefficients are reset and antinoise starts to build from initial conditions. It can be seen that as the power of the reference signal varies, ANC system stabilizes itself on its own.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>ANC response with absence of noise and occurrence of divergence</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-7.tif"/>
</fig>
</sec>
<sec id="s4">
<label>4</label>
<title>Causality Condition for ANC Operation</title>
<p>For effective noise cancellation, antinoise must be available by the time the noise signal arrives at the speaker. It implies that the acoustical delay must be greater than the electrical delay. This is referred to as causality condition. This is a time constraint imposed by the ANC system and the real-time implementation of ANC algorithms must adhere to this condition. <xref ref-type="fig" rid="fig-8">Fig. 8</xref> depicts the delays involved in both acoustic and electrical domain.</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>ANC casualty condition</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-8.tif"/>
</fig>
<p>The acoustic delay from the input microphone to the speaker is given as,<disp-formula id="eqn-18"><label>(18)</label>
<mml:math id="mml-eqn-18" display="block"><mml:mrow><mml:mi mathvariant="normal">A</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">L</mml:mi></mml:mrow><mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:msub><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula>where,</p>
<p>A&#x2013;Acoustical delay.</p>
<p>L&#x2013;Distance between reference microphone and speaker in meters.</p>
<p><inline-formula id="ieqn-70">
<mml:math id="mml-ieqn-70"><mml:msub><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub></mml:math>
</inline-formula>&#x2013;Speed of sound in air in m/s.</p>
<p>Electrical delay is due to the delay involved in antinoise generation. The delay path involves the electronics and DSP processor. Apart from the application loop time of DSP, the lowpass filters contribute significantly to the electrical delay.</p>
<p>In case of helmet ANC, for typical distance of 20&#x2005;cm between reference microphones to speaker, the causality condition states that the DSP should operate at 14&#x2005;kHz, for 8<sup>th</sup> order butterworth filter [<xref ref-type="bibr" rid="ref-26">26</xref>]. To facilitate this condition, the algorithms have to be coded using processor specific assembly language only.</p>
</sec>
<sec id="s5">
<label>5</label>
<title>Real Time Evaluation of Dynamic ANC System</title>
<p>As shown in <xref ref-type="fig" rid="fig-1">Fig. 1</xref>, the reference noise from the cockpit is picked up using a high performance electret microphone. Microphones are fitted inside the helmet earcups for fetching error signals. The communication speakers fitted inside the earcups are used for ANC system as well. The ANC unit consists of a low power high performance DSP board based on TMS320C6748 and a signal conditioner board which consists of pre amplifiers for microphones, low pass filters, A/D and D/A converters, anti-aliasing filters, reconstruction filters and power amplifier for loud speakers. It also has an SD card slot for recording the residual noise inside the helmet earcup (error microphone signal) for offline analysis of ANC performance. The ANC unit is powered by a 9 V rechargable battery. The AMU simulator mixes the pilot microphone signal with the communication signals received from Air Traffic Control (ATC).</p>
<p>To meet the computational requirements of the algorithms, they are coded with pre-estimated secondary path coefficients on DSP processor using processor specific hand optimized assembly language coding. With optimized coding, s sampling frequency of 14&#x2005;kHz was achieved which greatly increases the processing speed of the DSP. The operating noise frequency range of ANC is largely affected by the the execution speed of ANC algorithm on the DSP board. As the Nyquist sampling criteria suggests: to avoid aliasing, the operation bandwidth should always be less than half of the sampling frequency, i.e., <inline-formula id="ieqn-72">
<mml:math id="mml-ieqn-72"><mml:mrow><mml:mi mathvariant="normal">B</mml:mi></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">f</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:math>
</inline-formula> [<xref ref-type="bibr" rid="ref-40">40</xref>]. Hence the ANC cutoff frequency was set to 4&#x2005;kHz (i.e., ANC will satisfactorily operate to the noise components having frequencies upto 4&#x2005;kHz).</p>
<p>The experiments were conducted in an acoustically treated semi-anechoic chamber at CSIR-NAL (<xref ref-type="fig" rid="fig-9">Fig. 9</xref>). Recorded cockpit noise is played using a 100W loudspeaker and the audio signals from error microphones are recorded in the SD card during ANC is Off and On.</p>
<fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>Experimental setup for testing helmet ANC system</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-9.tif"/>
</fig>
<p>The Power Spectral Density (PSD) of the cockpit reference noise, residual noise signals during ANC is Off and On are computed. The Noise attenuation in terms of decibels at particular frequencies is shown in <xref ref-type="fig" rid="fig-10">Fig. 10</xref>. It can be observed from <xref ref-type="fig" rid="fig-10">Fig. 10</xref> that the helmet filters out much of the high frequency noise components of cockpit noise (passive noise attenuation) and the ANC unit effectively handles low frequency noise components within 4 kHz.</p>
<fig id="fig-10">
<label>Figure 10</label>
<caption>
<title>Dynamic ANC system performance in frequency domain</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="SV_15634-fig-10.tif"/>
</fig>
<p>The ANC system performance is normally defined as the attenuation achieved in terms of Signal to Noise Ratio (SNR) in dB, which is computed using,<disp-formula id="eqn-19"><label>(19)</label>
<mml:math id="mml-eqn-19" display="block"><mml:mi>S</mml:mi><mml:mi>N</mml:mi><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn><mml:mtext>&#x00A0;</mml:mtext><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mtext>&#x00A0;&#x00A0;</mml:mtext><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mi>e</mml:mi><mml:mrow><mml:mi>A</mml:mi><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>O</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mi>e</mml:mi><mml:mrow><mml:mi>A</mml:mi><mml:mi>N</mml:mi><mml:mi>C</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>O</mml:mi><mml:mi>f</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math>
</disp-formula></p>
<p>The passive and active noise attenuation achieved by the Helmet and dynamic ANC respectively are tabulated in <xref ref-type="table" rid="table-2">Table 2</xref>.</p>
<table-wrap id="table-2"><label>Table 2</label>
<caption>
<title>Performance of dynamic helmet ANC</title></caption>
<table><colgroup><col align="left"/><col align="left"/><col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left"/>
<th align="left">Passive noise attenuation achieved by the helmet without ANC compared to noise outside the helmet</th>
<th align="left">Noise attenuation achieved by dynamic ANC compared to noise inside the helmet without ANC</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Attenuation achieved</td>
<td align="left">26&#x2005;dB</td>
<td align="left">18.06&#x2005;dB</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The ANC helmets and headsets discussed in [<xref ref-type="bibr" rid="ref-8">8</xref>&#x2013;<xref ref-type="bibr" rid="ref-16">16</xref>], give passive noise attenuation of 10&#x2013;15&#x2005;dB and active noise reduction of 5&#x2013;10&#x2005;dB. Compared to these, the proposed dynamic ANC system gives passive noise reduction of 26&#x2005;dB and active noise attenuation of 18.06&#x2005;dB as seen from <xref ref-type="table" rid="table-2">Table 2</xref>.</p>

</sec>
<sec id="s6">
<label>6</label>
<title>Conclusion</title>
<p>In this paper, a dynamic ANC system has been presented which proves suitable for a fighter aircraft pilot helmet. The ANC unit caters the noise entering through helmet using FFANC. The noise entering through AMU is catered using adaptive noise canceller. The robustness of the system was increased by using VSSG FxLMS algorithm which facilitates faster convergence and lower residual noise. Energy based detectors used for ANC operation control saves battery charge life cycle. The processor specific assembly language used for coding algorithms facilitated higher sampling rate enabling the generation of more samples of antinoise per second. The real-time evaluation shows that the dynamic helmet ANC system is capable of attenuating significant amount fighter aircraft cockpit noise.</p>
</sec>
</body>
<back>
<glossary content-type="abbreviations" id="glossary-1">
<def-list>
<title>Nomenclature</title>
<def-item>
<term><inline-formula id="ieqn-1">
<mml:math id="mml-ieqn-1"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Primary path</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-2">
<mml:math id="mml-ieqn-2"><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Secondary path</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-3">
<mml:math id="mml-ieqn-3"><mml:msub><mml:mrow><mml:mover><mml:mi>S</mml:mi><mml:mo stretchy="false">&#x005E;</mml:mo></mml:mover></mml:mrow><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Secondary path estimate with <italic>M</italic> taps</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-4">
<mml:math id="mml-ieqn-4"><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Reference input noise signal</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-5">
