PRELIMINARY OPERATIONS FOR CALIBRATING A PHASED MICROPHONE ARRAYS FOR AIR TRAFFIC MONITORING Orsola Petrella, Vincenzo Quaranta and Salvatore Ameduri CIRA, Centro Italiano Ricerche Aerospaziali, Via Maiorise 80143 Capua (CE), Italy e-mail:
[email protected]
Giovanni Betta Università degli Studi di Cassino, Via Di Biasio, 43, 03043 Cassino (FR), Italy The present paper describes the preliminary operations necessary for the calibration of Phased Microphone Arrays aimed at monitoring and protecting air traffic during the most critical operations (i.e. take-off and landing). The pressure signals acquired by these antennas are suitably elaborated through the beamforming technique: the array is virtually oriented towards specific directions by adding suitable delays to the sensors signals, without physically rotating the antenna. This assures high directivity and high signal-noise ratio. Delays measured for a certain source direction depend primarily on microphones geometrical position. Other parameters, directional diagram and electrical and mechanical features of the sensors, anyway, can affect measurements. In practice, it is possible to define the so called “acoustic” location of the sensors, also including the effects of these other parameters. The measurement of the acoustic position (array calibration) can be performed through the triangulation technique, consisting in the estimate of the phase shift between the signals transduced by a reference microphone and by each array microphone, in presence of tonal sources. The positioning of both sources and reference microphone is not a trivial task for the arrays considered in this work. Available narrow space of an anechoic room in comparison with array large dimensions could not guarantee, for all array microphones, a time shift delay lower than calibrating signal period, with consequent measurement uncertainties. The several positioning operations thus required to cover a large number of microphones would lead to a dramatic increase of experimental efforts. A genetic optimization was thus implemented to reduce as much as possible these operations, identifying sources and reference microphone locations satisfying time shift delay condition for the largest number of microphones of two arrays designed within the GUARDIAN national Project. Achieved results were expressed in terms of minimum required positioning operations to cover all microphones.
1.
Introduction
The air traffic control inside ATZ (Aerodrome Traffic Zone) is a key activity for airport management services to meet increased security and a low environmental impact on air transport systems. In recent years an increasing demand has interested airports and the related air traffic management authorities. The risk of collisions between taking off and landing aircrafts and between aircrafts and ground vehicles ICSV19, Vilnius, Lithuania, July 8-12, 2012
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19th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8-12, 2012 due to increased air traffic are issues that have highlighted the need to improve airborne surveillance systems by means of real time aircraft identification and tracking procedures in aerodrome zone. State-of-theart ATM (Air Traffic Management) systems for aerodrome surveillance include especially radar technology. On the other hand, there is currently a significant increase of interest in the definition of alternative acoustic systems for locating, tracking and identifying moving acoustic sources, with particular attention on intruder aircrafts and on movement of ground forces. This interest stems primarily from the fact that unlike radar detection, acoustic detection can be performed with totally passive sensors only by listening to the noise of the target. This represents an obvious advantage from the environmental point of view (no emissions of any kind), safety (no possibility of locating the sensor in the absence of emission, inability to drastically reduce the noise of the target), and costs (reduced energy consumption due to lack of transmission power, lack of critical components working at microwave, etc.). The GUARDIAN Project funded by MIUR (Italian Ministry of University and Research) is aimed at designing and developing a novel acoustic system for the improvement of co-operative management of ATZ control [1]. The GUARDIAN sensor system is a multi-modal, in-air passive acoustic device working in arrayed/sparse configuration, by means of an innovative ensemble of digital processing stages, based on “Delay and sum Beamforming” technique. This system allows the tracking of in flight aircrafts through the passive detection and the spectral analysis of airplane acoustic emission. The system prototype (see Figure 1) consists of two planar acoustic sensors, one rotating (Master) and one fixed antenna (Slave), based on a passive phased array of randomly distributed microphones and on a control unit enabling the user to manage and visualize tracked data. Figure 1 shows the sketch of the system.
