IMPLEMENTATION OF TDOA POSITIONING WITH DIFFERENT ARRAYS OF MICROPHONE USING GCC-PHAT AND CHAN ALGORITHM

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1 Cumhuriyet Üniversitesi Fen Fakültesi Fen Bilimleri Dergisi (CFD), Cilt:36, No: 4 Özel Sayı (2015) ISSN: Cumhuriyet University Faculty of Science Science Journal (CSJ), Vol. 36, No: 4 Special Issue (2015) ISSN: IMPLEMENTATION OF TDOA POSITIONING WITH DIFFERENT ARRAYS OF MICROPHONE USING GCC-PHAT AND CHAN ALGORITHM Kobra MAHDINEJAD 1,*, Solmaz BAZREGAR 1, Morteza Ziaee SEGHALEH 2 1 Department of Electrical Engineering, Eshragh Institute Of Higher Education, Bojnurd, Iran 2 Department of Electrical Engineering, Asrar Institute of Higher education, Mashhad, Iran Received: ; Accepted: Abstract. The problem of positioning an unknown target has been one of the most important issues in many fields (radar, sonar, seismology, geophysics, ultrasonic, hands-free communications, etc.). An effective technique in locating a source is based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors. This paper presents an implementation of TDOA positioning using different arrays of four microphones which are used to receive sound signals. GCC-PHAT is used to estimate time delay and Chan algorithm which is an accurate method of solving hyperbolic equations is used for positioning. We will discuss the effect of different microphone arrays arrangement such as linear, square, rectangle, rhombus, parallelogram, trapezoid and so on and the distance between microphones on accuracy estimation based on some experimental results in room acoustic environments with reverberation and noise. Keywords: Time Difference of Arrival (TDOA), Time delay estimation (TDE), Cross-Correlation (CC), General Cross-Correlation (GCC), Maximum Likelihood (ML) 1. INTRODUCTION Source localization using sensor arrays has been one of the most significant problems in many field of study (radar, sonar, navigation, geophysics, acoustic tracking and so on). For the past few decades, a wide variety of techniques have been proposed to find the position of source consisting active and passive localization. Passive positioning are so preferred because no beam need to send by receivers, therefore it cannot be tracked and it is very appropriate in tracking [5, 6] especially in military that secret tracking is so preferred. In addition it can be used in curing some disease such as epilepsy and by all means because of no radiation it is not harmful for people's bodies. There are different ways which are used for passive positioning. Four more common methods are mentioned below. Angle of Arrival (AOA): AOA that are sometimes referred to as Direction Of Arrival (DOA), is one of passive positioning methods works based on estimating the direction of arrival of the signal of interest received by at least two antenna. Usually multiple DOA estimates are used to improve the estimation accuracy by using the redundant information. Figure 1 shows the method where the source location is found by the intersection of DOA of the signal for three antenna arrays. * Corresponding author. k_mahdinejad@yahoo.com Special Issue: Technological Advances of Engineering Sciences Faculty of Science, Cumhuriyet University

2 MAHDINEJAD, BAZREGAR, SEGHALEH Although DOA methods are practical in many field, for example wireless positioning, they have some drawbacks. For accurate DOA estimates, it is crucial that the signals coming from the source to the antenna arrays must be coming from the Line-Of-Sight (LOS) direction and it is not possible in populated environments. Another considerable factor is the cost of installing antenna arrays. Needing to regular calibration is another disadvantage of this method, since a minute change in the physical arrangement of the array because of winds or storms, may result in considerable position location error. Another problem with this technique is the complexity of the DOA algorithms. Although there are some exceptions such as ESPIRIT algorithm [10], these algorithms usually tend to be highly complex because of the need for measurement, storage and usage of array calibration data and their computationally intensive nature [11]. Figure 1. Positionig by AOA method. Received Signal Strength (RSS): In this method the received signal strength is measured in each receiver. In RSS method, the propagation path losses from the mobile station (MS) to the receivers are measured and then converted to distances between them. For two dimensional positioning each RSS measurement will provide a circle centered at the corresponding receiver. In RSS technique that at least three receivers are needed, the source is located in the intersection of circles made by RSS measurement. In this method there is no need to expensive antenna array. In addition receivers and source do not have to be synchronized. However, here the characteristics of channel such as the way of reducing power by distance or, changes produced by obstacle and reverberation have to be known and these parameters of channel affect positioning accuracy a lot [3]. Time of Arrival (TOA): Time of arrival (TOA), sometimes called time of flight (TOF), is the travel time of a radio signal from a single transmitter to a remote single receiver. The distance can be directly calculated from the time of arrival as signals travel with a known velocity. x = v. t (1) This technique uses the absolute time of arrival at a certain base station. Time of arrival data from two base stations will narrow a position to a position circle (figure2); data from a third base station is required to resolve the precise position to a single point. However, this method has some drawbacks many radio location systems, including GPS, use TOA [7, 8]. The problem this method could face is highly susceptible to timing errors in the absence of LOS, as there would be 946

