### ACOUSTIC VECTOR SENSOR BASED DOA ESTIMATION OF SNOW AVALANCHES WITH

### INFRASOUND MODELING

### RAJANI AKULA

### CENTRE FOR APPLIED RESEARCH IN ELECTRONICS INDIAN INSTITUTE OF TECHNOLOGY DELHI

### April 2018

### ACOUSTIC VECTOR SENSOR BASED DOA ESTIMATION OF SNOW AVALANCHES WITH

### INFRASOUND MODELING

by

### RAJANI AKULA

### Centre for Applied Research in Electronics

### Submitted

in fulfillment of the requirements of the degree of Doctor of Philosophy

### to the

### Indian Institute of Technology Delhi

### April 2018

### © Indian Institute of Technology Delhi (IITD), New Delhi, 2018

### Certificate

This is to certify that the thesis entitled “Acoustic vector sensor based DoA estimation of Snow avalanches with infrasound modeling”, submitted by Rajani Akula, a research scholar in the Centre For Applied Research In Electronics, Indian Institute Of Technology, Delhi, for the award of the degree of Doctor of Philosophy, is a record of an original re- search work carried out by her under our supervision and guidance. The thesis has fulfilled all requirements as per the regulations of the institute and in our opinion has reached the standard needed for submission.

(Dr. Monika Aggarwal) Associate Professor

Centre For Applied Research In Electronics Indian Institute of Technology Delhi

New Delhi - 110 016, India.

(Dr. Arun Kumar) Professor

Centre For Applied Research In Electronics Indian Institute of Technology Delhi

New Delhi - 110 016, India.

Date:

Place: New Delhi.

### To

### My dear parents

### Late. Sri. Raja Rao Akula Smt. Vijaya Kumari Geddam

### The Creator

### who gave meaning to my existence

ii

### Acknowledgements

I would like to express my deepest gratitude to all those people who directly and indirectly sup- ported in the realization of this work. First and foremost, I would like to thank my supervisors, Professor Arun Kumar and Dr. Monika Aggarwal, for their continuous guidance, support, and encouragement during my Ph.D. study at Indian Institute of Technology Delhi, India. Their invaluable suggestions and precious ideas have helped me walk through various stages of my research, while their passion and extraordinary dedication to research inspired and encouraged me to work harder.

Professor Arun Kumar’s commitment towards his students is an inspiration to me, despite having the most demanding work schedules, he always makes time for his Ph.D students. His thought provoking questions, suggestions, vision and encouragement helped me through out my research and for writing this thesis. Dr. Monika Aggarwal given her timely help and support and encouragement through out this work and its been invaluable. Their wide expertise is a great help for me. I am greatly indebted to both my guides. Without their inputs, I could not have finished this work.

I am grateful to the members of my dissertation committee, Prof Rajender Bahl, CARE Department, Prof S.D.Joshi, of Electrical Engineering Department, and Prof Ananjan Basu, Head of CARE Department, for their constructive suggestions and excellent advice for the progress of this research work. I am also thankful to the faculty in my department and Electrical Engineering department for the concern and encouragement provided during the period of my stay.

I would also like to thank my fellow students in the department Lokesh, Hemalatha, Rinky Gupta, Sharbari Benarjee, Abhimanyu, Kapil Tyagi, Mohd.Wajid, Prashanth, Bipin Patel, Arun goel, Akanksha, Ashish Malik, Akaash, Nithin, Ambika, Reshmi, Surya Prakash, Kamini, Payal, Ruchi, Farheen, Sheena, Ayush for the unconditional support and friendship. I thank all of them for making our lab such a friendly place to work. I would like to acknowledge the

help provided by the office staff of CARE, Mr Joseph and Mr Purshottam. I want to thank my colleagues at J.N.T.U.H college of engineering, Hyderabad, for the friendship. I take this opportunity to thank the J.N.T.U.H. University authorities for granting QIP leave.

I would like to express my sincere thanks to my parents for the unconditional love, support and the sacrifices they have done in life to ensure my continuous progress. Whatever I am today is because of my parents instillation of valuing education and striving towards knowing the truth. I wish to extend my sincere thanks to my brothers, sisters in law and brothers in law and their families for their cooperation, and support during all these years of my studies.

I owe thanks to a very special person, my husband, Mallesham for his continued, unfailing support and understanding during my pursuit of Ph.D degree that made the completion of thesis possible. You were always around at times I thought that it is impossible to continue.

