AbstractâIn this paper we propose a high accuracy indoor positioning system based on broadband ultrasonic signals and time of arrival (ToA) measurements.
2012 IEEE 11th International Conference on Trust, Security and Privacy in Computing and Communications
High Accuracy 3D Indoor Positioning Using Broadband Ultrasonic Signals Sérgio I. Lopes, José M. N. Vieira and Daniel Albuquerque Departamento de Electrónica, Telecomunicações e Informática, Universidade de Aveiro IEETA - Instituto de Engenharia Electrónica e Telemática de Aveiro Aveiro, Portugal Email: {sil,jnvieira,dfa}@ua.pt
Experiment 2) Quantitative evaluation of the 3D positioning system when the mobile node was placed at fixed positions;
Abstract—In this paper we propose a high accuracy indoor positioning system based on broadband ultrasonic signals and time of arrival (ToA) measurements. Using low cost transducers we were able to use acoustic chirps of between 20 and 45KHz as pulse signals. This overcomes most of the problems faced by the narrow band signals usually used with common piezoultrasonic transducers, which include poor resolution, low environment noise immunity, short range and low robustness to the Doppler effect. Using synchronized ultrasonic anchor nodes and time division multiplexing to share the medium, we build a GPS-like system for indoor pervasive applications. A set of experiments were performed to evaluate the proposed system. Very stable 3D position estimates were obtained (absolute standard deviation less than 2.3cm) and a position refresh rate of 350ms was achieved.
Experiment 3) Qualitative evaluation of the positioning system (2D case) when the mobile node was in a moving trajectory. II. POSITIONING PROCESS The positioning process can be split into three distinct stages [4]: coordination, measurement and localization, see figure 1. Normally, before ranging, network nodes coordinate with each other typically for synchronization purposes. Depending on the method used in positioning, time synchronization can be a problem that cannot be ignored. The measurement stage is typically related to signal transmission and is normally used to measure distances between nodes. This distance value between two nodes is known as the internode distance and this can be measured using different signal types and different ranging techniques. The precision of these measurements is directly related to positioning accuracy. This work focuses on the improvement of the measurement stage using broadband ultrasonic chirp pulses and ToA measurements to enhance the accuracy of the distance measurements.
Keywords-Indoor positioning, Ultrasonic localization, Multilateration, Broadband acoustics, GPS, LPS.
I. I NTRODUCTION GPS is the most widely used method for outdoor localization and provides global coordinates with an accuracy to within 10 meters [1]. On the other hand, GPS signals are too weak to penetrate buildings, which makes them useless for indoor positioning. Other methods, particularly RF based methods, i.e., received signal strength (RSS) and connectivity, are highly variable and have been less than successfully used indoors, mainly because of a low accuracy of the order of tens of meters [2]. This paper describes a 3D positioning system that takes advantage of broadband ultrasonic chirp pulses to obtain high accuracy distance measurements. The increased bandwidth overcomes most of the problems faced by the narrowband signals usually used with common piezoultrasonic transducers (with a typical bandwidth of 2KHz), which include poor resolution, low environment noise immunity, short range and low robustness to the Doppler effect. The use of ultrasonic signals with lower frequency band content (20KHz-45KHz), rather than the higher frequency 35KHz-65KHz bands (see system presented in [3]) led us to a reduced anchor node density, which resulted in an improved system coverage area. Three main experiments were performed, using just four anchor nodes, in a room of approximately 200m3 :
Figure 1: Positioning Process. Adapted from [4].
A. Coordination The coordination stage is normally related to synchronization purposes. Synchronization is important in the measurement stage because it is used to notify all the intervenient nodes that a measure will be taken. In this paper, time division multiple access (TDMA) was used based in a centralized architecture with all the anchor nodes synchronized. In figure 2 is presented the time slot structure used in the coordination process. For each anchor node is reserved
Experiment 1) Quantitative evaluation of distance measurements (ranging) using broadband ultrasonic chirp signals; 978-0-7695-4745-9/12 $26.00 © 2012 IEEE DOI 10.1109/TrustCom.2012.172
2008
of several unbranded and commercially available piezotweeters before choosing one. In figure 3 is presented the frequency response versus the sound pressure level per Volt (SPL/V) of the selected piezo-tweeter. This graph was obtained when the transmitter and receiver were at 1m of distance, considering the zero-degree case of its radiation pattern. We used a Brüel & Kjær 4954A reference microphone for measurement and calibration. Looking to the frequency response we opted to use, as possible, the bandwidth that is above 70 dBSPL, in order to maximize the transmitted energy. This criterion lead us to a usable bandwidth of B=25KHz, in the band 20KHz-45KHz.
