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Direction Finding Determine the Direction to a Transmitter with Randomly Placed Sensors

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Direction Finding Determine the Direction to a Transmitter with Randomly Placed Sensors DEGREE PROJECT IN ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019 Direction Finding Determine the direction to a transmitter with randomly placed sensors FERNANDO FRANZÉN KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Direction Finding Determine the direction to a transmitter with randomly placed ground-based sensors by Fernando Franz´en March 2019 Master of Science Thesis TRITA-EECS-EX 2019:XXX School of Electrical Engineering and Computer Science KTH Royal Institute of Technology SE-100 44 STOCKHOLM Radiopejling Best¨amriktningen till en s¨andaremed slumpm¨assigplacering av mottagare av Fernando Franz´en Mars 2019 Examensarbete TRITA-EECS-EX 2019:xx Skolan f¨orElektronik och Datavetenskap KTH Kungliga Tekniska H¨ogskolan SE-100 44 STOCKHOLM Master of Science Thesis TRITA-EECS-EX 2019:XXX Direction Finding Determine the direction to a transmitter with randomly placed sensors Fernando Franz´en Approved: Examiner: 2019-03-XX Daniel M˚ansson Abstract There are a lot of stand-alone and mobile platforms using transmitters today. Some want to be found while others do not. In our modern society there is a great demand of mobility and communication abilities. This means that several mobile platforms could potentially carry a sensor to record incoming signals to be used in Direction Finding. This thesis identifies the possibility to determine the direction to a transmitter with randomly placed sensors. By conducting a literature review well-known meth- ods such as Time Difference Of Arrival (TDOA) and MUltiple SIgnal Classification (MUSIC) where chosen as methods in this analysis. The methods are applied on two antenna arrays, an Uniform Circular Array (UCA) and a Random Circular Ar- ray (RCA). The RCA is generated with randomly placed sensors. The performance in the Direction Of Arrival (DOA) is investigated in presence of time synchroniza- tion error and with different numbers of elements, radius and Signal to Noise Ratio (SNR). The ambiguity in the arrays is also investigated to insure a ambiguity-free DOA estimation. The results from this analysis identifies that the accuracy in the DOA estimation is dependent on the number of elements, SNR, the elements positions and the radius of the DF array. Furthermore, the accuracy of a UCA is greater than a RCA when the elements are randomly distributed within the area of a circle with radius R. Finally, it has shown that if time synchronization error occurs between the sensors, then the MUSIC method the accuracy will decrease greatly. Keywords: Direction Finding, TDOA, MUSIC, UCA, Random Array, DOA i Examensarbete TRITA-EECS-EX 2018:XX Radiopejling Best¨amriktningen till en s¨andaremed slumpm¨assigplacering av mottagare Fernando Franz´en Godk¨ant: Examinator: 2019-03-xx Daniel M˚ansson Sammanfattning Det finns m˚angaindivider och mobila platformar som anv¨ander s¨andare idag. Vissa vill bli hittade, andra inte. I v˚aratmoderna samh¨alle¨ardet en stor efterfr˚aganp˚a r¨orlighetoch kommunikationsm¨ojligheter.Detta inneb¨aratt m˚angamobila plattfor- mar skulle kunna spela in signaler f¨oratt anv¨andasi radiopejling. Denna uppsats identifierar m¨ojligheten att best¨ammariktningen till en s¨andare med slumpm¨assigt placerade sensorer. Genom litteraturstudien identifierades de v¨alk¨andariktningsmetoder som Time Difference Of Arrivial (TDOA) och MUlti- ple SIgnal Classification (MUSIC) som vidare valdes som metoder i denna analys. Tv˚aantennstrukturer anv¨andsi analyserna. Den ena ¨aren Uniform Circular Ar- ray (UCA) och den andra ¨ar en Random Circular Array (RCA). RCA ¨ar gener- erad med slumpm¨assigtutplacerade sensorer. Prestandan i riktningsuppskattnin- gen unders¨oksn¨ardet existerar ett tidssynkroniseringsfel, olika antal sensorer i an- tennstrukturerna, varierande radier och olika signal- och brusf¨orh˚allanden. Aven¨ tvetydigheter unders¨oksi strukturerna f¨oratt s¨akerst¨allaatt en entydig riktnings- best¨amning kan utf¨oras. Resultaten implicerar att noggrannheten i riktningsbest¨amningen¨arberoende av antalet element, SNR, elementens position och radien i antennmatrisen. Ut¨over detta visar resultaten att en UCA har h¨ogrenoggrannhet ¨anen RCA d˚aelementen ¨arslumpm¨assigtutplacerade inom en cirkelradie, R. Slutligen, om tidssynkroniser- ings fel uppst˚armellan sensorerna kommer detta resultera i minskad noggrannhet n¨arMUSIC metoden till¨ampas. Nyckelord: Direction Finding, TDOA, MUSIC, UCA, Random Array, DOA ii Acknowledgements I would like to start with thanking the Department of Electromagnetic Engineering for good support during the working progress of this thesis. My time at KTH has been an interesting journey that will soon