I greatly value his contribution and deeply appreciate his belief in me. I appreciate my sons, Master Dheeraj and Master Suraj, for bearing my absence and the patience they showed during my research time. Words would never say how grateful I am to both of you. During my stay at IITD I had an opportunity to meet several people of different bands in the campus and out of campus, who have enriched me in leading my life and I would like to thank all of them for their friendship, support and prayers. I consider myself blessed by God, to have such a caring family, friends, guides, elders and relatives.

Date: April 2018

Place: New Delhi Rajani Akula

iv

## Abstract

Snow avalanches are one of the natural phenomenon among the less understood, more unpredictable and dangerous disasters. Snow is formed by condensation of water vapour because of atmospheric variations and type of snow formed varies with atmospheric conditions and wind, creating the possibility of snow avalanches.

On mountain slopes avalanches causes destruction of burying whatever comes on its way and blocking the roads, thereby causing inconvenience to transportation. So its monitoring and localization is crucial for the safety and convenience of people.

For this purpose, the infra sound generated from the movement of snow avalanches is used. The time evolution of infrasound emitted by snow avalanches depends on different types of snow like wet (dense) or dry (powder) and their interaction with air. The governing differential equations of the generation of sound from a dipole are modeled into a signal processing framework comprising of an input, a time-varying linear system and an output that is the observable infrasound signature of the snow avalanche at a distant receiver. Using Fourier analysis, the relation between the snow mass size and spectral content of pressure is analyzed. In this thesis, a parameterized signal processing model is given to synthesize realistic infrasound signatures for varying values of the size of the avalanche and speed profile.

Finding direction of arrival (DoA) of a source is traditionally done with an array of sensors arranged in a particular geometry. The spatial resolution of an array depends on the aperture and frequency of the source. For the low infrasonic fre- quencies the array aperture needs to be of the order of 50-150 m to provide useful angular resolution. But in the mountain regions getting this large area to install such an array is too difficult which motivated to look for alternate solutions of a

more compact structure having similar capabilities. An acoustic vector sensor (AVS) which measures pressure and particle velocity in three orthogonal directions at the same time, is more promising alternative in terms of its size and spatial resolution characteristics. There are two types of AVS, namlely p-u AVS and p-p AVS. In this thesis the latter one is chosen to obtain 2D-DoA, which calculates particle velocity in X, Y directions with finite difference approximation of pressure gradient using Euler’s relation. For this approximation to be valid the factor kd 1 is required where k is the wavenumber and d is the inter- sensor separation. To study the performance of p-p AVS for estimating DoA, three pressure sensors are taken and placed in L- shaped geometry. The performance metrics of DoA estimation viz, bias and RMSE are calculated for p-p AVS with MUSIC and Arc-Tan DoA estimation algorithms. By considering the proposed L- shaped geometry to be an array, MUSIC algorithm is applied and compared with p-p AVS MUSIC and Arc-Tan methods.

The performance evaluation of all the three algorithms is done in the presence of uncorrelated noise, correlated noise and wind noise. Simulations are done for both narrowband and broadband sources. From the results, it is shown that for d less than 0.15 λ better performance is obtained using AVS-MUSIC, Arc-Tan compared to Array-MUSIC. When performance is compared for correlated and uncorrelated noise, performance is improved for correlated noise compared to uncorrelated noise using AVS-MUSIC algorithm. For both narrowband and broadband sources, RMSE reduces with increase in signal to noise (SNR) ratio.

Snow avalanche regions mostly occupied with mountains of different heights and
slope profiles. There is a possibility of getting strong multipath signals at the
monitoring systems installed in these regions. To take care of this situation, the
performance of DoA algorithms is studied with two uncorrelated sources and cor-
related sources. The two sources are resolved with SNR greater than 40 dB when
the angular separation is larger than 30^{◦}. To test the feasibility of installing the

vi

proposed p-p AVS, we have experimentally studied the performance of AVS in anechoic room at 200 Hz, 200-300 Hz and also with data acquired at 20 Hz, 25 Hz, 30 Hz, 35 Hz in open air environment. The results are encouraging towards use of the proposed system in real snow avalanche environment.

