A non-line-of-sight identification algorithm in automatic microphone localization for experimental acoustic modal analysis Giampiero Accardo a) Bram Cornelis b) Karl Janssens c) Bart Peeters d) Siemens Industry Software NV, Interleuvenlaan 68, B-3001 Leuven, Belgium Paolo Chiariotti e) Universit´a Politecnica delle Marche, Via Brecce Bianche 12, 60131 Ancona, Italy Milena Martarelli f) Universit´a degli Studi e-Campus, Via Isimbardi 10, 22060 Novedrate (CO), Italy In the past few years an increasing interest in the minimization of interior noise levels has been observed in the automotive industry. Within this context, experimental Acoustic Modal Analysis (AMA) tests play a crucial role in the optimisation process of the acoustic parameters of car cavities. A first challenging task of such tests is the creation of an accurate geometrical wireframe model representing the 3D positions of the microphones instrumented inside the car cabin. In this paper, an automatic microphone localization procedure is presented and validated with real experimental data. The technique is based on multilateration concepts: four or more acoustic sources (anchors) are utilized for measuring the time-of-arrival (TOA) between sources and microphones (targets), so that the targets can be localized in 3D space. However, typical obstructions inside a car cabin lead to non-line-of-sight (NLOS) links between the anchor and the target. As a consequence, range estimates may have an erroneous positive bias. A robust technique is proposed, which identifies and prunes the NLOS measurements, so that the microphones can be localized using the LOS distances only. An experimental case study on a fully trimmed sedan car will be shown in order to demonstrate the effectiveness of the algorithm. a)
email: email: c) email: d) email: e) email: f) email: b)
[email protected] [email protected] [email protected] [email protected] [email protected] [email protected]
1
INTRODUCTION
In the past few decades, the minimization of interior noise levels in automotive cabins has become a very active research area, mainly encouraged by the need for weight reduction and the current trend towards environmentally compatible hybrid-electric powertrain concepts. To improve the interior noise performance, CAE predictions have gained importance, especially in the early development stage when it is still possible to make changes without negatively affecting the vehicle development time. It is obvious that the effectiveness of this approach greatly depends on the accuracy of the predictions made using such a model. Hence, in order to understand the modelling challenges and improve the overall modelling know-how which will be useful in the car development phase, the experimental acoustic characterization of the cabin plays a crucial role. When performing an interior acoustic study, it is important to relate the acoustic responses to the intrinsic system behaviour of the cabin, which can be achieved by Acoustic Modal Analysis 1 . Among the various specific challenges of this analysis, the test setup itself is a nontrivial task, as it includes the creation of a geometrical wireframe model that represents the 3D position of the sensors. An (acoustic) modal analysis test can easily consist of hundreds of degrees of freedom, particularly when the results are used for validating and updating finite element (FE) models. Establishing a precise test geometry then relies on the capability of the operator to instrument exactly at predefined locations. It is clear that in many realistic cases this task can be rather challenging, above all when the structure is complex. In current practice one has to measure the geometry of the test object by hand, which is extremely time-consuming and which typically yields inaccurate results. Automatic methods, which reduce this setup time and which yield more accurate results, are therefore highly sought for. Currently available solutions include photogrammetry 2 and geometry scanning systems 3 . Although these solutions are effective, they often require expensive devices, which moreover can only be used by highly specialized technicians. This paper presents a fast, accurate and cost-effective procedure to automatically localize microphones in a car cabin. The microphone localization procedure is based on multilateration: the distances between four or more sources (anchors), whose coordinates are known or estimated a priori, and a microphone (target) are utilized to determine the unknown position of the target in three-dimensional space. Hence the estimation of target coordinates comprises two steps: i) acoustic ranging measurements, ii) multilateration. However, due to the complex