come to an end. I'd like to thank the institution for helping me in gathering knowledge that I can put to good use in the future, developing products that will help people in their daily lives. This also would not have been possible without support from my classmates, to whom I send my deepest gratitude. Finally, I would like to thank my love who has been understanding and supporting throughout the working progress of this thesis. Fernando Franz´en iii Contents Abstract i Sammanfattning ii Acknowledgement iii List of Figures vii Nomenclature viii 1 Introduction 1 1.1 Background . .1 1.2 Problematization and Purpose . .4 1.3 Research Question . .5 1.4 Delimitations . .5 1.5 Disposition . .6 2 Methods 7 2.1 Localization Methods . .7 2.1.1 Triangulation . .7 2.1.2 Time Difference Of Arrival (TDOA) . .9 2.1.3 Homing . 12 2.2 Direction Finding Methods . 13 2.2.1 Time Difference Of Arrival (TDOA) . 13 2.2.2 Watson-Watt . 15 2.2.3 Phase Interferometer . 17 2.2.4 MUltiple SIgnal Classification (MUSIC) . 18 2.2.5 Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) . 22 3 State of the Art Technology 23 3.1 GNSS . 23 3.2 Rhode & Schwarz . 23 4 Methodology 24 4.1 Localization Methods . 24 4.2 DF Methods . 24 5 Results 26 5.1 ULA with time Synchronization Error . 26 5.2 Ambiguities in a 2-Element ULA . 31 5.3 UCA with Noise . 32 iv 5.4 Ambiguities in a UCA . 34 5.5 Random Circular Array (RCA) . 38 5.6 Ambiguities in an RCA . 40 5.7 RCA and UCA Comparison . 43 5.8 Plane Wave Approximation . 46 5.9 Drones with Time Synchronization Error . 47 6 Discussion & Conclusion 49 6.1 Discussion . 49 6.2 Conclusion . 51 7 Recommendations for Future Work 53 References 54 Appendix 58 Appendix A . 58 Appendix B . 60 v List of Figures 1 Hopping frequency illustration. .2 2 Multipath illustration. .3 3 Illustration of the triangulation method. .8 4 Uncertainty ellipse illustration. .8 5 Illustration of the localization method TDOA. .9 6 Hyperbola geometry. 10 7 Accuracy of the localization method TDOA. 12 8 An hyperbolic equation with its asymptotic line. 14 9 Illustration of the Watson-Watt method and an Adcock antenna of four dipoles. 15 10 Illustration of the Phase interferometer . 17 11 An illustration of the sub-matrices of a ULA which the method ES- PRIT is using. 22 12 Two sensors located on the x-axis separated by the distance d and the incident angle of the plane wave is θ................. 26 13 When there is a large distance between the two sensors, the time synchronization error has less effect on the DOA estimation when using the method TDOA. 27 14 When there is a large distance between the two sensors, the time synchronization error has less effect on the DOA estimation when using the method TDOA. In this case the frequency is 300 MHz and λ ≈ 1m. .................................. 28 15 When increasing the distance between the two sensors, the time syn- chronization error has less effect on the DOA estimation when using the MUSIC method. In this case, the frequency is 300 MHz and λ ≈ 1m. .................................. 29 16 When the time synchronization error increases, the effect on the DOA estimation has a periodic behavior when using the MUSIC method. In this case, the frequency is 300 MHz and λ ≈ 1m. 29 18 An increased distance between the elements increase the number of peaks in the MUSIC spectrum. 31 19 A UCA where φi is the angle to the i-th element, R is the radius and DOA of the plane wave is θ........................ 32 20 UCA with different numbers of elements and their different radii ver- sus the accuracy in the DOA estimation. 33 21 UCA with seven elements and different radii versus SNR and the accuracy in RMS. 33 22 MUSIC "Pseudo Spectrum" with a 4-element UCA with radius λ and where the DOA is 0 degrees. 34 vi 23 MUSIC "Pseudo Spectrum" with a 3-element UCA. 35 24 MUSIC "Pseudo Spectrum" with a 4-element UCA. 35 25 MUSIC "Pseudo Spectrum" with a 5-element UCA. 36 26 MUSIC "Pseudo Spectrum" with a 6-element UCA. 36 27 MUSIC "Pseudo Spectrum" with a 7-element UCA. 37 28 Random element placement where Ri and φi is the radius and angle to each element in the random array. 38 29 RCA with different numbers of elements and their different radii ver- sus the accuracy in the DOA estimation. 39 30 SNR VS Rmax............................... 39 31 MUSIC "Pseudo Spectrum" with a 3-element RCA. 40 32 MUSIC "Pseudo Spectrum" with a 4-element RCA. 41 33 MUSIC "Pseudo Spectrum" with a 5-element RCA. 41 34 MUSIC "Pseudo Spectrum" with a 6-element RCA. 42 35 MUSIC "Pseudo Spectrum" with a 7-element RCA. 42 36 An RCA and a UCA, both with 7 elements. 43 37 The accuracy of a UCA and an RCA. 44 38 The accuracy of a UCA and an RCA. 44 39 The accuracy of a UCA and an RCA. 45 40 The accuracy of a UCA and an RCA. 45 41 The difference in the DOA between the senors when the transmitter is located at different distances from the senors.
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