Small aperture microphone arrays provide many advantages for portable devices and hearing aid equipment. In this paper, a subspace based localization method is proposed for acoustic source using small aperture arrays. The effects of array aperture on localization are analyzed by using array response (array manifold). Besides array aperture, the frequency of acoustic source and the variance of signal power are simulated to demonstrate how to optimize localization performance, which is carried out by introducing frequency error with the proposed method. The proposed method for 5 mm array aperture is validated by simulations and experiments with MEMS microphone arrays. Different types of acoustic sources can be localized with the highest precision of 6 degrees even in the presence of wind noise and other noises. Furthermore, the proposed method reduces the computational complexity compared with other methods.
Microphone array based acoustic source localization is widely used in many application scenarios. However, a big array aperture may greatly limit its applications. In recent years, due to the development of microelectromechanical system (MEMS) technology, small aperture array shows its potential superiority for portable applications. Microphone arrays for hearing aid [
In general, acoustic source localization using microphone arrays is achieved by differences of the signals received from different microphones. The two aspects of the differences are the amplitude change and the phase difference.
The aspect of the amplitude change, concerning array apertures, is related to the solution of the spherical wave model and the plane wave model of the signal [
The aspect of the phase difference forms the essence of localization using spatial information [
In this paper, a low complexity subspace based method is proposed for small aperture microphone array by applying compact planar model. The array aperture, frequency, and variance of the source are discussed as parameters related to localization performance. Under a small aperture, the method reduces the computational complexity as well as achieving high accuracy in general scenarios.
The remainder of this paper is organized as follows. In Section
We first establish here the notations used in this paper. The text in bold denotes vectors. The superscript Let Let
The MUSIC algorithm is a well-known subspace based method. Generally, the DOA estimation of the acoustic sources can be obtained through the use of the plane model under a small array aperture [
The signal
Array manifold (i.e., the columns of
The MUSIC algorithm is based on the fact that array manifold and the noise eigenvectors
The array manifold changes as the frequency varies, while the decrease in the array aperture will make the change of array manifold smaller. In other words, the error caused by frequency dispersion declines as the array aperture becomes smaller. The approximation error of array manifold is derived below with the array aperture and other parameters. In this paper,
According to (
Plane wave propagation in a small aperture.
With respect to the definition of array aperture
Note that (
Hence,
It can be derived from (
Consequently, the proposed method mainly focuses on two aspects: one is to simplify the array manifolds of different frequencies to a single frequency
Collect
Associate bandwidths of acoustic source and environment to limit the processed bandwidths to relatively higher bandwidths of
Construct the
Estimate
Calculate
Isolate the source locations as the maxima of the pseudospectrum
Traditionally, the acoustic sources such as vehicle, music, and human talking are treated as wideband sources. The method for acoustic localization includes ISM and CSM. Among them, the SSA, RSS, and TCT are representative methods. TCT have the best performance. The basic idea for TCT is focusing. However, this will greatly improve the computation. Instead of focusing, we choose a proper approximation for
Concerning the simple uniform distribution,
The essence of the algorithm in this paper is that when the aperture of array is very small, the acoustic signal which is band-limited could be viewed as narrowband signal or approximate narrowband signal. However, there is no explicit definition of narrowband signal for array signal. The 3 expressions listed below show some of the characteristics of narrowband array signal which is widely accepted [ if the bandwidth of a signal is such that the second eigenvalue of the signal’s noise free covariance matrix is larger than the noise level in the signal plus noise covariance matrix, then that signal may not be described as narrowband [
The first expression is the basic understanding of narrowband signal. The second expression describes the narrowband signal for array signal. The third definition is more complicated. The definition of narrowband signal is a function of bandwidth, AOA, SNR, array gain, and dimension of the array.
The conclusion drawn from the 3 definitions is consistent with Section
Comparison with other methods is performed in this part. And the error of DOA caused by frequency error with aperture
Comparing our method with TCT(CSM) [
Considering one source impinges on the array from 108.5 degrees. The aperture of the uniform circular array is 1/3 and 1/6 of the wavelengths of the center frequency. The bandwidth of the signal is 20% of the center frequency. RMSE is defined as
RMSE of the DOA estimation versus SNR for the different methods. The aperture of the uniform circular array is (a) half and (b) 1/5 of the wavelengths of the center frequency.
The computational complexity is compared in Table
Time elapses for different methods.
TCT | RSS | SSA | TDE | Ours |
---|---|---|---|---|
0.0724 s | 0.0614 s | 0.1020 s | 0.0022 s | 0.0074 s |
As shown in Table
The performance of method is not worse than ISM and CSM under small aperture. However, the computational complexity is much lower than ISM and CSM.
As is discussed in Section
The simulation signal is a wideband signal with bandwidth ranging from 200 to 1000 Hz. The real DOA is 108.5 degrees. The array is a uniform circular array. Table
Array aperture and error frequency boundary.
Array aperture (m) | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 | 0.11 | 0.12 | 0.13 |
|
||||||||||||
Error frequency boundary (Hz) | >2000 | >2000 | >2000 | >2000 | 1584 | 1284 | 1058 | 884 | 764 | 634 | 542 | 464 |
As is shown in Table
Simulation of DOA error versus signal frequency and frequency error.
We conclude in Section
Simulation of DOA error versus signal frequency and frequency error.
RMSE versus signal frequency at different SNR.
As presented in Section
(a) Signal power spectra of
As shown in Figure
Our method is based on the fact that small array aperture could decrease the manifold error caused by the frequency error. However, some negative influences of small aperture should be mentioned.