### सार

बर्फ के हिमस्खलन कम समझाए गए, अहिक अप्रत्याहित और खतरनाक आपदाओं में से एक प्राकृहतक घटना िै।

वायुमंडल की हवहविता और बर्फ के प्रकार के कारण जल वाष्प के घनत्व से बर्फ का गठन वायुमंडलीय पररस्थिहतय ं और िवा के साि बदलता िै, हजससे हिमपात की संभावनाएं पैदा ि ती िैं। पवफत ढलान ं पर अविेष ं का कारण बनता

िै ज सड़क ं क अवरुद्ध करता िै और सड़क ं क अवरुद्ध करता िै, हजससे पररविन के हलए असुहविा ि ती िै।

इसहलए ल ग ं की सुरक्षा और सुहविा के हलए इसकी हनगरानी और थिानीयकरण मित्वपूणफ िै। इस उद्देश्य के हलए, बर्फ अविेष ं के आंद लन से उत्पन्न इन्फ्रा ध्वहन का उपय ग हकया जाता िै। बर्फ अविेष ं द्वारा उत्सहजफत इंरासाउंड का

समय हवकास गीले (घने) या िुष्क (पाउडर) और िवा के साि उनकी बातचीत जैसे हवहभन्न प्रकार की बर्फ पर हनभफर करता िै। एक डीप ल से ध्वहन की पीढी के िासकीय हवभेदक समीकरण ं क एक इनपुट, एक समय-हभन्न रैस्खक प्रणाली और एक आउटपुट ज एक दूरथि ररसीवर पर बर्फ हिमस्खलन के अवल कनिील इंरासाउंड िस्ताक्षर समेत हसग्नल प्र सेहसंग रेमवकफ में मॉडहलंग हकया जाता िै। र्ूररयर हवश्लेषण का उपय ग, बर्फ द्रव्यमान आकार और दबाव की वणफक्रमीय सामग्री के बीच संबंि का हवश्लेषण हकया जाता िै। इस िीहसस में, हिमस्खलन और गहत प्र र्ाइल के

आकार के हवहभन्न मूल् ं के हलए यिािफवादी इन्फ्रासाउंड िस्ताक्षर क संश्लेहषत करने के हलए पैरामीटरयुक्त हसग्नल प्र सेहसंग मॉडल हदया जाता िै।

एक स्र त के आगमन (डीओए) की हदिा ख जना परंपरागत रूप से एक हविेष ज्याहमहत में व्यवस्थित सेंसर के साि

हकया जाता िै। एक सरणी का थिाहनक संकल्प स्र त की एपचफर और आवृहि पर हनभफर करता िै। कम इन्फ्रेंसैहसक आवृहिय ं के हलए सरणी एपचफर क 50-150 मीटर के ऑडफर के हलए उपय गी क ण रेज़ल्ूिन प्रदान करने की

आवश्यकता िै। लेहकन पिाड़ क्षेत् ं में इस तरि के एक सरणी क थिाहपत करने के हलए इस बड़े क्षेत् क प्राप्त करना

बहुत मुस्िल िै ज समान क्षमताओं वाले अहिक कॉम्पैक्ट संरचना के वैकस्ल्पक समािान ं क देखने के हलए प्रेररत िै।

एक ध्वहनक वेक्टर सेंसर (एवीएस) ज एक िी समय में तीन ऑिोग नल हदिाओं में दबाव और कण वेग क मापता िै, इसके आकार और थिाहनक ररज़ॉल्ूिन हविेषताओं के संदभफ में अहिक आिाजनक हवकल्प िै। द प्रकार के एवीएस

िैं, अिाफत् पी-यू एवीएस और पी-पी एवीएस। इस िीहसस में बाद वाले क 2 डी-डीओए प्राप्त करने के हलए चुना जाता िै, ज एक्स, वाई हदिाओं में कण वेग की गणना करता िै हजसमें यूलर के संबंि का उपय ग करके दबाव ढाल के सीहमत अंतर अनुमान के साि ि ता िै। इस अनुमान के हलए वैि ि ने के हलए कारक की आवश्यकता ि ती िै जिां 'के' wavenumber िै और 'डी' अंतर सेंसर अलगाव िै। डीओए का अनुमान लगाने के हलए पी-पी एवीएस के प्रदिफन का

