Sound Source Localization Using a 2D Acoustic Vector Sensor

Transcription

1 Sound Source Localization Using a 2D Acoustic Vector Sensor Elizabeth Schermerhorn University of Twente P.O. Box 217, 7500AE Enschede The Netherlands e.a.schermerhorn@student.utwente.nl ABSTRACT In this research, a two dimensional acoustic vector sensor is used to determine the direction of arrival (DOA) of a sound source relative to the sensor. Existing solutions have focussed on using two acoustic vector sensors (AVS) or an array of AVS and not on using one AVS. This paper focusses on the accuracy of a sound source localization algorithm and the influence of ambient noise and reflections. Measurements show that as long as the signal-to-noise ratio (SNR) is equal to or larger than 14, the algorithm has a deviation (procentual difference between measured and expected value) of less than 5%. Two experiments have been conducted, one to show that the DOA does not influence the accuracy and a second to show the influence of the SNR on the accuracy. Keywords Acoustic vector sensor (AVS), particle velocity sensor, Signalto-noise Ratio (SNR), Direction of arrival (DOA), Fast fourier transformation (FFT). 1. INTRODUCTION Locating sound sources is a technique which has many applications nowadays. Examples of the use of the sound source localization include localizing people during calamities and the automatic pointing of video cameras to dangerous situations. Commonly used hardware for sound source localization is a microphone array, which is a setup consisting of multiple pressure sensors. Using the localization algorithm Near-field acoustic holography (NAH) [5, 6] the location of the sound source relative to the microphone can be determined. Such a microphone array is based on the difference in arrival time of the acoustic sound wave of the source to the different microphones. This method works but is relatively computational expensive. Furthermore, these arrays are big, especially for low frequency measurements. The particle velocity sensor is one sensor and much smaller. An alternative sensor is an acoustic vector sensor, this sensor measures the particle velocity component of a sound wave in a certain direction. There are two algorithms for an array of particle velocity sensors, namely MUSIC [13] and ESPRIT [1]. There is also an algorithm Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. 23 rd Twente Student Conference on IT June 22 nd, 2015, Enschede, The Netherlands. Copyright 2015, University of Twente, Faculty of Electrical Engineering, Mathematics and Computer Science. Figure 1. Right: Signal with small influence of noise. Left: Signal with great influence of noise. Figure 2. Reflection of sound waves designed for two particle velocity sensors [9]. This algorithm is based on knowing the exact location of the two sensors and measuring the difference in arrival of time. There has not been any research done on the topic using one sensor to locate multiple sources using a 2D acoustic vector sensor (AVS). The influence on the accuracy of the algorithm will be investigated in this paper with respect to the ambient noise and reflections. 1.1 Ambient noise Ambient noise is a collection of all sound waves, which are measured by the sensor but are not the sound waves originating directly from the sound source. Examples of ambient noises are: cars driving by, the sound of air conditioning and the sound of printers. However as there is more ambient noise and the power of the source remains the same, the influence of the ambient noise increases. In Figure 1 two measured signals are shown, both sources have the same power. The left graph is measured in an environment with less ambient noise and the right graph is measured in an environment with more ambient noise. 1.2 Reflection Reflection is the sound that is registered by the AVS that has been bounced off of objects before reaching the AVS. In Figure 2 a visual representation of reflection is shown. 1.3 Use of multiple sources for sound source localization Two sensors In [9] an algorithm is discussed for two, 3 dimensional, 1

2 Figure 3. The particle velocity sensor Figure 5. The longitudinal waves of sound Figure 4. The (x, y, z)-plane AVS placed at a certain distance from one another. By knowing the exact positions of the sensors and calculating the difference in arrival time of the sound at both sensors, using triangulation the exact coordinates can be determined. The advantage of this algorithm and setup is that by using only two sensors it is possible to determine the exact location N Acoustic vector sensors (AVS) An extra extension to the above discussed situation is to take an array of N AVS and place them at arbitrary distances from one another. Where N is usually a number between 6 and 10. There exist two different types of algorithms for the setup, one type can locate a maximum of N-1 sources when N sensors are used. The second makes it possible to locate more than N sources when N sensors are used. Locating N-1 sources. MUSIC[16, 13] and ESPRIT[1] are two algorithms which can maximally determine N-1 sources when N AVS are used. ESPRIT is an improvement of MUSIC on certain aspects and has two large advantages compared to MU- SIC, i.e.,it is computationally less expensive and suffers less from the SNR. Even though ESPRIT has these two advantages, MUSIC tends to be more accurate than ESPRIT [3]. Locating more than N sources. In [17] an algorithm is described for locating more sources than AVS are used. According to [17] The approach is based on the Khatri-Rao product by exploiting the subspace characteristics of the time variant covariance matrices of the uncorrelated quasi-stationary source signals. 