(a)
(b)
Figure 1. Acoustic antenna systems realised in GUARDIAN Project: fixed (a), rotating (b).
Several monopole acoustical point sources with known positions and a reference microphone are used to compute the locations of the microphones in three dimensional space. The triangulation or Multidimensional Scaling methods [1] [3] are used to perform the calibration process. The paper at hand describes the preliminary activities required for the calibration of the acoustic antennas developed in GUARDIAN Project. Among the others, the triangulation method is used to this purpose. A critical aspect is represented by the delay between signals transduced by the reference and the array microphones. The cross correlation algorithm applied to these signals (sinusoidal) is based on the assumption that the delay L to be estimated is lower than the ratio between the frequency f and sound speed c: f L< (1) c Due to the wide dimensions of the arrays, the large amount of microphones, the explored frequency range (1 – 2 khz) and room available space (15 x 20 x15 m), it is difficult if not impossible to satisfy such a condition for all array microphones with a unique layout of sources and a reference microphone. A dedicated theoretical model was thus implemented to verify the possibility of satisfying, for all microphones, condition (1); after demonstrating the impossibility of covering all array with a unique layout, a dedicated 2
19th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8-12, 2012 optimisation strategy was adopted, aiming at covering the widest microphone number through a certain layout, with a consequent reduction of the experimental efforts. The choice of this optimal layout (i.e. the coordinates of the three sources and of the reference microphone) was performed through a genetic optimisation driven by tailored constrain conditions, this way assuring a practical value to the solution. A second optimisation was then implemented on the array microphones not covered by the previous layout, this time assuming only the reference microphone coordinates as optimisation parameters, thus strongly reducing both computational and experimental positioning efforts.
2. Array microphones description Delay and sum Beamforming technique needs an accurate knowledge of microphone positions, achievable through the calibration of signal amplitude and phase. Especially delay phase measurement plays a fundamental role. This value in fact depends on different factors as the electrical and mechanical features of the microphone and the difference between acoustic and geometric position. This last aspect, strictly related to an imperfect reception pattern, causes a delay in the signal reception. In Figure 2, two different reception conditions are sketched: for the microphone on the left the source signal crosses the array pattern (not symmetric) on a local minimum, differently from what happens for the microphone on the right; this phenomenon leads to a different delay perception, and a consequent deviation between the location (geometric) measurable through an interferometer and the location (acoustic) measured through a triangulation technique.
source geometric position acoustic position reception pattern
Figure 2. Geometric and acoustic location of a microphone and their effect on signal reception.
Several measurements related to different calibration methods can be found in literature [1][2]; however, arrays and operational frequency considered are much smaller with respect to the requirements of GUARDIAN Project: 256 microphones per antenna, distributed on 6.3 x 6 m and 4.3 x 4.3 m planes, operating within 1 ÷ 2 khz range. The performance of an acoustic array is determined by its geometry (shape, number and spatial position of microphones), which defines the response of the array, called Array Pattern. Depending on array geometry, working frequency and antenna pointing direction, the Array Pattern exhibits an attenuation of the signal coming from directions different from the pointing one. Is thus possible to define the MSL (Maximum Side Lobe Level) parameter, which is the ability of the array in reducing noise coming from no pointing directions, and the resolution, which is the minimum angular distance allowing for distinguishing two nearby sources in space. These parameters were computed for the antennas of GUARDIAN and summarised in Table 1 and Table 2 [1]. The elevation linear resolution has been evaluated at a distance of 7 km. The range of the antenna, i.e. the maximum distance in the steering direction at which the array can yet detect the sound source, has been determined by considering a tonal (fixed frequency of 1250 Hz) sound source with an SPL of 140 dB at 10 m and a tonal (at the same frequency) background noise with an SPL of 60 dB. Only the sound attenuations due to air absorption (frequency dependent) and spherical divergences were considered. As reported in Table 3 a detection range of 7 km can be theoretically achieved for a sound source with a tonal frequency of 1250 Hz and an array with MSL 3
19th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8-12, 2012 of -16 dB (i.e. with 256 microphones). These features, jointly with above mentioned room dimensions (15 x 20 x15 m), make the calibration not a trivial task, as it will be demonstrated in “Preliminary operations for calibration” paragraph. Table 1. Antennas performance vs steering elevation.