अध्ययन करने के हलए, तीन दबाव सेंसर हलया जाता िै और एल-आकार वाली ज्याहमहत में रखा जाता िै। डीओए अनुमान के प्रदिफन मीहटिक जैसे पूवाफग्रि और आरएमएसई की गणना संगीत और आकफ-टैन डीओए अनुमान एल्ग ररदम के साि

पी-पी एवीएस के हलए की जाती िै। प्रस्ताहवत एल-आकार वाली ज्याहमहत क एक सरणी मानने पर हवचार करके, संगीत एल्ग ररदम लागू ि ता िै और पी-पी एवीएस संगीत और आकफ-टैन हवहिय ं की तुलना में हकया जाता िै। सभी तीन एल्ग ररदम का प्रदिफन मूल्ांकन असंबद्ध ि र, सिसंबंहित ि र और वायु ि र की उपस्थिहत में हकया जाता िै।

हसमुलेिन द न ं संकीणफ बैंड और ब्रॉडबैंड स्र त ं के हलए हकया जाता िै। पररणाम ं से, यि हदखाया गया िै हक 0.15 एल से कम 'डी' के हलए एआरएस-म्यूहसक, आकफ-टैन का उपय ग ऐरे-म्यूहसक की तुलना में बेितर प्रदिफन प्राप्त हकया जाता

िै। जब सिसंबंहित और असंबद्ध ि र के प्रदिफन की तुलना की जाती िै, त एवीएस-संगीत एल्ग ररदम का उपय ग

करते हुए असंबद्ध ि र की तुलना में सिसंबंहित ि र के हलए प्रदिफन में सुिार ि ता िै। द न ं संकीणफ और ब्रॉडबैंड स्र त ं के हलए, आरएमएसएस ि र (एसएनआर) अनुपात में संकेत में वृस्द्ध के साि कम करता िै

बर्फ हिमस्खलन क्षेत् ं में ज्यादातर ऊंचाइय ं और ढलान प्र र्ाइल के पिाड़ ं पर कब्जा कर हलया जाता िै। इन क्षेत् ं में

थिाहपत हनगरानी प्रणाली पर मजबूत मल्टीपाि हसग्नल प्राप्त करने की संभावना िै। इस स्थिहत का ख्याल रखने के हलए, डीओए एल्ग ररदम का प्रदिफन द असंबद्ध स्र त ं और सिसंबंहित स्र त ं के साि अध्ययन हकया जाता िै। द स्र त ं क 40 डीबी से अहिक एसएनआर के साि िल हकया जाता िै जब क णीय पृिक्करण 300 से बड़ा ि ता िै। प्रस्ताहवत पीपी

एवीएस थिाहपत करने की व्यविायफता का परीक्षण करने के हलए, िमने एंज इक कमरे में 200 िट्फज, 200-300 िट्फज पर एवीएस के प्रदिफन का प्रय ग हकया िै और खुले वायु पयाफवरण में 20 िट्फज, 25 िट्फज, 30 िट्फज, 35 िट्फज पर अहिग्रहित डेटा के साि भी। पररणाम वास्तहवक बर्फ हिमस्खलन पयाफवरण में प्रस्ताहवत प्रणाली के उपय ग की हदिा में प्र त्साहित कर रिे िैं।