1.4 Height of the sources The height influences the determination of the direction of arrival (DOA), here the focus shall lay on locating sound in two dimensions. 2. UNDERLYING PRINCIPLE OF THE AVS In Figure 3 the acoustic vector-sensor used in this research is shown [10]. This sensor measures the particle velocity component of a sound wave. The 2 dimensional plane represented by the sensor can be seen in Figure 4. Since a 2 dimensional sensor is used, the 3 dimensional component is neglected. 2.1 Transformation from particle velocity to input signal In the top part of Figure 5 an acoustic sound wave is shown. This acoustic sound wave consists of two parts, a pressure wave and a particle velocity wave. The denser areas in Figure 5 show the pressure wave. The particle velocity wave is shown in Figure Power of the signal The amplitude of the measured particle velocity wave is dependent on the power of the sound source. When the power of the source increases, the amplitude of the particle velocity wave increases. A higher amplitude, in the long-term, means a more accurate localization. When the amplitude is larger and the ambient noise stays constant, the localization will be more accurate because the ambient noise will have a smaller influence on a stronger signal. 2.3 The sampling frequency The input signal is sampled at equal intervals dt, measured by the audio card MAYA44 and read to a computer. The dt value is dependent on the frequencies that have to be measured. The chosen interval determines the highest frequency possibly to be measured. Since acoustic sound is used in this experiment the frequencies measured should not surpass 22 khz. This value is chosen because the human hearing hearable frequencies range between 20 Hz and 20 khz. This means that the dt interval must be small enough so that this frequency can be measured too. Choosing as sampling frequency means that at most 44100/2=22050 Hertz can be detected, the time interval is set as: Interval = 1/samplingfrequency To make sure that the complete range can be measured the sampling frequency is chosen as instead of to register frequencies which just pass the Hz limit. 2.4 Determining the SNR in db The signal-to-noise ratio is a value which is modeled by: SNR = P s P n,where P s is the power of the signal and P n is the power of the noise, both are in db. The two output signals of the sensor are the sum of all sound waves captured by the sensor, which are registered by the sensor. The higher the SNR is, the lower the influence of the ambient noise. On the other hand, the lower the SNR, the higher the influence of ambient noise. The strength of reflections is dependent on the strength of the sound source, the more power the source has, the higher the reflections become and vice-versa. In Figure 1 two input signals can be seen, on the left two signals with a high SNR and on the right two signals with a low SNR. 2

3 Figure 6. Source in a 3D environment 2.5 The influence of the height of the source with respect to the sensor The sensor is a two dimensional sensor and therefor the elevation will be neglected. The elevation is not of influence on the measurents by this sensor because it is a 2 dimensional sensor. In Figure 6 this principle is shown with the sensor being at (0, 0). 3. HARDWARE RESTRICTIONS There are certain restrictions to the capabilities of the AVS, these are discussed below. 3.1 Determining distance to sources Since only one sensor is being used, it is not possible to calculate the distance to the sources. To calculate the distances triangulation is needed and this cannot be achieved with one sensor, as a minimum two sensors are needed to be able to compute the triangulation. In [9], a localization algorithm is shown with two sensors to locate a source. 3.2 Determine the quadrant Figure 3 illustrates that there are 4 quadrants that can be determined in the same manner in which an x,y coordinate system can be determined. For convenience beginning in the top quadrant and rotating clockwise numbering each quadrant I through IV 4. The sensor however makes no distinction in the direction of arrival when the coordinates are exactly opposite of each other. Meaning that when a source is placed on (-x,-y) in quadrant III the sensor can not determine whether the source is on (x,y) in quadrant I or in quadrant III on (-x,-y). This is due to the fact that the sensor is symmetric and receives exactly the same inputsignals from opposite quadrants. 