a specific time slot for ultrasonic signal transmission. Each time slot has a total duration time of 85ms, and can be split in three distinct periods, for each i slot: 1) sig i - signal transmission period (30ms) 2) list i - listening period (60ms) 3) gtime - guard time period (25ms) The signal transmission period is the time that the transmitter needs to send the ultrasonic signal. In our experiments were used signals with 30ms duration. The listening period is the time slot used by the mobile node to estimate the range measurement. Take note that the listening period includes the signal transmission period, which means that the system is also acquiring data when the signal transmission period is happening. In this case, the effective listening period is given by the difference between the listening period and the signal transmission period, which result in 30ms and can be used to measure distances up to 10m. The guard time period was added to reduce the impact of the room reverberation. The room reverberation time was measured using the ISO 3382 standard and resulted in a T60 reverberation time of 25ms [5].
SPL/V @ 1m (Re 20μPa)
70 60 50 40
0
10
20
30
40 50 60 Frequency (KHz)
70
80
90
100
Figure 3: SPL Vs. Frequency in the piezo-tweeter @1m(re 20μPa).
In figure 4 is presented the sensitivity of the WM61A microphone versus its frequency. This response was obtained after calibration with a Brüel & Kjær 4954A reference microphone. Looking to figure 4 in more detail, one can observe that sensitivity decreases almost linearly from 30KHz (S=-35dB) to 45kHz (S=-45dB). This results in a sensitivity reduction of about 10dB which is acceptable for this application.
80
30
90
Figure 2: Time Division Multiplexing slots.
B. Measurement The measurement stage is based on time of flight estimation. Low cost transducers were selected to transmit broadband ultrasonic chirp pulses. This overcomes most of the problems faced by the narrow band signals usually used with common piezo-ultrasonic transducers such as, poor resolution, low environment noise immunity, short range and low robustness to the Doppler effect. The probability of detection of an transmitted signal is directly related with the signal-to-noise ratio (SNR) rather than the exact waveform of the received signal [6]. Cross-correlation, i.e. matched filtering, between the transmitted and received signals is used to maximize the SNR at the output of the correlator, when a known signal plus noise are passed throughout the correlator. Other advantage of using cross-correlation is the pulse compression rate obtained after correlation, which means that the time resolution in the peak position estimation can be greatly improved, leading to distance measurements with higher accuracy. 1) Broadband Transducers: As transducers we opted for a piezo-tweeter speaker and a Panasonic WM61-A electret microphone. Piezo-tweeters are commonly used in ultrasonic animal repeller systems and may easily be found at electronic local stores. We measured the frequency response
−20 −25
Sensitivity (dB)
−30 −35 −40 −45 −50 −55 −60
0
10
20
30
40 50 60 Frequency (KHz)
70
80
90
100
Figure 4: Sensitivity Vs. Frequency in the Panasonic WM61-A electret microphone.
In figure 5, it is possible to observe the acoustic node with the piezo-tweeter and the Panasonic WM61-A introduced before. 2) Signal design: Signals with time and frequency diversity, e.g. linear frequency modulated signals or chirps, are well known in RADAR and represent a case where time and frequency are booth used to increase the probability of detection. At this time it is important to introduce the concept of time bandwidth product (TBP). TBP gives us the relation between the time duration of a signal and the
2009
ranging applications, see [8]. The advantages mentioned before, i.e. increase in the SNR and pulse compression, are easily observed in figure 6 c) and 6 f) by comparing both autocorrelation functions in time. Two important figures of merit were used to describe the pulse compression gain, the compression ratio (CR) and the peak sidelobe level (PSL). CR was measured by looking to the time interval that the autocorrelation peak is above a -6 dB threshold line. PSL is the interval, in dB, between the autocorrelation peak and the nearest sidelobe. In table I are condensed all the figures of merit introduced before, and can be used to compare the broadband and narrowband chirp pulses. Considering the CR figure of merit of both signals we can estimate the worst-case error in a distance measurement due to the peak position detection jitter imposed when SNR degrades. For example, considering c = 343 m/s, the maximum jitter in peak detection imposes a distance measurement error of: Δd = 14 mm and Δd = 222 mm for the broadband and narrowband chirp pulses, respectively.