## Contents

Certificate i

Acknowledgements iii

Abstract v

List of Figures xi

List of Tables xvi

List of Acronyms xvii

List of Symbols xx

1 Introduction 1

1.1 Background about snow avalanches . . . 2

1.2 Literature survey . . . 6

1.2.1 Modeling of snow avalanches . . . 6

1.2.2 Infrasound modeling . . . 10

1.2.3 Avalanche DoA estimation . . . 11

1.2.4 DoA of two sources . . . 14

1.2.5 Correlated noise . . . 15

1.2.6 Uncorrelated noise . . . 15

1.2.7 Wind noise . . . 16

1.3 Problem statement and Research contributions . . . 21

1.4 Organization of the thesis . . . 24

2 Sound Source Modeling 26 2.1 Introduction . . . 27

viii

Contents

2.2 Wave equation . . . 28

2.3 Sources of sound . . . 32

2.3.1 Point Monopole . . . 33

2.3.2 Point Dipole . . . 34

2.3.3 Point Quadrupole . . . 35

2.4 Modeling of sound from avalanches . . . 36

2.4.1 Dense part as LTV system with dipole source . . . 38

2.4.2 Powder part as quadrupole source . . . 41

2.5 Simulation Results . . . 42

2.5.1 For Dipole source: . . . 42

2.5.2 For Quadrupole source: . . . 47

2.6 Conclusions . . . 51

3 DoA estimation of single source 52 3.1 Introduction . . . 53

3.2 Array based DoA estimation . . . 56

3.2.1 MUSIC algorithm . . . 57

3.3 AVS based DoA estimation . . . 59

3.3.1 Derivation of particle velocity by Finite difference approximation . . . . 59

3.3.2 Derivation of acoustic intensity in p-p method . . . 60

3.3.3 Arc-Tan Method of DoA estimation . . . 62

3.3.4 AVS-MUSIC Method of DoA estimation . . . 62

3.4 Correlated noise . . . 63

3.5 Wind noise . . . 65

3.6 Simulation Results . . . 66

3.6.1 Narrow band source . . . 68

3.6.2 Broadband source . . . 87

3.7 Conclusions . . . 92

4 DoA estimation of two sources 93

Contents

4.1 Introduction . . . 94

4.2 Resolving two sources . . . 96

4.3 Data model for scalar array with two sources . . . 97

4.4 Data model for Arc-Tan method with two sources . . . 98

4.5 Data model for single p-p AVS with two sources . . . 98

4.6 Simulation Results . . . 99

4.6.1 Uncorrelated narrowband sources . . . 100

4.6.2 Uncorrelated Broadband sources . . . 103

4.6.3 Correlated sources . . . 104

4.7 Conclusion . . . 105

5 DoA estimation with representative real data 106 5.1 Introduction . . . 107

5.2 Experimental setup for anechoic room . . . 107

5.2.1 Correcting the sensitivity factor . . . 108

5.3 Experimental setup for open air . . . 109

5.3.1 Aliasing . . . 109

5.3.2 Reducing data storage space . . . 109

5.3.3 Wind noise shields . . . 110

5.4 Experimental Results . . . 112

5.4.1 Anechoic room . . . 112

5.4.2 Open air . . . 113

5.5 Conclusion . . . 141

6 Conclusions 142 6.1 Conclusions . . . 143

6.2 Future scope of work . . . 146

Bibliography 146

List of Publications 155

x

List of Figures

Biodata 157

## List of Figures

1.1 Cross section of a mixed avalanche showing the different parts of avalanche. . . . 2

1.2 Cross section of a mixed avalanche showing the different parts of avalanche. . . . 3

2.1 Impulse response h(t) with sphere radius R . . . 43

2.2 Frequency response H(f) with sphere radius R . . . 44

2.3 Avalanche front velocity calculated from PDR data . . . 45

2.4 Pressure with LTV system. . . 45

2.5 Frequency spectrum for pressure generated using LTV system . . . 46

2.6 Pressure spectrum in logarithmic scale for LTV model . . . 46

2.7 Intensity for varying frequency . . . 47

2.8 Pressure for varying frequency . . . 48

2.9 Pressure with varying density ρ from 1 to 5 Kg/m^{3}. . . 48

2.10 Pressure with varying flow dimension D from 10 m to 18 m. . . 49

2.11 Pressure time series from AR process . . . 50

2.12 Pressure spectrum from AR time series . . . 50

2.13 Pressure spectrum in logarithmic scale from AR time series . . . 51

3.1 Wind noise correlations in down wind direction with inter-sensor separation in wavelengths λ. . . 66

3.2 L shape geometry . . . 67

3.3 Variation of bias in DoA estimate with DoAs taken in the range of 1^{0} to 90^{0}
without noise. . . 69

xii

List of Figures

3.4 Variation of RMSE in DoA estimate with DoAs taken in the range of 1^{0} to 90^{0}

without noise. . . 69

3.5 Variation of Bias with inter sensor separation without noise . . . 70

3.6 Variation of RMSE with inter-sensor separation without noise . . . 70

3.7 Variation of Bias with inter-sensor separation without noise using FEM data . . 72

3.8 Variation of RMSE with inter-sensor separation without noise using FEM data . 72 3.9 Variation of bias with SNR for correlated noise . . . 73