3 Implementation OF TDOA Positioning With Different Arrays Of Microphone Using GCC-PHAT and Chan Algorithm no way to reduce the errors induced because of multiple signal reflections. Furthermore, in TOA technique receivers and transmitter (target) have to be synchronized. Time Difference of Arrival (TDOA): TDOA techniques are based on estimating the difference in the arrival times of the signal from the source at multiple receivers which leads to the measurement of the difference in distance to two or more stations at known locations that broadcast signals at known times. x ij = v. t ij (2) Unlike measurements of absolute distance or angle, measuring the difference in distance results in an infinite number of locations that satisfy the measurement. When these possible locations are plotted, they form a hyperbolic curve. To locate the exact location along that curve, a second measurement is taken to a different pair of stations to produce a second curve, which intersects with the first (figure3). Figure 3. Positionig by TDOA method. This method offers many advantages over other competing techniques. This technique does not require any special type of antennas; therefore it is cheaper to put in place than the DOA finding methods. There is no need to accurate characteristic of channel so it works better than RSS and in this technique just receivers need to be synchronized and like TOA the synchronization of receivers and source is not necessary. 947

4 MAHDINEJAD, BAZREGAR, SEGHALEH Time Difference of Arrival (TDOA) Position Location Technique Among passive positioning introduced, TDOA is more accurate and it is one of the most common methods of positioning which are used nowadays. A lot of research has been done on this topic so far. The research can be divided into two groups. Some of them study about TDOA or time delay estimation (TDE), and the others study about positioning algorithms based on TDE. TDE Algorithms: Several methods are suggested to calculate TDE. Cross correlation (CC) technique is one of the most commonly used methods to estimate TD. It is also the most straightforward and the earliest developed TDE algorithm, which is formulated based on the single-path propagation model [4]. In this technique to estimate TDOA, the autocorrelation of one signal at a receiver and cross-correlation of that signal with signal received on the other receiver has been calculated. The difference between peaks of these two function considered as TDOA which is so accurate in none reverberation environment. Figure (4) shows computing of TDOA using CC. this technique is not appropriate for multipath and reverberation environment [4], therefore the generalized cross-correlation (GCC) algorithm can be used as an improved version of the CC method. Figure 4a. Audio siglas recieved by two microphone considering noise and delay. Figure 4b. Autocorrelation of one signal (left signal), and cross-correlation of that signal with signal of other receiver (right signal). In this method some weighting functions (sometimes called a prefilter) are used to give some elements more weight or influence on the result than other elements in the same set. There are some algorithms in the GCC family depending on how the weighting function is selected. Commonly used weighting functions include the constant weighting, the smoothed coherence transform (SCOT), the Roth processor, the Echart filter, the phase transform (PHAT), 948