structure and obstructions typical of a car cabin (e.g. seats, dashboard, etc.), the direct path may be obstructed, a so-called Non-Line-Of-Sight (NLOS) condition. As a consequence, acoustic range estimates based on the time-of-arrival (TOA) may have an erroneous positive bias, i.e. the signal arrives at a target through reflections instead of through the direct (shortest) path. The (overestimated) NLOS distances may subsequently lead to large 3D position errors. In this work, we focus on the problem of NLOS identification: the erroneous NLOS measurements are detected and pruned by a so-called “Pruning algorithm”, so that the microphones are localized using the LOS distances only, hence yielding more accurate 3D localization results. The paper is organized as follows. Section 2 presents the used notations, the assumed system model, and the entire microphone localization procedure (including the novel Pruning algorithm). In Section 3 the procedure is tested with experimental data from two different measurement campaigns: the first in a controlled laboratory room, the second in a fully trimmed sedan car. Finally, in Section 4 some concluding remarks are given. 2
MICROPHONE LOCALIZATION PROCEDURE
In this section the entire microphone localization procedure is presented. First, the used notations and assumed system model are introduced. Second, the acoustic ranging method is described. Third, once the observed distances are obtained, the 3D coordinates of the targets can
be determined by solving a non-linear optimization problem, where the target coordinates are the optimization variables and where the distance equations involving target coordinates form a non-linear objective function. Finally, the so-called “Pruning Algorithm”, which identifies and removes NLOS distances, is presented. 2.1 Notations and Model Let M = {1, 2, . . . , M } be the set of indices of M anchors, whose locations are known a priori at {xi = [xi yi zi ]T , i ∈ M}, and let {x = [x y z]T } be the unknown target location, which we wish to determine. The received signal emitted by the i-th anchor can be modelled as 4 : ri (t) = Ai s(t − τi ) + ni (t), for i ∈ M (1) where s(t) is the transmitted signal, τi and Ai are the time delay and the signal amplitude respectively, and ni (t) is an additive noise term with a Gaussian noise distribution with spectral density N0 /2. In a synchronous communication system the time delay is: τi =
||x − xi || , c
for i ∈ M
(2)
where c is the speed of sound in the acoustical medium, and || • || is the Euclidean norm. 2.2 Acoustic Ranging Measurements A crucial first step in the microphone localization procedure is to acoustically measure the ranges, i.e. the distances between the anchors and the targets. Range estimates can for example be obtained using time-of-arrival (TOA) estimation techniques 5 . TOA-based range measurements rely on the fact that, if the transmitted signal is known, the time delay estimation can be obtained by calculating the cross-correlation function (CCF), Rrs (τ ) between the transmitted signal s(t) and the received signal r(t): Rrs (τ ) = E[ri (t)s(t + τ )] = Ai Rss (τ − τi )
(3)
where Rss (τ − τi ) is the autocorrelation function of s(t) shifted to have its peak value at τ = τi . Indeed, the properties of the autocorrelation function show that, when τ = τi , Rrs (0) is the maximum. Therefore the argument τˆ that maximizes Rrs (τ ) provides an estimate of delay: τˆi = arg max Rrs (τ ),
(4)
τ
and, hence, from Eq. (2), an estimate of distance. s(t)
CROSSCORRELATION
Rrs (τ )
THRESHOLD BASED PEAK-DETECTION
dobs i
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c ni (t)
ri (t)
Fig. 1 – Flowchart of the Ranging Process
However, in a reverberant environment each sensor receives multiple delayed and attenuated replicas of the transmitted signal (due to reflections of the wavefront from boundaries and objects) in addition to the direct-path signal. As a result, the energy of the direct path is not always the strongest, so that the maximum peak in the CCF may correspond to a (longer) reflection path
instead of the direct path, hence leading to an erroneous positively-biased ranging estimate. A straightforward solution to overcome this issue may be to select the first most significant peak over a certain threshold. A scheme of the ranging process is shown in Fig. 1. Nevertheless, it cannot be ruled out that erroneous ranging estimates will still occur in practice. In addition, the existence of typical obstacles in a car cabin (such as the seats, the dashboard, etc.) may also result in NLOS conditions in which the target and the anchor do not share a direct link, i.e. because only reflections of the transmitted signal arrive at the target. Therefore, there is a need for removing (“pruning”) such erroneous NLOS measurements by the later pruning algorithm (cf. infra). 2.3 3D Localization as an Optimization Problem In absence of noise and NLOS bias, the actual distance ri between the target and the i-th anchor defines a sphere around the i-th anchor corresponding to possible target locations, i.e. (x − xi )2 + (y − yi )2 + (z − zi )2 = ri2 ,