3.10 Variation of RMSE with SNR for correlated noise . . . 74

3.11 Variation of bias with inter-sensor separation for correlated noise . . . 74

3.12 Variation of RMSE with inter-sensor separation for correlated noise. . . 75

3.13 Variation of bias with Angles for correlated noise . . . 76

3.14 Variation of RMSE with angles for correlated noise. . . 76

3.15 Variation of bias with SNR for correlated noise . . . 77

3.16 Variation of RMSE with SNR for correlated noise . . . 77

3.17 Variation of bias with inter-sensor separation for correlated noise . . . 78

3.18 Variation of RMSE with Separation for correlated noise . . . 78

3.19 Variation of RMSE with Angles Uncorrelated noise . . . 79

3.20 Variation of Bias with SNR for uncorrelated noise . . . 80

3.21 Variation of RMSE with SNR for uncorrelated noise . . . 80

3.22 Variation of Bias with inter-sensor separation for uncorrelated noise . . . 81

3.23 Variation of RMSE with inter-sensor separation for uncorrelated noise . . . 81

3.24 Variation of Bias with inter-sensor separation for uncorrelated noise . . . 82

3.25 Variation of RMSE with inter-sensor separation for uncorrelated noise . . . 82

3.26 Variation of bias with SNR for uncorrelated noise . . . 83

3.27 Variation of RMSE with SNR for uncorrelated noise. . . 83

3.28 Wind noise from power spectral density . . . 84

3.29 Variation of bias with inter-sensor separation for wind noise . . . 85

3.30 Variation of RMSE with Separation for wind noise . . . 85

List of Figures

3.31 Variation of Bias with inter-sensor separation for wind noise . . . 86

3.32 Variation of RMSE with inter-sensor separation for wind noise . . . 87

3.33 Variation of Bias with inter-sensor separation for correlated noise . . . 88

3.34 Variation of RMSE with inter-sensor separation for correlated noise . . . 89

3.35 Variation of Bias with SNR for correlated noise. . . 89

3.36 Variation of RMSE with SNR for correlated noise . . . 90

3.37 Variation of Bias with SNR for wind noise,1-10 Hz signal . . . 91

3.38 Variation of RMSE with SNR for wind noise . . . 91

4.1 Variation of RMSE with Separation for uncorrelated noise with two uncorrelated sources . . . 100

4.2 Variation of RMSE with inter-sensor separation for correlated noise with two uncorrelated sources . . . 101

4.3 Variation of RMSE with SNR for correlated noise with two uncorrelated sources 102 4.4 Variation of RMSE with Separation for wind noise with two uncorrelated sources 102 4.5 Variation of RMSE with SNR for wind noise with two uncorrelated sources . . . 103

4.6 Performance with SNR for broadband two uncorrelated sources . . . 103

4.7 Performance with inter sensor separation for broadband two uncorrelated source 104 4.8 Two correlated sources performance with SNR for broadband . . . 105

5.1 Setup for generating infrasound source. . . 108

5.2 Three sensors placement for p-p AVS. . . 108

5.3 Setup for receiving data. . . 108

5.4 Types of windshields compared . . . 110

5.5 Experiment 1-To determine Wind noise attenuation . . . 111

5.6 Received Signal spectrum for 25 Hz arriving from 70^{◦} azimuth . . . 114

5.7 Received Signal spectrum for 25 Hz arriving from 70^{◦} upto 150 Hz . . . 115

5.8 Received Signal after filtering for 25 Hz arriving from 70^{◦} azimuth . . . 115

5.9 Received Signal DoA for 25 Hz arriving from 70^{◦} azimuth . . . 116

xiv

List of Figures

5.10 Received Signal spectrum for 25 Hz arriving from 110^{◦} azimuth . . . 117

5.11 Received signal spectrum for 25 Hz signal arriving from 110^{◦} azimuth upto 170 Hz117
5.12 Received Signal after filtering for 25 Hz arriving from 110^{◦} azimuth . . . 118