5 Implementation OF TDOA Positioning With Different Arrays Of Microphone Using GCC-PHAT and Chan Algorithm the maximum-likelihood (ML) processor, the Hassab-Boucher transform, and so forth. Combination of some of these functions is also reported in use [12]. This methods and another ways of TDE discussed thoroughly in [1]. [1] shows in this implementation GCC-PHAT do better. Algorithm steps of this method discussed in [1, 12]. Positioning Algorithms based on TDOA: As mentioned before TDOA leads to some nonlinear hyperbolic equations that are not easy to solve. Mathematical model of these equations will be debated bellow. In Cartesian coordinate system, (x, y, z) considered as position of source, (x i, y i, z i ) as position of ith receiver and, (x 1, y 1, z 1 ) as position of reference receiver. To simplify the equations the reference receiver can be located in origin of coordinate system so: (x 1, y 1, z 1 ) = (0,0,0) (3) Considering R i1 the distance between ith receiver and reference receiver and, R i the distance between ith receiver and source it can be modeled: R i1 = v. t i1 = R i R 1 (4) In (4), v is speed of sound and calculated : v T air (5) T air is temperature of air in Celsius degree. R i = (x i x) 2 + (y i y) 2 + (z i z) 2 (6) Using (3): R 1 = x 2 + y 2 + z 2 (7) Putting (6) and (7) in (4) make a hyperbolic equation. The intersection of these equations is source location. Different algorithms are proposed to solve these hyperbolic equations. In some research first nonlinear equations are converted to linear equations using Taylor series expansion, and then by an initial guess and an iterative approach the source position will estimate [13]. Initial guess is the most significant problem of this method because if it is not good enough, it will cause convergence problem. In other methods such as Friedlander [15], Intersecting Spherical method [16], Spherical Interpolation Method [17], and divide-and-conquer method [18], Least Square (LS) estimation is used. Solving equation in these algorithms needs statistic information about noise and estimation error which is not available most of the time and is an important issue for these algorithms. Finally in method such as Fang [19], and Chan [14], the accurate algebraic solution of equation has been used. These techniques lead to two answers for source position which can be solved by redundant TDOA measurement. 949

6 MAHDINEJAD, BAZREGAR, SEGHALEH Among these approaches which discussed thoroughly in [2], Chan is more accurate and suitable, hence it is used in this implementation. Implementation For Implementation of TDOA estimation and positioning, an almost ideal echoic environment is needed. Therefore this project has been done in a 2 3 room that the walls covered by accusative and the floor covered by a carpet to minimize reverberation. The hardware of this project which will describe latter putted on a scaled table. Almost more than 100 positions of source and microphones have been tested, different algorithms of TDOA estimation and effect of some parameters on accuracy of estimation are considered. Using the results of these tests, the best way of TDOA estimation has been chosen and based on this method time delay between microphones in an array with 4 microphones has been calculated. However, algorithms based on sequence repetition do better in reverberant places, but they have low speed and sometimes they do not converge. Therefore in on time implementation they cannot be used and in this project correlation algorithm is so preferred. For surveying the algorithms and effect of parameters, 17 different arrangements considered for four microphones and for each array, the source of sound has been located in 9 different positions. Totally more than 100 sounds were recorded and different algorithms were tested on them. Maximum sampling frequency which has been used in sound cards is samples each second. Time interval of recording sound is 10 seconds. First 3 seconds are used for calibrating and synchronizing the sound cards and last 7 seconds are used for TDOA estimating. In hardware implementation, sound cards are used for receiving sound. Below are four reasons why sound cards are used: first of all it can be recognized by Mathlab software. Secondly receiving sound has high quality. Thirdly sampling frequency is high in sound cards and last of all they connect to computer easily. Easy installation, appropriate cost and compatibility with sound chipset of motherboard are the reason why C-Media 8738 sound card [9] are used in this project, however in [9] Mr. James Scott and Mr. Boris Dragovic did their implementation in Linux but here the project is done with Windows operating system. In the beginning of sound cards installation, conflict error was happened. When a peripheral wants to access a resource, it sends an interrupt request to the processor in order to get its attention. The peripherals have an interrupt number that is called an IRQ (Interruption Request). Number of IRQ lines in CPU is limited, therefore it cannot respond to a limited number of requests in the same time. For solving this problem, some peripheral devices have to disable in BIOS setting and then IRQ lines will assign to PCI slots which the sound cards installs there. Hardware used in this project is shown in figure 5. As it can be seen capacitor microphone are used because they are small, so they increase the accuracy of estimation. In addition this kind of microphone is so sensitive and cheap. The only problem with this kind of microphones is that their output signals are so weak. For detecting sound by sound cards, the signal must be at least 23dB, hence after microphones there is a preamplifier for each of them, working based on low 950