GRID RANDOM ARRAY (6 x 6 m) Steering elevation Elevation angular Elevation linear resolu- MSL (dB) angle(deg) resolution (deg) tion (m) @7km 30 2.77 338.68 -16.07 60 4.80 587.81 -16.36 GRID RANDOM ARRAY (4 x 4 m) Steering elevation Elevation angular Elevation linear resolu- MSL (dB) angle(deg) resolution (deg) tion (m) @7km 30 3.96 484.58 -16.79 60 7.07 868.17 -16.72 Table 2. Antennas performance vs steering elevation.
Sound sourcearray distance (m) 10 40 100 400 1000 3000 5000 7000 9000 10000
Spherical divergence attenuation(dB) 0.00 12.4 20.00 32.04 40.00 49.54 53.96 56.90 59.08 60.00
Air absorbing attenuation(db) 0.05 0.20 0.51 2.02 5.05 15.15 25.25 35.35 45.45 50.50
Gain over Background Noise(dB) 95.95 83.76 75.50 61.94 50.95 31.31 16.77 3.75 -8.53 -15.50
3. Calibration strategy and optimisation approach The computation of the positions of the array microphones is carried out in two steps, individually performed for every microphone of the array [3]. In practice (referring to the setup of Figure 3 (a)) the signal produced by the ith source is received with a certain delay from the reference microphone r and the jth array microphone. This delay, named in this work as Wi,j, is estimated through the cross correlation algorithm. After collecting all delays, microphone array vector positions x aj are computed by minimising the following relation N
∑
xis − x aj − Wi , j
(2)
i
being xis the vector position of the ith source. In case of sinusoidal signals, if the time delay is larger than the period T, the cross correlation algorithm gives incorrect results: a time delay of T+φ is erroneously computed as φ, due to the periodic nature of elaborated signal. To avoid such problem, it is necessary to preliminarily verify the satisfaction of condition (1), stating the fact that the spatial delay L (path difference) has to be lower than sinusoid period (1/f) divided by the sound speed c. Unfortunately, as already mentioned, array dimensions and number of microphones, jointly with room available space, makes impossible the satisfaction of the time delay condition for all the microphones. To have a simultaneous fulfilment, in fact, the difference between the longest and the shortest distances between array microphones and a source (path excursion) has to be lower than max allow4
19th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8-12, 2012 able time delay, compatible with chosen frequency. Further the source, lower the path difference: this trend, consistent with available space, can be used to attenuate in some way path excursion (also the optimisation algorithm, as it will be shown in the next paragraph, tends to locate the sources as far as possible, practically on boundary domain).
Array microphones Reference microphone Sources
(a) (b) Figure 3. Application of the triangulation method to an acoustic array (a); geometric locus of source locations satisfying time delay condition (b). To exclude the possibility of meeting time delay condition for all microphones, the geometric locus of source locations with an acceptable path excursion was drawn, verifying that it is outside the room domain. Figure 3(b) illustrates this: the room is represented by a red box containing the acoustic antenna (blue); the geometric locus is instead represented by the two cones located outside.