for i ∈ M
(5)
The exact location of the target is then found at the unique intersection of all the spheres. In practice however, the noisy distance measurements and NLOS bias yield spheres which do not intersect at the same point, resulting in the inconsistent equations 2
(x − xi )2 + (y − yi )2 + (z − zi )2 = dobs , i
for i ∈ M
(6)
Equation (6) can be solved by minimizing the sum of squared residuals, so that the 3D localization problem is reformulated as an optimization problem, i.e., ( M ) 2 X min ||x − xi || − dobs (7) i x
i=1
ˆ of the target location. whose solution yields the final estimate x In multilateration, at least four LOS anchors are required for a unique 3D solution. If there are more than four LOS anchors, the redundancy of these anchors can be utilized in a least square (LS) sense for a more accurate localization result. Minimizing the non-linear expression in Eq. (7) can be achieved by numerical search methods. Since the cost function is non-convex, the procedure may however converge to a suboptimal local minimum instead of to the global minimum. The initial guess given to the solver is therefore crucial: a close-to-optimum initial guess would converge to the global minimum relatively fast, while an inappropriate initial guess might lead to a local minimum. In such cases, a global optimization (GO) algorithm is needed to solve the problem. In this paper, we will instead perform a direct search optimization where the issue is limited by constraints, i.e. the components of the optimization variable x will be subjected to the boundary value constraints xmin ≤ x ≤ xmax
ymin ≤ y ≤ ymax
zmin ≤ z ≤ zmax .
(8)
The optimization solver used in this work is the Nelder-Mead simplex method, i.e. an unconstrained optimization solver. The boundary value constraints in Eq. (8) are therefore incorporated by modelling them as penalty functions in the objective function. Evidently, the optimization method will be most effective in estimating the location when only LOS distance measurements are combined. Therefore, there is a need for a so-called “Pruning algorithm”, which is able to identify the NLOS observed distances and exclude them in the LS calculation (cf. infra).
2.4 Pruning Algorithm The LS method is extremely sensitive to outliers, i.e. a single outlier (an erroneous NLOS measurement in our case) may already be sufficient to offset the LS estimator 6 . This paper therefore proposes a so-called pruning algorithm, which is able to identify the number L of LOS anchors and localize the target with them only. To achieve this, the algorithm performs a socalled delta test by which the squared residual of a set of distances is compared to a predefined threshold, ζ: obs ∆2i = dest i − di
2
< ζ2
(9)
where dest = ||ˆ x − xi || is the estimated distance between the i-th anchor and the target at i ˆ. estimated location x The algorithm flowchart is illustrated in Fig. 2. RANGING DISTANCES with M anchors xi , dobs LOS anchors L = M
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∆2i = dest − dobs i i
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< ζ2?
YES NON-LOCALIZABLE TARGET
STORE ˆ L, L, x
Fig. 2 – Flowchart of the Pruning Algorithm For the sake of illustration, assume M = 6, with some or all dobs i in LOS. The pruning algorithm ˆ , and compares the begins by checking if L = M = 6. It estimates the target location, x 2 residuals, ∆i . If all the residuals are below the threshold ζ (as determined by location accuracy requirements), then L = M , otherwise the optimization procedure moves to groups of (L − 1) anchors. The pruning algorithm stops when all the residuals of the k-th set of M anchors taken L are below the threshold, or when L = M min , i.e. the minimum number of anchors which are necessary for a unique localization result. 3
EXPERIMENTAL ACTIVITIES
The Pruning Algorithm has already been proven to be effective with simulated data 7 . In this section its performance is tested by using real experimental data. Two measurement campaigns have been carried out respectively: i) in the Laboratories of the Department of Industrial Engineering and Mathematical Sciences (DIISM) at Universit`a Politecnica delle Marche in Italy (UNIVPM); ii) in the facilities of Siemens Industry Software (SISW) in Belgium.