Figure 5: Acoustic node with speaker and microphone.
range of frequencies (Bandwidth) necessary to re-construct the signal [6]. In RADAR, chirps with large TBP are used to obtain narrow compressed peaks with large amplitude due to SNR maximization, resulting in a signal with increased probability of detection, but also when Doppler tolerance is needed. Chirps can achieve up to ±B/10 Doppler tolerance, improving the detection probability for large Doppler shifts [7]. By increasing TBP and using adequate weighting in the signal design is possible to increase: the SNR, the pulse compression (better time resolution) and the Doppler tolerance, which highly improves the probability of detection in static and dynamic positioning scenarios [6]. The signal used in experiments is a broadband ultrasonic chirp with 30ms of duration and frequencies rising from 20KHz to 45KHz, i.e. a signal bandwidth B=25KHz and a TBP=750. In figure 6 c), is plotted the autocorrelation function of the chirp described before. In figure 6 it is possible to compare the used broadband chirp (left side) with a narrowband chirp signal (right side) with the same energy, but with a B of 2KHz and a resulting TBP of 60. The narrowband chirp version is shown in the same figure, right side, and was designed to occupy the available bandwidth existent in typical 40KHz piezo-ultrasonic transducers, commonly used in ultrasonic
Table I: Figures of merit of the chirps presented in figure 6. Chirp Broadband Narrowband
B 25 kHz 2 kHz
TBP 750 60
CR 0.042 ms 0.646 ms
PSL 65 dB 14 dB
3) Ranging Algorithm: In figure 7 is presented the algorithm used to compute a distance measurement for each time slot. After each time slot, a sampled version of the received ultrasonic signal is available for processing. Noise floor estimation is used to improve the first peak detector performance. The goal relies on post-validation of each peak detected. The first peak detector was implemented to guarantee optimum peak detection in non line-of-sight cases.
!
!
Figure 6: Example LFM Chirps: Broadband Chirp (a) Time Vs. Frequency, (b) Magnitude Spectrum, and (c) Time Autocorrelation Function; Narrowband Chirp (d) Time Vs. Frequency, (e) Magnitude Spectrum, and (f) Time Autocorrelation Function.
Figure 7: Ranging algorithm for each time slot.
Figure 8, shows the signals involved in a distance mea-
2010
surement, when transmitter and receiver were at a distance of 3m with a transmitted power of 94 dBSPL (re 20μPa @ 1m). By observation, is possible to observe an increase of more than 30dB in the SNR, and the resulting pulse compression obtained, that is directly related to the high ultrasonic signal’s TBP.
(n f e) computed for each specific time slot. A guard interval, Δ, is added to ensure that false positives do not appear, see equation 5. n f e = max(20 log10 xc [n]) + Δ
C. Localization Localization is the process of position estimation using the distances previously measured. In this paper, position estimation was obtained using multilateration. In this configuration, if a mobile node knows its distance to all the anchor nodes in the network, a 3D position estimate can be computed by solving a linear system of equations using the minimum mean square error (MMSE) estimation method. Once distance measurements are always noisy, (e.g. thermal noise, external acoustic noise, sound velocity changes, etc.) the position estimation can be seen as an optimization problem. One solution is to find the position that minimizes the squared error intersection point for all the spheres centered at each anchor node position with radius equal to the previous distances obtained [1], see equation 6. fi = ri (xi − xm )2 + (yi − ym )2 + (zi − zm )2 (6)
(5)
Figure 8: Signals example for 3m distance measurement. Is possible to observe a SNR gain after correlation of approximately 30dB.