5.13 Received Signal DoA for 25 Hz arriving from 110^{◦} azimuth . . . 118

5.14 Received Signal spectrum for 25 Hz arriving from 140^{◦} azimuth . . . 119

5.15 Received Signal spectrum upto 150 Hz for 25 Hz arriving from 140^{◦} azimuth . . 119

5.16 Received 25 Hz signal arriving from 140^{◦} azimuth after filtering . . . 120

5.17 Received signal DoA for 25 Hz arriving from 140^{◦} azimuth . . . 120

5.18 Spectrum for 25 Hz signal arriving from 170^{◦} azimuth upto 150 Hz . . . 121

5.19 Received Signal DoA for 25 Hz arriving from 170^{◦} . . . 121

5.20 Received Signal spectrum for 30 Hz arriving from 70^{◦} azimuth upto fs/2 . . . . 122

5.21 Received Signal spectrum for 30 Hz arriving from 70^{◦} azimuth upto 150 Hz . . . 122

5.22 Received Signal for 30 Hz arriving from 70^{◦} azimuth after filtering . . . 123

5.23 Received Signal DoA for 30 Hz arriving from 70^{◦} azimuth . . . 123

5.24 Received Signal spectrum for 30 Hz arriving from 110^{◦} azimuth upto fs/2 . . . 124

5.25 Received Signal spectrum upto 150 Hz for 30 Hz arriving from 110^{◦} azimuth . . 124

5.26 Received Signal after filtering for 30 Hz arriving from 110^{◦} azimuth . . . 125

5.27 Received Signal DoA for 30 Hz arriving from 110^{◦} . . . 125

5.28 Received Signal spectrum for 30 Hz arriving from 140^{◦} azimuth upto fs/2 . . . . 126

5.29 Received Signal spectrum for 30 Hz arriving from 140^{◦} azimuth upto 130 Hz . . 126

5.30 Received Signal for 30Hz arriving from 140^{◦} azimuth after filtering . . . 127

5.31 Received Signal DoA for 30 Hz arriving from 140^{◦} azimuth . . . 127

5.32 Received Signal spectrum for 30 Hz arriving from 170^{◦} azimuth upto fs/2 . . . . 128

5.33 Received Signal spectrum for 30 Hz arriving from 170^{◦} azimuth upto 150 Hz . . 128

5.34 Received Signal DoA for 30 Hz arriving from 170^{◦} azimuth . . . 129

5.35 Received Signal spectrum for 35 Hz arriving 70^{◦} azimuth upto fs/2 . . . 129

5.36 Received Signal spectrum for 35 Hz arriving from 70^{◦} azimuth upto 130 Hz . . . 130

5.37 Received Signal after filtering for 35 Hz arriving from 70^{◦} azimuth . . . 130

List of Tables

5.38 Received Signal DoA for 35 Hz arriving from 70^{◦} azimuth . . . 131
5.39 Received Signal spectrum upto fs/2 for 35 Hz arriving from 110^{◦} azimuth . . . . 131
5.40 Received Signal spectrum for 35 Hz arriving from 110^{◦} azimuth upto 110 Hz . . 132
5.41 Received Signal for 35 Hz arriving from 110^{◦} azimuth after filtering . . . 132
5.42 Received Signal DoA for 35 Hz arriving from 110^{◦} azimuth . . . 133
5.43 Received Signal spectrum for 35 Hz arriving from 140^{◦} azimuth upto fs/2 . . . . 133
5.44 Received Signal spectrum for 35 Hz arriving from 140^{◦} azimuth upto 80 Hz . . . 134
5.45 Received Signal for 35 Hz arriving from 140^{◦} azimuth after filtering . . . 134
5.46 Received signal DoA for 35 Hz signal arriving from 140^{◦} azimuth . . . 135
5.47 Received Signal spectrum upto fs/2 for 35 Hz arriving from 170^{◦} azimuth . . . . 135
5.48 Received Signal spectrum for 35 Hz arriving from 170^{◦} azimuth upto 110 Hz . . 136
5.49 Received Signal for 35 Hz arriving from 170^{◦} azimuth after filtering . . . 136
5.50 Received Signal DoA for 35 Hz arriving from 170^{◦} azimuth . . . 137
5.51 Received Signal DoA for 25 Hz arriving from 140^{◦} azimuth with AVS-MUSIC . . 138
5.52 Received Signal DoA for 25 Hz arriving from 170^{◦} azimuth with AVS-MUSIC . . 138
5.53 Received Signal DoA for 30 Hz arriving from 140^{◦} azimuth with AVS-MUSIC . . 139
5.54 Received Signal DoA for 30 Hz arriving from 170^{◦} azimuth with AVS-MUSIC . . 139
5.55 Received Signal DoA for 35 Hz arriving from 140^{◦} azimuth with AVS-MUSIC . . 140
5.56 Received Signal DoA for 35 Hz arriving from 170^{◦} azimuth with AVS-MUSIC . . 140