7 Implementation OF TDOA Positioning With Different Arrays Of Microphone Using GCC-PHAT and Chan Algorithm noise operational amplifier (Figure 6). At the end of each preamplifier there is a potentiometer to adjust the amplitude of sound signals. After amplifying the received sound it has been send to the switch. Other circuits which are used in hardware are driver, multivibrator, switch and sound generator which is used to calculate time delay between cards (Figure 7). When sound cards start receiving the sound, pin 21 of IC (sound card) produce a square wave. This wave enters latch circuit and produce down trigger that runs monostable multivibrator. By entering down trigger, monostable multivibrator produces a pulse with definite time interval. During this time the switch has been activated and sound cards received sound from sound generator (UM66 chipset), therefore the time delay between cards can be calculated. After this time, the circuit receive sound of microphones. Figure 5. The whole hardware that are used in TDE estimating. Figure 6. Preamplifiers of capacitor microphones. Figure 7. The circuit of multi vibrator. Figure 8. Sound cards using in hardware. Because of small different frequency between crystals of sound cards, in long time interval the delay occurs between cards. In a practical test after receiving samples, at most 2 to 10 samples delay have seen between cards. For solving this problem, one side of crystals attached together to equalize frequency of sound cards pulse. The sound cards and the hardware of synchronization are shown in Figure 8. Experimental Results As mentioned before, Chan algorithm has been used in the implementation. This is an accurate method; it means if there was no error on TDE, positioning would be precise enough. Consequently, the amount of error happened in different array is because of noise, reverberation 951

8 MAHDINEJAD, BAZREGAR, SEGHALEH and so on which affect TDE error. Positioning in this project has been done on a surface, it means in Chan equations, z = 0. Chan equations on surface have been solved in [2] completely. Using the equation in [2], the final solution for source coordinate is: [ x y ] = [x 2 x 1 y 2 y 1 x 3 x 1 y 3 y 1 ] 1 A (8) Which A is a matrix introduce as: A = [ R 21 ] R R [R x y 2 1 x y R x y 2 1 x y ] (9) 3 Four microphones have been used in this implementation hence, three TDOA measurements are available. Two of them ( R 21 and R 31 ) are used in (9), which result in two answers for source location. Third TDOA measurement (R 41 ) will use to choose the correct answer. Different microphone arrays such as linear, square, rectangle, rhombus, parallelogram, trapezoid and so on arrangements have been tested in the project. Linear arrangement is one of the tests in the implementation that does not reply well and that is because in this array B = 0 which matrix B defines as: B = [ x 2 x 1 y 2 y 1 x 3 x 1 y 3 y 1 ] (10) So no answer can be found for target position and this array has not been tested. Another tested array is rhombus arrangement. This arrangement has been tested in two states. In first one which the distance of receivers were almost cm, less than λ/4 *, considerable error has been seen in the result but, in second one which the distance of receivers increase, error decrease dramatically. This array is shown in figure 9. Square and rectangle arrangements have been tested as well. Square arrays tested with sides of 30cm, 45cm and 60cm. Increasing in length of sides lead to accurate positioning. Furthermore, the more distance between source and reference receiver, the more precise estimations can be obtained. This result can be seen in rectangle arrangement which has been tested in 45cm 60cm and 60cm 75cm arrangement. The last arrangement is one of the best arrangement result in very accurate positioning. Figure 10 shows this array. * Sound speed is 343 meter per second. Therefore in 200Hz, λ=1.715m and in arrangement it is better than the distance of receivers have to be more than 43cm. 952

9 Implementation OF TDOA Positioning With Different Arrays Of Microphone Using GCC-PHAT and Chan Algorithm Figure 9. Rhombus arrangement, distance of receivers 2 and 3 to reference receiver is 42.43cm. Figure 10. Rectangle arrangement with width of 60cm and length of 75cm. Figure 11. Trapezoid arrangement. Parallelogram arrangement, another tested array does not work so well as another arrangement but, trapezoid arrangement results in extremely accurate positioning which improves by increasing receivers distance. One of the best trapezoid arrays indicates in figure 11. Some scattered arrangements with no definite geometric shape have been tested as well. In some of them three receivers located on a straight line (figure 12), but the reference receiver is not located on that line and on the other arrays three receivers make a triangular, but the reference receiver is located separately (figure 13). The results of Square and rectangle arrangements also have been seen here. 953