3.1 First Experimental Test For multilateration, the source should ideally be a monopole. It means that, within the frequency range of interest, the characteristic length of the source must be smaller than the minimum wavelength, and the source itself must be always omnidirectional. Various techniques can be adopted for this purpose 8 . However, since the frequency range of interest for current AMAs is still limited to a low frequency range and the measurement of hundreds degrees of freedom 1 is extremely timeconsuming, the implementation of a simple tool capable of quickly identifying sensor coordinates with a reasonable accuracy of a few centimetres can be considered sufficient at this stage. It is obvious that this cannot be acceptable for analyses demanding a higher accuracy, such as sound source localization, health monitoring, etc. Nevertheless, improvements for achieving this goal will follow in future. Hence, with the goal of having a preliminary quantification of the level of accuracy by using a simple loudspeaker, without any particular designing expedients to make it as a monopole-like sound source, the following first test have been held at UNIVPM. Furthermore, in the test described below, a database containing different propagation conditions in a controlled, obstructed environment has been created. A. Experimental Setup and Measurement Arrangement Five microphones were fixed on a vertical grid and placed randomly (Fig. 3). The coordinates of each microphone were measured with a 6-axis articulated robot (DENSO Robot VM-G) 9 . For this purpose, a stinger was adapted on the flange face of the robotic arm (Fig. 4a) in order to touch the tip of the microphone and have an accurate estimate of its position. 0.25
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Fig. 3 – Microphones distribution on the grid. Once the coordinates of the microphones were obtained, a loudspeaker was mounted on the flange face. Hence, a roving source has been moved in 20 different, random positions in the 3D space (Fig. 9). The acoustic centre of the speaker was previously calibrated, defined in the tool coordinates of the robot software, and assumed stable in the excitation bandwidth. During the measurements, the averaged temperature of the environment was constantly recorded in order to calibrate the speed of sound. The acquisition was performed using an LMS SCADAS frontend together with LMS Test.Lab software. The maximum sampling rate of fs = 204.8 kHz provided by the acquisition system has been used so as to have the highest possible temporal resolution of the CCF. In order to have a high resolution, the pulse length must be short to avoid the overlapping of near echoes in the CCF. This is not a trivial requirement, as it is difficult to emit sharp pulses with general purpose loudspeakers. In addition, the signal has to be emitted with the highest
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(a) DENSO Robotic arm and stinger.
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Fig. 4 – Stinger configuration and anchors positions. power available in order to increase the SNR, and to minimise the Cramer-Rao Lower Bound (CRLB) 10 . Nevertheless the SNR is proportional to pulse duration 11 . The contradiction is solved by long duration signals with short duration correlation functions, so when the received signal goes through an appropriate template signal, the output will be a short pulse. A signal commonly used in radar application in order to achieve pulse compression is the linear frequency modulated (chirp) signal. Hence, such a signal will be used in the ranging phase. The source is able to emit a broadband sound between 2-20 kHz. The power spectral density (PSD) of the sound source and its directivity pattern in the horizontal plane are displayed in Fig. 5. −40
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Fig. 5 – PSDs and Directivity of the sound source. B. Ranging Performances The voltage signal from the loudspeaker to the SCADAS was used as template signal of the CCF. In addition, a peak fitting procedure has been used in order to improve the estimation of subsample time delays 12 . The collected database includes 100 measurements consisting of 91 waveforms captured in the LOS condition and 9 waveform in the NLOS condition. An obstacle was indeed placed between the anchor and one or more targets during the measurement phase in order to configure
a NLOS condition. Figure 6a shows the empirical Cumulative Distribution Functions (CDFs) of the ranging error over all the measurements. It can be seen that 90% of the measurements in LOS conditions has an error less than 4.5 mm. In a previous work 7 , it has been reported that the localization algorithm, with such an error in the ranging, would provide an estimate of each microphone position affected by a localisation error of around 5 mm, when the LOS anchors are at least five. As already said, such errors are negligible for AMA purposes, but they may not be acceptable for applications that, covering a higher frequency range or relying on an accurate inter-sensor positions, demand a better level of accuracy. The observed discrepancies could be due to the directivity of the source and to a non-proper calibration of the acoustic centre. Nevertheless it is worth noticing that still an acceptable accuracy (always within half a centimetre) can be achieved without any particular designing efforts, and by using a general purpose loudspeaker. On the other hand, it is also impressive that only 9% of the measurement in NLOS condition can affect significantly the ranging, hence the localization accuracy. 100
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(b) Influence of the number of LOS anchors on the localization accuracy.