4. SOUND SOURCE LOCALIZATION AL- GORITHM In Figure 5 an acoustic wave is shown. A particle velocity sensor measures the particle velocity wave and expresses this in sin(v) and cos(v) to model the amplitude. In Figure 8 the determination of the particle velocity from a soundwave is shown. The arrow points in the direction of the sound source and depending on the angle of incidence the amplitudes of the x and y input signals are larger or smaller as can be seen in 8. In Figure 7, a visual representation is shown of the proposed algorithm and its steps. All steps are derived from two input signals. These signals are never altered, but other values are calculated from the input signals. These steps shall be elaborated step by step below. 4.1 Measuring the input signals Two input signals are measured using a MAYA44 USB audio card, one from the x direction and one from the y direction. Every dt seconds a value is taken from both of these signals and placed in an array for respectively the x Figure 7. Representation of the algorithm Figure 8. Determination of the particle velocity 3

4 Figure 10. Left: reach maxima at same moment Right: reach maxima exactly π later Figure 9. An FFT with the calculated threshold values and y values. The dt value is determined by using a sampling frequency of 44.1 khz. The signal is modeled with a constant signal of 1kHz. The wave functions depend on the generated sound wave. 4.2 Determining threshold between sources and noise To determine the threshold which will be used later in the algorithm, the number of peaks (extrema) are calculated from the x input signal. The threshold is used to determine whether a frequency is a relevant acoustic source in the FFT. An FFT of the two input signals is shown in Figure 9. This FFT will be used further on in the algorithm. The black line shows the determined threshold. The amount of peaks of the input signals give a value for the amount of ambient noise and reflections influencing the signal. Because the x and y input signals are correlated (they originate from the same acoustic wave) only the peaks of one of the two signals have to be determined as they will return more or less the same value. The threshold will be determined by the number of peaks which are present, this way the threshold is flexible and adjusts itself to environments with lots of ambient noise and reflections (more peaks) and environments with little ambient noise and reflections (fewer peaks). The threshold is a function of the total power of the signal and decreases when there is more noise while increasing when there is less noise. 4.3 Fourier Transformation to determine sources The fourier transformation [15] takes the input signals of x and y seperately and calculates for both input signals all frequencies with their corresponding amplitudes. In Figure 9 the fourier transformation is shown for two input signals and one acoustic source. The black line represents the threshold which was determined for the two input signals. The large peak which reaches above the threshold is the sole source which was present in that environment. The value of the frequency of this peak will be the value of the frequency of the source. 4.4 Calculating amplitudes of sources The fourier transformation will be used for this step to determine all the peaks above the threshold. In this step, peaks higher than the threshold, will be considered as relevant sources and their angles will be calculated. The frequency along with its amplitude is stored in a matrix for further use. The amplitude is the information needed and the corresponding frequency is kept to remember which amplitude it corresponds to. 4.5 Determining DOA All amplitudes higher than the threshold in the FFT are likely to be a source. For the frequencies corresponding to these amplitudes, the DOA will be determined with the following equation: angle = arctan(amp y/amp x) The angle relative to the x-axis in the positive quadrant is being determined. The amp y and amp x are respectively the amplitudes of y and x at the same frequency. 4.6 Determining quadrant In Section 3.2, the issue has been discussed with determinig the quadrant. In Figure 10, two possibilities are shown, left is when both input signals reach their maxima at the same time. While right shows when they have a phase shift of exactly 180 degrees. This principle difference makes it possible to determine the quadrant. The method of determining which of the two applies to a certain situation is done by multiplying the two input signals. For example, take two input signals x = sin(t) and y = sin(t), where t is time and x and y are the input signals. In this example both functions are positive (or negative) which generate the following function: x y = sin(t) 2. This generates a positive function moving it to the positive quadrant and oscillating around a positive integer instead of 0. On the other hand, when x or y (not both or neither) represents a negative function, then the multiplication would become x y = sin(t) 2. This moves the result to the negative quadrant giving other information so that the quadrant of arrival can be determined. When x y is positive the source is in quadrant I or III, when x y are negative the source is in quadrant II or IV. In Figure 4 the quadrants are drawn. 4.7 Drawing direction of arrival At last the source can be plotted in a graph giving the calculated angle and the quadrant which it was determined in. 5. ACCURACY DEPENDENT VARIABLES The accuracy of the algorithm is dependent on certain properties and their values. The two properties among which the accuracy depends on are The ambient noise and reflections The soundintensity 5.1 Ambient noise and reflections These are two aspects of the environment in which the algorithm will be tested. When the ambient noise and reflections are larger, the signal will suffer more from non 4