4) Noise Floor Estimation: The noise floor estimation method is used for distance measurement validation, in order to improve the first peak detector performance. With this is possible to reduce outlier measurements based on this simple criterion: a valid distance measurement is taken if the first peak is above the noise floor estimate. If the first peak measured is below the noise floor estimate, the measured distance is considered invalid and should not be taken into account in the position estimation algorithm. Consider that x[n] = s[n] + w[n] were s[n] represents the signal that carries information with length N, and is affected with Additive White Gaussian noise, w[n], with variance σ2n . The detection of the transmitted signal, s[n] is obtained by correlation, see equation 3. One way to estimate the noise floor for each measurement can be performed by using the magnitude peak of the initial N correlated samples of the received signal x[n] in the time slot under observation. This method can be described by, xc [n] = = =
A solution to the previous set of equations is given by the non-linear objective function presented in equation 7. F(xm , ym , zm ) = min ∑ fi2
The solution for the set of equations given in 6 is obtained by applying the previous objective function, see 8: fi = ri (xi − xm )2 + (yi − ym )2 + (zi − zm )2 = 0 (8) Re-arranging the system of equations presented in 8 we can obtain a linear set of equations that can be given in matrix form, see equation 9,
N−1
∑ s[−n]x[n]
(1)
∑ s[−n](s[n] + w[n])
(2)
n=0 N−1 n=0 N−1
N−1
n=0
n=0
∑ s[−n]s[n] + ∑ s[−n]w[n]
Axˆ = b
(3)
ki2 = xi2 + y2i + z2i ⎡
x1 A = ⎣ x2 x3
N−1
∑ s[−n]w[n]
(9)
where matrices A and b are given by:
Observing the previous equation, when s[n] is not present, the first term is equal to zero and the output of the correlator approximates to equation 4. xc [n] =
(7)
(4)
y1 y2 y3
⎡ 2 ⎤ ⎤ k1 − r12 + r02 z1 1 z2 ⎦ b = ⎣ k22 − r22 + r02 ⎦ 2 z3 k32 − r32 + r02
(10)
(11)
The solution to this set of linear equations gives a position estimate x, ˆ and can be obtained directly by the equation 12.
n=0
From equation 4, since noise is uncorrelated with s[n], we can use its maximum value as our noise floor estimator
xˆ = (AT A)−1 AT b
2011
(12)
III. E XPERIMENTAL VALIDATION
A1
All experiments were made under equivalent laboratory conditions. The room temperature was measured, and the sound-speed was estimated using the equation 14 [9]. c = 331.3 + 0.606 × T = 342.5m/s
7 6 Y−axis (m)
= 18◦C
T
(13) (14)
5 4 3 2
A set of three experiments were performed to evaluate the proposed system: Experiment 1) Quantitative evaluation of distance measurements (ranging) in straight line, using broadband ultrasonic chirp signals. Experiment 2) Quantitative evaluation of the 3D positioning system when the mobile node was placed at fixed positions. Experiment 3) Qualitative evaluation of the positioning system (2D case) when the mobile node was in a moving trajectory.
A3
8
1 0 A0 −1 −1
A2
0
1
40 30 20 10 0 −10 −20
Error(mm)
Error(cm)
3
4 d(m)
5
6
7
8
Note that, no outlier measurements are present, which can be justified by the fact that measurements were taken in laboratory in a controlled acoustic environment, i.e. acoustic noise bellow 40dBSPL.
40 30 20 10 0 −10 −20
10
2
6
A3 : (3.70, 8.35, 1.70)m
20
1
5
A0 : (0.00, 0.00, 2.52)m A1 : (0.00, 8.15, 2.52)m A2 : (7.25, 0.00, 2.52)m
30
0
3 4 X−axis (m)
Figure 10: Experiment 2) : XY positioning results. Real positions - black cross; Estimated positions - red points; Anchor nodes circles A0, A1, A2 and A3.
A. Experiment 1: Distance measurements Distances were measured between a transmitter and a receiver in straight line for fixed positions, with distance in steps of 1m, from 1 to 7m. The transmitter and receiver nodes were positioned at 1.5m above the floor. For each position were computed one hundred distance measurements. The signal used in this experiment was the broadband chirp defined in the section 2.2. The mean absolute error obtained in distance measurements is 12mm and its mean standard deviation is 1mm.
2
40 30 20 10 0 −10 −20
7
Figure 9: Experiment 1) : Distance measurement error and standard deviation, for distances from 1 to 7m.
Position: (1,7)
x y z Position: (1,4)
x y z Position: (1,1)
x
y
z
40 30 20 10 0 −10 −20 40 30 20 10 0 −10 −20 40 30 20 10 0 −10 −20
Position: (4,7)
x y z Position: (4,4)
x y z Position: (4,1)
x
y
z
40 30 20 10 0 −10 −20 40 30 20 10 0 −10 −20 40 30 20 10 0 −10 −20
Position: (6,7)
x y z Position: (6,4)
x y z Position: (6,1)
x
y
z
Figure 11: Experiment 2) : Coordinates error and standard deviation in all positions described in figure 10.