Fig. 6 – CDFs of the ranging error and localization error values for different numbers of LOS anchors. C. Localization Performances Before showing the performance of the pruning algorithm, a study on the influence of the number L of the LOS anchors on the accuracy of the results is conducted. The target-anchor geometry plays an important role in determining the localization accuracy 13 . In order to mitigate the effect of the geometry, the localization error as a function of L has been computed as follows. Given K = M CL the number of combinations of M anchors taken L at a time, the localization error εkj for the k-th set of anchors will be: ˆ kj || εkj = ||xref −x j
(10)
where xref is the location of the j-th target, whose coordinates have been measured by the j ˆ kj is the location estimated by using the k-th set robotic arm and assumed as a reference, and x of L anchors. The mean localization error ε¯ will be: K N 1 1 XX k ε¯ = ε K N k=1 i=1 j
(11)
Figure 6b display the influence of the number L of LOS anchors where the dot marks are obviously the values ε¯ and the error bars indicate the standard deviation. As already observed from simulation experiments 7 , the localization accuracy improves with increasing the number
of LOS anchors. At the same time, the standard deviation decreases as well. Furthermore, as foreseen above, the mean localization error settles around 5 mm. In conclusion, one can say that, to achieve the wished accuracy on the localization, it is advisable to have a sufficient number of LOS anchors (more than those actually required for a unique 3D solution). Nevertheless, to drastically increase the quality of the localization, the ranging phase must be definitely improved, i.e. more robust designing expedients must be considered. D. Pruning Algorithm Performances The following three cases have been investigated: i) M = 6; ii) M = 8; iii) M = 10. From case to case, two more anchors are added to the previous set. The anchor-target condition is displayed in Tab. 1. In this case, a threshold value ζ equal to 6 mm and a minimum number of sources Mmin equal to 5 have been imposed for all the three cases. Fig. 7a shows the localization error values when the pruning is active or not in the entire process.
# Microphone
Table 1 – Anchor-target condition 1 2 1 LOS LOS 2 LOS LOS 3 LOS LOS 4 NLOS LOS 5 LOS LOS
3 LOS LOS LOS NLOS LOS
4 LOS LOS LOS LOS LOS
# Source 5 6 7 8 9 LOS LOS LOS LOS LOS LOS LOS LOS LOS LOS NLOS LOS LOS LOS LOS LOS LOS NLOS LOS LOS LOS LOS LOS LOS NLOS
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Fig. 7 – Localization error values for different number M of anchors and localized sensors for M = 8. In Fig. 7b the estimated microphone locations are plotted. The full coloured circles are placed at the actual coordinates and their colour is an indication of the localization error (blue: small error, purple: large error), whereby the localization error values were mapped in a scale between 0 and 10 mm. Hence, one can observe how the pruning process has been proven effective with the currently considered experimental data. Nevertheless, a laboratory room where the obstacles have been created artificially, and where the reflective boundaries are not similar to the ones in a car, is not representative of the real-life environment. A second experimental test has therefore been performed in a real car cabin and it will be described below.