In a real microphone array system, the difference of the amplifying circuit cannot be avoided and will cause amplitude error and phase difference for different array elements, which will affect the array manifold.
Based on the Nyquist-Shannon sampling theorem, then
The DOA errors in Figure
DOA errors under different array apertures.
In other words, in order to achieve high accuracy, the small aperture array should be highly consistent in the amplifying circuit.
Another question caused by high space sampling rate (small array aperture) is the resolution, as for multiple signals, it is more difficult to separate closely spaced signals. When the array size is not limited,
Figure
(a) The MUSIC spectra for two signals of different aperture. (b) The MUSIC spectra for one signal of different aperture.
Even though the resolution of small aperture is lower than that of large aperture, our method is still able to distinguish multiple signals. It works well for single signal.
Several experiments are carried out by real microphone array in this section. MEMS microphone is chosen as the sensor to ensure the array aperture is small enough. The package dimensions of MEMS microphone below are 3.35 × 2.5 × 0.88 mm.
After the array for localization was properly designed, six arrays were proposed to validate the algorithm with different shapes. Table
Six arrays for validation of the algorithm.
Number | Array | Number of array elements | Aperture (m) |
---|---|---|---|
1 | Uniform circular | 4 | 0.04 |
2 | Uniform circular | 4 | 0.02 |
3 | Uniform circular | 4 | 0.005 |
4 | Equilateral triangle | 3 | 0.04 |
5 | Equilateral triangle | 3 | 0.02 |
6 | Equilateral triangle | 3 | 0.005 |
MEMS arrays in Table
A turntable was designed to test the changes of DOA. It was driven by a stepping motor controlled by a microcontroller with a constant rotating speed of 25.71 degrees/s. The acoustic source is a famous Chinese folk song Jasmine (Molihua) played by piano. The sampling rate of the array system is 8192 Hz, the band is limited to 200–2000 Hz, and
As shown in Figure
Results of linear fit of DOA for the arrays in Table
Number 1 | Number 2 | Number 3 | Number 4 | Number 5 | Number 6 | |
---|---|---|---|---|---|---|
Intercept (degree) | 1.17304 | 2.55845 | 5.44434 | 3.41981 | 7.40605 | N/A1 |
Slope (degree/s) | 26.05438 | 25.21226 | 24.65839 | 26.92926 | 26.29049 | N/A |
Relevant coefficient | 0.99979 | 0.99935 | 0.99786 | 0.99924 | 0.99571 | N/A |
Standard deviation (degree) | 2.106 | 3.74889 | 6.64365 | 4.13669 | 9.87195 | N/A |
(a) The song Jasmine in frequency domain. (b) DOA estimated from array number 1.
In comparison of arrays number 1, number 4 and number 2, number 5, a larger number of sensors result in better estimated DOA, because the former acquires more information. However, array number 6 could not be localized, because in order to minimize the aperture of an equilateral triangle, the sound hole was arranged as an equilateral triangle, but the MEMS microphone array was not equilateral. For the position of the MEMS microphone that sense sound may not be the exact sound inlet, the shape of the array is not equilateral, which leads to the indeterminacy of the array manifold and the invalidity of the estimated DOA. Nevertheless, the result of number 3 shows that our method could work at very small aperture as 5 mm.
An application of the proposed method to locate moving vehicles using a 0.04 m microphone array (array number 1) will be elaborated in this part. The experiment was conducted on a cement road after a light rain with wind levels from 0 to 2 during November 2012, on an island in Zhejiang Province, China.
Scheme of the localization experiment.
Four typical types of vehicles are used for localization: an electric bicycle, a tricycle, a car, and a truck. Their signals are shown on (A) in Figure
Acoustic signals (A), spectrum amplitudes (B), and fits of DOA (C) of (a) electric bicycle, (b) tricycle, (c) car, and (d) truck.
Considering the width of the road, as the driver drives on the right side,
Results of fit of DOA.
|
|
|
|
Deviation of DOA (degree) | Relevant coefficient | |
---|---|---|---|---|---|---|
E-bicycle1 | 89.28 | 10.23 | 13.36 | 3 | 5.82 | 0.99247 |
Tricycle | 90.43 | 10.55 | 14.98 | 3 | 5.56 | 0.99598 |
Car | 90.78 | 22.10 | 8.70 | 5 | 2.76 | 0.99958 |
Truck | 91.71 | 13.50 | 16.52 | 5 | 3.61 | 0.99812 |
According to our initial parameter analysis in Section
In the application scenarios considered in this part, the proposed method has been applied to more than 200 experiments for over 20 types of vehicles. The maximum estimation error of DOA is no bigger than 6°. According to the results in this section and computational complexity comparing with other methods in Section
In this paper, an acoustic source localization method using small aperture array was proposed. The method could be used in real time processing systems such as vehicle localization and videoconference due to low computation complexity. As the proposed algorithm is featured by small aperture, array response obeys a plane wave propagation model and the consistency of the amplifying circuit is very important, which is often ignored for the discussion of ordinary arrays. The accuracy of DOA estimation could be improved by taking advantage of the source’s relatively higher band and confining the signal to a certain band. Simulations and experiment show that the proposed method can effectively localize different acoustic sources and has a lower computation complexity compared with the existing methods.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to thank the associate editor and anonymous reviewers for their valuable comments and suggestions to improve this paper. This work has been supported by fund 9140C18020211ZK34.