B. Experiment 2: Fixed position estimation In figure 10 is presented the XY-grid plane used as the ground-truth in this experiment. A mobile node was placed at each test position (marked with a black cross), with a constant height of 1.75m. One hundred position estimations were computed for each test position. All the estimated measurements for all the positions, are plotted overlapped in the same XY-axis graph, see figure 10. The anchor nodes are represented by the black circles, and were placed at:
In figure 11 for easy result analysis is presented the mean error and its correspondent standard deviation obtained for each axis in all the positions. All measurements were made using a fixed z-coordinate, which means that all the measurements must lie in a z-plane with offset equal to the height to which the receiver was placed, i.e. the z-plane with 1,75m height. By observation, the error in z-axis, is the largest (when compared with other axes) and its existence
2012
suggests that position estimates does not fall in the expected z-plane, but rather, in a diagonal plane with diversity in the z-coordinate. This is an obvious source of error obtained in distance measurements. In table II is presented a resume of the mean error for all independent coordinates and the correspondent absolute positioning error and standard deviation.
3 2.5
x 3.2 0.7
y 9.0 0.4
z 17.8 2.2
Mean 10.0 1.1
2D Abs 9.6 0.8
A2
z−axis
A3
1.5
A0
1 0.5 0
Table II: Mean and absolute errors. Error (cm) Std (cm)
A1
2
9
3D Abs 20.2 2.3
8
7
6
5
4
3
2
1
1
2
5
4
3
6
7
x−axis
y−axis
Figure 13: Simulated noise-free position estimation. Real positions - black points; Estimated positions - red points; Anchor nodes A0, A1, A2 and A3.
C. Experiment 3: Dynamic position estimation In this experiment, a qualitative evaluation of the positioning system (2D case) was performed. The results were obtained when the mobile node was in a moving trajectory. Four anchor nodes were used at the same positions of the experiment 2. A moving person with the receiver on top of the head was used to evaluate the positioning system in a moving trajectory, see figure 12.
A1
Figure 13 shows a simulation of the position estimates when four anchor nodes are used in the positions used in the experiment 2), see section 3.2. For each position four distance measurements are computed, each corresponding to the distance between an anchor node and an XY-grid point placed at a fixed z-coordinate, in this case 1.7m. The absolute 3D error obtained in the simulation, see figure 13, has values of between 31 and 33 cm, mainly due to the contribution of the z-plane offset bias. At this point, we relate the error obtained in position estimation with the error obtained in distance measurements (distances between anchor nodes and the mobile station) used to estimate a position with the proposed algorithm.
A3
8 7
Y−axis (m)
6 5 4
30 20 10 0 −10 −20 −30
3 2 1
A0 −1 −1
0
Error(cm)
0 A2 1
2
3 4 X−axis (m)
5
6
7
8
30 20 10 0 −10 −20 −30 30 20 10 0 −10 −20 −30
Figure 12: Experiment 3 : Qualitative results of the positioning system (2D case) for a moving trajectory. Real trajectory - solid black line; Estimated positions - red points; Anchor nodes - circles A0, A1, A2 and A3.
In this experiment, only a qualitative evaluation can be performed because errors introduced by the human movement cannot be extracted due to difficulty in ground-truth validation.
Position: (1,7)
d0 d1 d2 d3 Position: (1,4)
d0 d1 d2 d3 Position: (1,1)
d0 d1 d2 d3
30 20 10 0 −10 −20 −30 30 20 10 0 −10 −20 −30 30 20 10 0 −10 −20 −30
Position: (4,7)
d0 d1 d2 d3 Position: (4,4)
d0 d1 d2 d3 Position: (4,1)
d0 d1 d2 d3
30 20 10 0 −10 −20 −30 30 20 10 0 −10 −20 −30 30 20 10 0 −10 −20 −30
Position: (6,7)
d0 d1 d2 d3 Position: (6,4)
d0 d1 d2 d3 Position: (6,1)
d0 d1 d2 d3
Figure 14: Distance measurement errors for the positions described in figure 10.
In figure 14 the average error obtained for each distance measurement is plotted for each position in experiment 2). Note that the error obtained in distance measurements is approximately ten times greater than the error obtained in the distance measurements in experiment 1). One reason for the increase in distance measurement error, is the fact that the distance measurements in experiment 1) were obtained with
IV. E RROR A NALYSIS Theoretically, the positioning algorithm, when fed with noise-free distances, computes position estimates that fall in a z-plane with an offset bias error introduced by the asymmetry existing in the anchor node positions.