3.2 Second Experimental Test The second test campaign has been performed in the facilities of Siemens Industry Software in Belgium. A fully trimmed sedan car has been selected for qualitatively investigating the performance of the algorithm. A. Experimental Setup and Measurement Arrangement A total of 28 microphones (targets) were placed both at the boundary surface and inside the cavity. As visible in Fig. 8, microphones are present: in the front compartment (A - blue dots), in the rear compartment (B - green dots), between the front windshield and the dashboard (C cyan dots), and in the foot region (D - magenta and red dots). The acoustic sources (anchors) are spread over the entire cabin (Fig. 9). 13 anchors have been placed in the front and 9 in the rear compartment in strategic positions in order to localize all the microphones. A mobile, compact tweeter was utilized as acoustic source. Anchors and targets were preliminarily defined by means of a CAD model of the cabin, allowing for a qualitative comparison with the acoustic localization results. The same acquisition parameters as in the previous test were defined, similarly the voltage from the speaker to the SCADAS were used as template signal for the CCF.
(a) Microphones distribution in a fully trimmed sedan car.
(b) Targets (microphones) distribution.
Fig. 8 – Targets distribution in a fully trimmed sedan car.
(a) Sources distribution in a fully trimmed sedan car.
(b) Anchors (acoustic sources) distribution.
Fig. 9 – Anchors distribution in a fully trimmed sedan car.
B. Results In order to have a qualitative idea of the effectiveness of the Pruning Algorithm, the coordinates from the CAD model are assumed as a reference. The discrepancies between the (inaccurate) CAD positions and the acoustically estimated coordinates do not allow for an absolute localization error quantification, but they are sufficient for demonstrating the effectiveness of the Pruning Algorithm in a complex scenario, such as a car cabin. In Fig. 10, a comparison is made between a localization algorithm were pruning is not applied (i.e. NLOS distances remain present), versus the considered localization algorithm were erroneous distances are removed by the Pruning Algorithm. As visible in Fig. 10, the application of the Pruning Algorithm is not only effective, but also essential for a correct localization of all targets, in particular for targets at difficult locations such as the front windshield. CAD Positions
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Fig. 10 – Targets distribution in a fully trimmed sedan car. 4
CONCLUSIONS
The determination of the 3D positions of microphones based on acoustic distance measurements is a well-established technique. However, when performing acoustic distance measurements in a complex acoustic environment such as a car cabin, the measured distances can be positively biased when NLOS measurements are present. This paper has presented a socalled pruning algorithm, which identifies and removes (prunes) the erroneous NLOS distances. The entire microphone localization procedure (including the novel pruning algorithm) has been tested with real experimental data, both in a controlled and in a realistic scenario, i.e. a laboratory room and a fully trimmed sedan car respectively. In both cases the pruning algorithm has been proven effective. The first experimental test has shown how an error in the ranging affects the localization highlighting the need for more robust designing strategies to guarantee higher accuracy. Nevertheless, the experiment has shown that a general purpose speaker, whereby the acoustic centre was not accurately defined, is sufficient to localize the microphones with a reasonable accuracy for AMA purposes. Furthermore, the test has confirmed the results obtained with simulation experiments in previous works. A second experimental test was conducted in a realistic fully-trimmed sedan car. This experiment has qualitatively proven the effectiveness of the Pruning Algorithm, and moreover has confirmed the necessity of the Pruning Algorithm in complex scenarios such as a car cabin. In future works the ranging measurement phase will be improved. The use of global optimization solvers and the implementation of an adaptive threshold value in the Pruning Algorithm will also be the subject of future investigations.
5
ACKNOWLEDGEMENTS
The authors would like to thank Antonio D’Antuono from UNIVPM for his help with the robotic arm and for his time. The financial supports of the European Commission (EC), through its FP7 Marie Curie ITN EID project ”ENHANCED” (Grant Agreement No. FP7-606800), are gratefully acknowledged. 6
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10. Y. Qi and H. Kobayashi, “On relation among time delay and signal strength based geolocation methods”, in Proceedings IEEE Global Communications Conference (GLOBECOM), 4079–4083 (2003). 11. C. E. Cook and M. Bernfeld, Radar Signals. An Introduction to theory and application (Academic Press) (1967). 12. A. K. Nandi, “On the subsample time delay estimation of narrowband ultrasonic echoes”, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 42, 993–1001 (1995). 13. P. Misra, B. P. Burke, and M. M. Pratt, “GPS Performance in navigation”, in Proceedings of the IEEE (Special issue on GPS), volume 187, 65–85 (1999).