10 MAHDINEJAD, BAZREGAR, SEGHALEH Figure 12. Scattered arrangement, three receivers located on a straight line, but not the reference receiver. Figure 13. Scattered arrangement, three receivers located as a triangle, but not the reference receiver. CONCLUSION In this paper different arrangements of four microphones have been tested. GCC-PHAT method has been used to estimate time delay and because of redundancy in measurements, Chan algorithm has been used to find the intersections of hyperbolic curves. More research on arrangements with high accuracy such as scattered, trapezoid and so on showed in arrays which the distance of microphones are less than λ/4, a considerable error occurred. In addition, increasing the distance of microphones led to accurate positioning. Furthermore, the results showed that if the three microphones which are farther to the source of sound are used for positioning, the location of source can be estimated precisely. Acknowledgements The authors would like to thank the Ista Ertebat Kavoshgar company (Mashhad, Iran), and the Amn Gostare Mooud (AGM) company (Bojnourd, Iran). Part of this work was supported by these two companies 954

11 Implementation OF TDOA Positioning With Different Arrays Of Microphone Using GCC-PHAT and Chan Algorithm REFERENCES [1] K. Mahdinejad, M. Ziaee Seghale, " Implementation of Time Delay Estimation Using different Weighted GeneralizedCross Correlation in Room Acoustic Environments", Life Sci J 2013; 10(6s): [2] Muhammad Aatique, " Evaluation of TDOA Techniques for Position Location in CDMA Systems", Virginia Polytechnic Institute and State University, [3] Gordon L. Stüber. James J. Caffery, Jr, The Communication Handbook,Second Edition, Chapter 77: Radiolocation Techniques, John Wiley & Sons Publication, [4] Jingdong Chen, Jacob Benesty, and Yiteng (Arden) Huang Time Delay Estimation in Room Acoustic Environments: An Overview, EURASIP Journal on Applied Signal Processing,Volume 2006, Article ID 26503, Pages [5] Montse Nájar, Josep Vidal, "Kalman Tracking based on TDOA for UMTS Mobile Location", Dept. of Signal Theory and Communications, Universitat Politècnica de Catalunya, Campus Nord, Modul D5, Jordi Girona, 1-3, Barcelona, SPAIN. [6] Myrna B. Montminy, "Passive Geolocation of Low-Power Emitters in Urban Environments Using TDOA", Department of Electrical and Computer Engineering, Air Force Institute of Technology, Air University, [7] Laurence Mailaender, "Comparing Geo-Location Bounds for TOA, TDOA, and Roundtrip TOA", The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, [8] R. L. Fante, J. J. Vaccaro, " Reduction of Multipath-Induced Bias of GPS Time-of-Arrival", IEEE, Position Location and Navigation Symposium, [9] James Scott and Boris Dragovic, Audio Location: Accurate Low-Cost Location Sensing,Intel Research Cambridge [10] R. Roy and T. Kailath, "ESPIRIT - Estimation of Signal Parameters via Rotational In- variance Techniques", IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 7, pp. 984{995, July [10] Ziskind and M. Wax, "Maximum Likelihood Localization of Multiple Sources by Altering Projection", IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 36, no. 10, pp. 1553{1560, October [11] Y. (Arden) Huang and J. Benesty, Adaptive multichannel time delay estimation based on blind system identification foracoustic source localization, in Adaptive Signal Processing Applications to Real-World Problems, J. Benesty and Y. (Arden) Huang, Eds., chapter 8, pp , Springer, Berlin, Germany,2003. [12] W. H. Foy, Position-Location Solutions by Taylor-Series Estimation", IEEE Transactions on Aerospace and Electronic Systems, vol. AES-12, pp , March [13] Y. T. Chan and K. C. Ho, A Simple and Efficient Estimator for Hyperbolic Location, IEEE Transactions on Signal Processing, vol. 42, no. 8, pp , August [14] H. Stark and J. W. Woods, Probability, Random Processes and Estimation Theory for Engineers, Prentice-Hall, Inc., 2nd edition, [15] H. C. Schau and A. Z. Robinson, "Passive Source Localization Employing Intersecting Spherical Surfaces from Time-of-Arrival Di_erences", IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-35, no. 8, pp , August [16] J. O. Smith and J. S. Abel, The Spherical Interpolation Method for Source Localization", IEEE Journal of Oceanic Engineering, vol. OE-12, no. 1, pp. 246{252, January [17] J. S. Abel, A Divide and Conquer Approach to Least-Squares Estimation, IEEE Transactions on Aerospace and Electronic Systems, vol. 26, pp. 423{427, March [18] B. T. Fang, Simple Solutions for Hyperbolic and Related Fixes, IEEE Transactions on Aerospace and Electronic Systems, vol. 26, no. 5, pp , September

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