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## List of Tables

3.1 Performance metrics of simulated data for without noise . . . 73

3.2 Performance metrics of FEM data for without noise . . . 73

3.3 Performance metrics of simulated data for correlated noise . . . 75

3.4 Performance metrics of FEM data for correlated noise . . . 79

3.5 Performance metrics of simulated data for wind noise . . . 86

3.6 Performance metrics of FEM data for wind noise . . . 87

5.1 Wind shield attenuation with distance between fan and sensor=100 cm . . . 111

5.2 Wind shield attenuation with distance between fan and sensor=30 cm . . . 111

5.3 Signal attenuation by wind shields . . . 112

5.4 Statistical parameters of DoA estimation with 200 Hz in anechoic room . . . 112

5.5 Statistical parameters of DoA estimation with bandlimited white noise from (200-300) Hz in anechoic room . . . 113

5.6 Statistical parameters of DoA estimation in open air with Arc-Tan . . . 137

5.7 Statistical parameters of DoA estimation in open air with AVS-MUSIC . . . 141

## List of Acronyms

DoA Direction of arrival AVS Acoustic vector sensor SNR Signal to noise ratio

VSG Voellmy, Salm, and Gubler PCM Perla Cheng McClung VARA VAlangheRAdenti

NIS Norem, Irgens, Schieldrop

MN2L Modified NIS model for 2 layer flows

D2FRAM Dynamical Two-Flow-Regime Avalanche Model RAMMS Rapid Mass Movements

DAS Delay and sum

SCB Standard Capon beamformer

SINR Signal to interference plus noise ratio MUSIC Multiple signal classification

ESPRIT Estimation of signal parameters via rotational invariance MODE Method of direct estimation

DI Directivity index ML Maximum likelihood

TS Turbulent wind and Sensor TT Turbulence-Turbulence TMS Turbulence Mean shear

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List of Acronyms

LTI Linear time invariant LTV Linear time variant MAV Micro air vehicles

CPSD Cross power spectral density TDoA Time delay of arrival

RMSE Root mean square error PDR Pulse doppler radar

AR Auto Regressive

## List of Symbols

V11(k1) Power spectral density of the wind velocity

k_{1} Wave number in the wind direction assuming Taylor’s hypothesis
k^{0}_{1} Reference wave number at which there is a good fit

P_{s}(k_{1}) Pressure power spectral density due to TS interaction
P_{t}(k_{1}) Pressure power spectral density due to TT interaction
P_{m}(k_{1}) Pressure power spectral density due to TMS interaction
P_{rms} Root-mean-square value of pressure

Pref Reference pressure of 2x10^{−5} Pa
u_{t} total fluid velocity

p_{t} total fluid pressure

u_{0},U Uniform or mean value of velocity
p_{0},ρ_{0} Uniform values of pressure, density
f external force field density

I Unit tensor

τ Viscous stress tensor
s_{t} Entropy of the source

T Temperature

n Unit vector in the direction of propagation u Acoustic particle velocity

I Acoustic intensity

λ Wavelength

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List of Symbols

r The distance from the origin q(x , t) Sound source strength

m Mass source term

β Volume fraction occupied by the injected mass ξ Point volume source

σ(t) Source strength

θ_{d} An angle to the dipole axis
ρ_{0}∂^{2}β/∂t^{2} Unsteady injection of volume
Q Strength of the monopoles
δ_{ij} Kroneckerδ-function

c_{0} Sound speed

∂f_{i}/∂x_{i} Dipole field induced by external force fields
ρtutiutj Non-linear Reynolds stress

τij Viscous forces

R Radius of the dipole in x direction

Z Sensor height

u^{2} Mean of the squared velocities in the downwind, crosswind, and vertical directions
h(t) impulse response

k =ω_{0}/c_{0} the wave number

w_{0} source radian frequency

s1(t) vector of received signal due to source 1
a_{1}(θ_{1}) steering vector for source 1

a_{2}(θ_{2}) steering vector for source 2
U_{s} signal subspace

Λ_{s} diagonal matrix with eigen values of signal
U_{n} noise subspace

P source covariance matrix

bπ orthogonal projector onto noise subspace projector

List of Symbols

M(θ) MUSIC spatial spectrum

y_{t} received signal at sensor from two sources
R covariance matrix

a_{v}_{i}(θ) array manifold vector for AVS

θ source DoA

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