<mml:math id="mml-ieqn-5"><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Filtered input signal</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-6">
<mml:math id="mml-ieqn-6"><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Earcup noise</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-7">
<mml:math id="mml-ieqn-7"><mml:msub><mml:mi>W</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Main path filter with <inline-formula id="ieqn-8">
<mml:math id="mml-ieqn-8"><mml:mi>L</mml:mi></mml:math>
</inline-formula> taps</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-9">
<mml:math id="mml-ieqn-9"><mml:mi>y</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Antinoise</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-10">
<mml:math id="mml-ieqn-10"><mml:mi>e</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Residual noise at loudspeaker point</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-11">
<mml:math id="mml-ieqn-11"><mml:msub><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Residual noise picked by error microphone</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-12">
<mml:math id="mml-ieqn-12"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03BC;</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Step-size</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-13">
<mml:math id="mml-ieqn-13"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Input signal power</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-14">
<mml:math id="mml-ieqn-14"><mml:mi>&#x03B2;</mml:mi></mml:math>
</inline-formula></term>
<def>
<p>Forgetting factor which decides cutoff frequency</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-15">
<mml:math id="mml-ieqn-15"><mml:msub><mml:mi>G</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:math>
</inline-formula></term>
<def>
<p>Griffiths&#x00027; cross-correlation coefficient</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-16">
<mml:math id="mml-ieqn-16"><mml:mi>&#x03B1;</mml:mi></mml:math>
</inline-formula></term>
<def>
<p>Step-size adaptation rate</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-17">
<mml:math id="mml-ieqn-17"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03C3;</mml:mi></mml:mrow></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Residual noise tracker</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-18">
<mml:math id="mml-ieqn-18"><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Weight vector adaptation factor</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-19">
<mml:math id="mml-ieqn-19"><mml:mi>W</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:math>
</inline-formula></term>
<def>
<p>Noise canceller filter with <italic>L</italic> taps</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-20">
<mml:math id="mml-ieqn-20"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Noise estimate of noise canceller</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-21">
<mml:math id="mml-ieqn-21"><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Noise free speech signal</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-22">
<mml:math id="mml-ieqn-22"><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math>
</inline-formula></term>
<def>
<p>Energy of reference noise signal</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-23">
<mml:math id="mml-ieqn-23"><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:math>
</inline-formula></term>
<def>
<p>Energy of residual noise signal</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-24">
<mml:math id="mml-ieqn-24"><mml:mi>R</mml:mi></mml:math>
</inline-formula></term>
<def>
<p>ANC Resetting factor</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-25">
<mml:math id="mml-ieqn-25"><mml:msub><mml:mrow><mml:mi mathvariant="normal">f</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula></term>
<def>
<p>Sampling frequency</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-26">
<mml:math id="mml-ieqn-26"><mml:mi>B</mml:mi></mml:math>
</inline-formula></term>
<def>
<p>Bandwidth</p>
</def>
</def-item>
</def-list>
</glossary>
<ack>
<p>Authors acknowledge National Aerospace Laboratories, Bangalore for ANC laboratory setup where the experiments were carried out.</p>
</ack>
<sec><title>Funding Statement</title>
<p>The project was funded by <funding-source>National Programme on Micro and Smart Systems (NPMaSS), Aeronautical Development Agency (ADA)</funding-source>, Bangalore. Grant No. <award-id>ADA/NPMASS159/2015</award-id>, S. Veena, <ext-link ext-link-type="uri" xlink:href="https://ada.gov.in/">https://ada.gov.in/</ext-link>.</p>
</sec>
<sec sec-type="COI-statement">
<title>Conflicts of Interest</title>
<p>The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</sec>
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