2013
for each anchor node. By designing chirp-based signals with good correlation properties (i.e. orthogonality) one can remove the time slots and share the acoustic channel with increased position estimation rates.
the transmitter and receiver placed in front of each other, in a straight line, were the transmitter and the receiver have the highest directivity index. This degrades when the angle between the transmitter and receiver increases. All of these deterministic errors propagate to the position estimation through the positioning algorithm with a greater effect on the z and y coordinates. One way of reducing this deterministic error is to improve the first peak detection algorithm used in ranging. Another possibility is to increase the SNR through the use of chirp pulses with more energy, thus increasing its duration in time.
R EFERENCES [1] A. H. Sayeda, A. Tarighata, and N. Khajehnouri, “Networkbased wireless location,” IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 24–40, 2005. [2] N. Patwari, A. O. Hero, and J. A. Costa, “Learning sensor location from signal strength and connectivity,” in Secure Localization and Time Synchronization for Wireless Sensor and Ad Hoc Networks, R. Poovendran, S. Roy, and C. Wang, Eds., vol. 30, University of Michigan Dept. of Electrical Engineering and Computer Science Ann Arbor USA. Springer US, 2007, pp. 57–81.
V. C ONCLUSIONS In this paper we proposed an indoor positioning system that uses broadband ultrasonic chirps for ranging. Broadband chirps with high TBP were used to obtain narrow compressed peaks with higher SNR. This resulted in an increased Doppler tolerance and high accuracy distance measurements, an absolute mean error of 12mm with mean standard deviation of 1mm. The positioning system under evaluation uses just four anchor nodes arranged to obtain 3D coordinates in a room of approximately 200m3 . The results obtained showed an accurate and reliable positioning system with a mean absolute 3D positioning error of 20.2cm and a mean absolute standard deviation of 2.3cm. If we look only at the XY-axis, the results obtained look even better, with a mean absolute 2D positioning error of 9.6cm and a mean absolute standard deviation of 0.8cm.
[3] H. Schweinzer and M. Syafrudin, “Losnus: An ultrasonic system enabling high accuracy and secure tdoa locating of numerous devices,” in Indoor Positioning and Indoor Navigation (IPIN), 2010 International Conference on, sept. 2010, pp. 1 –8. [4] I. Amundson and X. D. Koutsoukos, A Survey on Localization for Mobile Wireless Sensor Networks. Springer-Verlag Berlin Heidelberg, 2009. [5] J. S. Bradley, “Using ISO 3382 measures, and their extensions, to evaluate acoustical conditions in concert halls,” Acoustical Science and Technology, vol. 26, no. 2, pp. 170–178, 2005. [Online]. Available: http://joi.jlc.jst.go.jp/JST.JSTAGE/ast/26.170?from=CrossRef
VI. F UTURE W ORK We need to propose a clock synchronization strategy that could be shared by all the anchor nodes as this would allow the inclusion of time difference of arrival (TDoA) in the ranging process. Another research direction would be to include audio bandwidth in the signal design process, where possible, so that the whole system is non-invasive for humans. This would involve using low frequency signals (in the audio range limit) to cover larger distances, thus overcoming the high attenuation of ultrasounds at higher frequencies. Another improvement relies on the increase of the position estimation rate. One way is to propose another method of sharing the acoustic channel, since TDMA limits the position estimation rate by imposing a fixed time slot
[6] N. Levanon and E. Mozeson, Radar Signals. Hoboken, New Jersey: John Wiley & Sons, Inc., 2004. [7] M. I. Skolnik, Ed., Radar Handbook, 2nd ed. McGraw-Hill, 1990. [8] J. N. Vieira, S. I. Lopes, C. A. C. Bastos, and P. N. Fonseca, “Ultrasound sensor array for robust location,” in Multi-Agent Robotic Systems, Proceedings, Sapaty, P and Filipe, J, Ed., 2007, Proceedings Paper, pp. 84–93, 3rd International Workshop on Multi-Agent Robotic Systems, Angers, FRANCE, MAY, 2007. [9] D. Havelock, S. Kuwano, and M. Vorlander, Eds., Handbook of Signal Processing in Acoustics. Springer, 2008.
2014