(1)Time delay on the jth array microphone
(2)Sources and reference microphone distance from array
(3)No coincidence between sources, reference microphone
(4)Sources position
mutual
L
d min
x is − x r s s xi − x j
′ > d min i≠ j
′ > d min
AND
Fitness = Fitness + 1
s s min x i − x j i≠ j < rmin s s max x i − x j i≠ j s s s s s s rank x 2 − x1 y 2 − y1 z 2 − z1 < 2 xs − xs ys − ys zs − zs 1 3 1 3 1 3
Figure 4. Algorithm kernel function. A dedicated optimisation strategy was then implemented with the aim of catching, through a single disposition of 3 sources and a reference microphone, the widest number of array microphones satisfying time delay condition. Due to the number of parameters to be defined (3 sources and reference microphone coordi-
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19th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8-12, 2012 nates for a total of 12) a heuristic (genetic) approach was adopted. The cost function was defined as proportional to the number of array microphones satisfying time delay condition. Finally, some additional con-
straints were assumed to guarantee a practical applicability to the final optimal solution: sources and reference microphone have to be at a certain distance from the array plane and not coincident each others; the triangle formed by the 3 sources has to be as regular as possible (no aligned vertices neither skewed) being their coordinates used for triangulation purpose. Just mentioned cost function and constraints led to the definition of kernel function illustrated in Figure 4 and applied by the algorithm for each microphone of the array. The time delay condition and the three just mentioned constraints were described in the boxes (1 - 4) on the left, while their mathematical formulations were reported aboard. The outcome of the four logical checks is compared within the “and” logic operator: only if all these conditions are satisfied, the fitness function is incremented. Proceeding in this way, the fitness of the current source - reference microphone configuration will be equal to the number of array microphones satisfying mentioned constraint conditions. Adopted mathematical formalism for the last three constraints is worth of some further explanation. The out of plane condition (box 2) was implemented by computing array plane equation and the distances from it, of sources and reference microphone: the minimum of these distances has to be greater than a minimum value, dmin, of 20 cm. The sign of these distances was used to exclude the space behind the array for a possible location. The not coincidence condition (box 3) was expressed by computing the distances of sources and reference microphone each others, verifying that it is greater than d’min = 1.25 m. The mutual position of the sources, finally, required two mathematical conditions (box 4): the no alignment condition expressed through inequality at 2 of the rank a matrix, whose rows are the coordinates of two triangle side vectors; the ratio between the minimum and the maximum triangle sides, to be greater than rmin (>0.2). A home made genetic algorithm was used. Moving from a population (whose individuals are represented by the different layout configurations considered), the fitness is computed, this way assigning to each individual a certain priority in transmitting own genetics to the next generation. This transmission is regulated by the crossover mechanism: couples of individuals interchange their chromosomes (in this case, the coordinates of layout components), thus generating novel individuals, potentially better. A certain percentage of these novel individuals then undergoes to the mutation process: some chromosome changes randomly, this way enriching population genetic contents and preventing from immature convergences. The final population is on average better than the previous one and has a richer content.
4. Results Two optimisations were performed: the first one with the purpose of identifying a layout satisfying aforementioned constraints for the widest number of microphones; the second one aimed at finding an additional layout not so different from the previous one, guaranteeing constraints satisfaction for all remaining array microphones.
(a)
(b)
Figure 5. Fitness evolution of the best layout (a), optimal layout values (b).
Due to the heuristic nature of the optimisation process, different initial populations were taken into account thus increasing the probability of finding the optimal solution and not just a local maximum. A number of 20 initial populations were considered for both the optimisations, each population constituted 6
19th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8-12, 2012 by 1000 layouts - individuals. A number of 1000 iterations was chosen for having a reasonable probability of getting convergence. After identifying 20 optimal layouts, a further optimisation was performed, introducing within the initial population these optimal layouts. No further improvements were found, thus confirming solution reliability.In Figure 5, maximum levels (a) reached moving by some populations and fitness evolution (b) of the layout chosen for the further optimisation process, are illustrated. It is worth to note that not the maximum fitness (obtained for the 4th initial population, Figure 5(a)) was selected for the next optimization process, but the 1st one.
Figure 6. 3D view of optimal layout and array microphones: microphones with time delay ≤0.7L (pink) and with time delay >0.7L (blue), reference microphone (green), sources (red).
This because of the specific layout configuration of this latter, that even not assuring the max number of microphones satisfying the time delay condition, gives a good starting point for the second optimisation process, being reaming microphones favourably grouped. In Figure 6, a 3D view of the array microphones and of the optimal layout is given. The optimal layout assures the satisfaction of the constraint conditions for 79 % of array microphones (i.e. 203 over 256 microphones). However, due to possible unavoidable positioning deviations of sources and reference microphone, a safety margin was assumed: only array microphones for which time delay is ≤0.7L (corresponding to 164 microphones) were considered covered by the optimal layout. These microphones were painted (Figure 6) in pink; sources and reference microphones were represented in red and green, respectively. Layout coordinates were reported in Table 3. Table 3. Optimal Layout coordinates with respect anechoic room bottom corner.