5 related information. This makes the localization less accurate when there is more ambient noise and more reflections. 5.2 Power of the source The higher the power of the source, the more accurate the localization when the noise remains constant. This is because the influence of ambient noise and reflections becomes less as the soundintensity increases. 6. SIMULATIONS Before the actual tests are run, simulations have been designed and tested to evaluate the performance of the algorithm. 6.1 Simulation input signal Since the amplitudes of the input signals are dependent on the angle of incidence and frequency of the sound source, the simulated functions must contain the angle of incidence and the frequency. This translates in: X = sin(angle π/180) sqrt(2) sin(2 π f t) Figure 11. Histogram of the calculated angles with various SNR(1,6,11) Y = cos(angle π/180) sqrt(2) sin(2 π f t) X and Y model input signals with a certain frequency f and an angle angle. Since the function is in radials the angle in degrees is transformed by multiplying with 180/π. The squareroot of two is taken to give the signal a power of 0dBW. The signal is modeled in this matter to make the addition of noise easier. These are two perfect input signals without ambient noise and reflections. Noise can be added to the X and Y input signals with the following function: X = awgn(x, SNR, 0) Y = awgn(y, SNR, 0) Noise is added by using a predefined function in matlab called awgn() which stands for add white gaussian noise. By changing the value of the SNR, more or less noise is added to the signal since the power of the signal always remains the same. The effect of adding noise, is that the signal gets distorted just like the real signal shall be. 6.2 Accuracy tests Two simulations have been conducted, the first simulation calculates the angle 100 times from the same input value for three different Signal-to-noise ratios. This gives different output values since the function awgn() and the fourier transformation are not deterministic. The second test calculates 100 times the angle with a SNR of 5 for each angle bewteen zero and 90 degrees Accuracy test dependent on SNR For this test the same angle (of 16 degrees) has been determined for three different values of the SNR. The three values used for the SNR are 1, 6 and 11. The following test has been conducted: 1. Calculating the same angle from the same input values 100 times. 2. Changing the signal-to-noise ratio(snr) for the next 100 calculations. In Figure 11 a histogram is shown. This histogram shows the 100 calculated values for each different SNR. From this histogram it is clear that the accuracy decreases when the SNR decreases. The bars of the histogram have been taken out for visual purposes. Figure 12. The calculated angles during the simulation and their occurance Accuracy per angle In Figure 12 a plot is shown with different angles which have been calculated 100 times with the same input (frequency, angle and SNR). The graph shows how often a certain angle is estimated and plotted. From left to right, the angles which should have been calculated are 5+k 10 and k [1, 8]. This figure shows that the accuracy does not depend on the angle. When the simulatoin is run multiple times, the results are different for each round. The DOA which has been calculated correctly most frequently changes with every new test. 7. EXPERIMENTS WITH AVS To test the algorithm in a real physical environment, two experiments have been conducted, one to determine the effects of the ambient noise on the signal and a second to measure the accuracy at certain angles. 7.1 setup The setup which has been used for the experiments can be seen in Figure Sensor 5

6 Figure 13. The experimental setup Figure 15. The accuracy of the algorithm as function of the SNR testing, there was a constant ambient noise of 46 db. For all values of steps of 10 from 50 db to 100 db have been measured and the deviation has been determined. For a period of 12 seconds the input signals were measured for all different SNRs. After this the algorithm has calculated the estimated angles of the different input signals. The deviation is a value which is computed with the following function: deviation = (angle1 angle2 )/angle2 Figure 14. The AVS used during the tests Here angle1 is the angle which the sensor has relative to the source, angle2 is the computed angle by the algorithm. The signal-to-noise ratio was calculated by the following function: In Figure 13 the sensor can be seen in the upper left corner. This is the position of the AVS in the setup. The sensor does not move during the tests to keep the data accurate and consistent. The sensor used during this experiment is a particle velocity sensor which is shown in