Source 1 Source 2 Source 3 Refer. micr (satisfying 0.7 time delay condition) Refer. micr. (satisfying time delay condition for remaining microphones)
X (m) 6.130 6.045 5.545
Y (m) 2.270 0.000 0.000
Z(m) 8.437 9.066 10.45
9.280
11.81
4.122
9.300
11.81
4.158
The contour graph of the ratio between the effective path delay and the maximum one allowable, L, (Figure 7 (a)) illustrates the zones on the array plane satisfying the condition. This graph gives an idea of the microphones that do not satisfy time delay condition (right zone) and outlines so called “border line” microphones, for which any error on location or on layout positioning could cause the no satisfaction of the time delay condition. Remaining microphones (i.e. the not covered by the optimal layout and the ones with a time delay greater than 0.7L) were object of the second optimisation process, involving only the reference microphone position. The final location of the reference microphone satisfying time delay condition for remaining array microphones, is reported in Table 3, last row. Related optimisation process is illustrated in Figure 7; as evident, less then 1000 iterations were necessary to 7
19th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8-12, 2012 get a fitness function value equal to 100%, corresponding to the satisfaction of the time delay condition on remaining microphones.
Figure 7. Current time delay normalised with respect to max allowable, L, vs. array plane; the microphones were represented through white dots (a); Fitness evolution for the 2nd optimisation process (b).
5. Conclusions and further steps In this work a preliminary procedure oriented to the calibration of wide acoustic antennas was presented and applied to the specific case of the acoustic array realised in GURADIAN Project. The specific features of this kind of antennas (large dimensions, low frequency range, wide amount of microphones), compared with anechoic room limited space, make the calibration task not easy to be performed. The triangulation method, used to estimate correct sensors locations, is based on the estimate, through the cross over algorithm, of the delay between signals perceived by the array microphones and the reference one. Unfortunately, such algorithm does not provide correct results if expected delay is greater than signal period. The problem of finding out the optimal location of sound sources and reference microphones satisfying this condition for the largest number of microphones was dealt with through a genetic approach. As result, a configuration was identified, covering 64% of the microphones. For the remaining ones, an additional optimisation was implemented, assuming as unique parameter the reference microphone position. Afore presented activity was aimed at guaranteeing the correct measure of sensor locations and, at the same time, at reducing experimental efforts in terms of source and reference microphone positioning operations. Moving from these results, further investigations will be performed with the purpose of identifying the optimal position of source and reference microphones, guaranteeing not only the satisfaction of the delay condition, but also the minimisation of standard deviation of phase error measurement, this way further reducing experimental efforts and increasing calibration accuracy.
6. References [1] V. Quaranta, S. Ameduri, D. Donisi, M. Bonamente, ”An in-air passive acoustic surveillance system for air traffic control: GUARDIAN Project”,ESAV 2011-Tyrrhenian International Workshop on Digital Communications-Enhanced Surveillance of Aircraft and Vehicles-2011,September 12-14, 2011, Island of Capri, Italy. [2] S. Kroeber , K. Ehrenfried, L. Koop, “Design and testing of sound sources for phased microphone array calibration”, Berlin Beamforming Conference, February 24-25, 2010,Berlin, Germany. [3] A. Lauterbach, K. Ehrenfried, L. Koop, S. Loose, “Procedure for the Accurate Phase Calibration of Microphone array“, AIAA 2009-3122,15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), May 13 – 14, 2009, Miami, Florida. [4] S. T. Birchfield, ”Microphone Array Position Calibration by Basis Point Classical Multidimensional Scaling”, IEEE Transactions on speech and audio processing,Vol.13 n 5, September 2005. 8