Figure 14. The particle velocity sensor in Figure 3 is in fact the small dot in the middle of the smaller square in Figure SN R = Ps Pr Ps is the sound intensity in db measured by the decibel meter and pr is the premeasured sound intensity of 46 db. This value was determined (using a decibel meter) before the testing started and is specific for this test and this environment. In Table 1 the determined values are shown. Here the angle at which the sensor was placed and which should have been calculated is rad (45 degrees). It was impossible to determine the angle for the first input of the SNR of 50-46=4, since there was no significant peak in the Fourier transformation. Sound source The sound source is a speaker with a frquency range of 20Hz to 22kHz. The speaker is used to generate single tones for the measurements. All tests are conducted with a frequency set at 1 khz and a varying amplitude. The sound intensity at the position of the sensor was measured using an acoustic sound db-meter Table 1. SNR and the influence on the deviation SNR calculated angle(rad) percentage deviation = = % = % = % = % = % Turnpad The turnpad turns the sensor so that different angles can be measured. Turning the sensor is the same as turning the source around the sensor. The turnpad is controlled by a computerprogram with a resolution of 2.5 degrees Low frequency filter Due to a great influence of the air conditioning in the test area the choice has been made to filter the low frequencies (below 180 Hz). By filtering these lower frequencies measuring was easier. The filter uses a first order highpass filter with a cut-off frequency of 180Hz to filter these disturbances. 7.3 Determining the accuracy per angle Algorithm accuracy with different SNRs In this experiment the angles have been determined to test wether the angle influences the accuracy. In Tabel 2 the results are shown with the expected angle, the calculated angle and the deviation between waht is expected and what is determined. The first experiment relates to determining the accuracy of the algorithm with different signal-to-noise ratios. During In Figure 16 the rotation used during the test is shown. First the source is in the first quadrant at 1/4π. Then the 7.2 6

7 Table 2. The calculated accuracy per angle(degrees) Expected calculated deviation 1.06% 5.6% 4.7% 3.11% 1.9% Expected calculated deviation 0.78% 0.8% 3.2% 1.6% 3.9% 3.2% Figure 16. The rotation during the second test through two quadrants source is moved in steps to the x-axis, or 1/2π. Here the source crosses over into the second quadrant continuing to move until it reaches 1/4π. In Table 2 the top part shows the movement from 1/4π till a 1/2π, and the bottom part from 1/2π in the second quadrant to 1/4π. The same measurments have been conducted with the a SNR of 40. This experiment shows that it does not matter which angle is measured, the angle has no influence on the accuracy of the algorithm. 8. DISCUSSION During the first simulation the conclusion was made that the greater the ambient noise, the less accurate the localization results are. This has been proven again by performing experiments in a realistic environment. Figure 15 shows the deviation in relation to different SNRs. The second simulation and experiment show that the angle does not influence the calculation of the angle. Due to the fact that a vector can be split into two components it would be expected that when one of these components becomes tiny (0 or 90 degrees), the accuracy would decrease. However this is not the case and the deviation lies between 1% and 3%. The deviation in accuracy could have resulted from: 1. The ambient noise increased for a short time 2. The set position was actually off by one or two degrees Since the deviations are so small these two are likely to have happened. The fact that it is possible to locate multiple sources using one sensor is a great advantage over previous methods of using multiple AVS to locate more sources. 9. CONCLUSION AND FUTURE WORK An algorithm has been designed and implemented in Matlab to locate acoustic sources. With simulations primary tests have been run to test the algorithm. Furthermore two experiments have been conducted, the first test was concerned with the influence of the SNR on the accuracy of the algorithm. Measurements were performed with different sound intensity levels.for a signal of 15 db the algorithm can determine the angle of incidence with a 5% accuracy. Whereas for 25 db the accuracy increases to 1%. The second test investogated if there was a difference in accuracy at various angles of incidence. This test has shown that between 0 and 180 degrees the angle does not influence the accuracy of the algorithm. The measurements show that the deviation stays below the 5%. Future work includes an extension of this algorithm. For instances, A second sensor can also be added, adding the second sensor the exact location of the source can be determined. When adding a second sensor, the same algorithm is used and theadditionally, a pressure sensor may be added to determine which quadrant the acoustic source originated from. 10. REFERENCES [1] J. 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