In this paper, we propose an acoustic indoor localization method for an embedded microphone of a smartphone using multiple stereo speakers installed indoors. In this configuration, although stereo speakers are synchronized, speakers not producing stereo sound are not synchronized. Therefore, a moving microphone could receive acoustic signals required for localization at different locations. This causes bias error in the conventional method. To address this issue, we propose a method that utilizes an asynchronous tracking filter and compensates the differences in locations of received signals using motion modelling. Through experiments, we verify that our proposed method can effectively reduce the bias error.
These days, mobile devices like smartphones are highly popular, and localization
using such devices are gaining attention [
Acoustic signals are suitable for accurate indoor localization using smartphones.
In a related work [
In these methods, highly precise time synchronization of all the speakers is required. Certain audio players that can synchronize several speakers are available. However, they are more expensive than commercial off the shelf (COTS) stereo speakers, which have only two channels owing to their limited application.
Therefore, we utilize COTS stereo speakers in this study. These speakers can produce two acoustic signals simultaneously from two sides. The receiver obtains the elliptical hyperboloid from the TDoA of the speaker signals. Using the TDoAs of multiple stereo speakers, the receiver’s location can be calculated. However, when the microphone is moving, TDoA can be observed at different locations, thereby rendering the intersection of elliptical hyperboloid to drift away from the true location. This is because speakers not producing stereo sound cannot produce signals simultaneously.
We herein propose an asynchronous tracking filter to compensate the difference of observation locations, and therefore reduce the bias error.
The rest of this paper is organized as follows. Chapter 2 describes the conventional method and its problem. Chapter 3 presents the proposed method for dealing with the above-mentioned problem of bias error. In Chapter 4, simulation experiments were conducted to evaluate the proposed method. Chapter 5 concludes this paper. 2
In indoor environments, some localization methods using acoustic signals utilize
the embedded speakers of smartphones and microphones installed at indoor
environment [
Acoustic indoor localization methods are of two types: ranging-based and
TDoAbased. The former utilizes range measurements between speakers and microphones.
The latter utilizes the difference in signal received times. Ranging-based localization
is typically more precise than TDoA-based localization. However, it requires high
accurate time synchronization (e.g., μ order) between speakers and microphones and
is therefore used for systems employing designated devices [
The relationship between the location and received time is represented as 1 − ( 1) − 1 − ( 1) − 2 − ( 2) = ⋅ ( 1 − 2) 3 − ( 3) = ⋅ ( 1 − 3) (1) where the term = ( , ) denotes the position vector of speaker , and ( ) denotes the position vector of microphone at time . ( = 1,2,3) denotes the received time of signal produced by speaker ,c is the sound speed, and (⋅) is the Euclidean distance. Equations in (1) represent hyperbolic curves of the microphone’s position ( ).
When the smartphone is stationary, the positions, ( 1), ( 2), ( 3) are the same and location can be calculated by solving equation (1). When the smartphone is moving, ( 1), ( 2), ( 3)are not the same. However, the differences are insignificant as bias error. is all the speakers are synchronized. Therefore, location can be obtained without large
To simultaneously produce signals from all speakers, a special device such as a multi-channel audio player is required. As such devices are expensive, we instead use a multiple COTS stereo speaker, which hereinafter is referred to as a unit.
In this configuration, although speakers from a same unit are synchronized, those from different units are not. The relationship between the location and received time ( 1 − ( 1)) − ( 2 − ( 2)) −
(( 21 −− (( 21)))) == ⋅⋅ (( 12 −− 12)).
where spectively; ， ，
are locations of speakers R and L, belonging to unit ( = 1,2), re are received times of signals produced by R and L, respectively.
When the smartphone is stationary, microphone positions, ( 1), ( 1), ( 2), and ( 2) are same, and the location can be easily estimated without bias error. When the smartphone is moving, equations ( 1) ≈ ( 1) and ( 2) ≈ ( 2) are satisfied owing to speaker synchronization. However, the differences between ( 1) and ( 2) can increase if the smartphone starts moving. In this case, the intersection of the hyperbolic curve is drifted away from the true position (refer Figure 1-(a)), and location estimated by solving (2) incurs bias error. (2) collide with each other at the microphone, thereby resulting in large errors. Therefore, the transmission time of each unit should be controlled using general communication systems such as Wi-Fi and Bluetooth.
Speaker time lags in conventional methods produce bias errors, therefore
necessitating a multiple-channel audio player to synchronize all speakers [
The smartphone’s current position is estimated using an asynchronous tracking filter when a TDoA is measured. The estimation is done by calculating the intersection between the predicted position and hyperbolic curve of TDoA, as shown in Figure 1(b), and it reduces the bias error as shown in Figure 1-(a), the details of which are described in the next section. 3.2
Asynchronous tracking filter.
state and position is represented as The state vector, comprises position and velocity [ ̇ ̇ ] where , are positions, ̇, ̇ are velocities, and is the transpose. The relationship between the 0 1 the TDoA observation time. denotes as the observation time of -th TDoA. TDoA measurement, comprising and . We herein define the lesser of or t as The TDoA measurement, received at , corresponding to unit is represented as = + − + = ℎ ( ) + − where , are the measured noises of received times produced by R and L of
equation (2), ℎ ( ) represents the unit , respectively. is the state vector [ ̇ ̇ ] at time . From ℎ ( ) = ( − ) − ( − ) distribution has the reproductive property.
The observation noises , are white Gaussian noise with zero-mean and
known variance
2 , 2 , respectively. The measurement error of TDoA is
− . Notably, we assume that nd are independent. In this case, is white Gaussian noise with zero-mean and variance 2 + 2 because Gaussian As the motion model of the microphone, we utilize the constant velocity model. = 1 0 0 1 −1 + = ( ) −1 + (6) (3) (4) (5) where is the process noise vector Δ is the difference of the observation times − −1 . the motion. and are white Gaussian noise with zero-mean and variance 2 .
which represents ambiguity of Algorithm state = measurement is inputted to the asynchronous tracking filter ( = 1), particles representing the microphone state are generated ( = 1, … , ). Each element of the is generated by uniform random numbers. The ated ( ≥ ticle. weight is updated. weight k of the state is given as k = 1/ . When and k were already gener 2), the prediction based on the motion model (6) is conducted for each parIn the updating step, the likelihood of each particle is calculated using and the (7) =
1 √2 2 exp −
− ℎ ( ) 2 2
2 The estimated state is obtained by the weighted sum ∑=1 ⋅ .
When the next measurement is inputted, the above-mentioned process is repeated
with the resampled particles [
We conducted following simulation experiments for the evaluation of our proposed method. Figure 2 shows the microphone route and the four speaker locations. The microphone moves at a speed of 1 m/sec and receives its first TDoA measurement at the route’s starting position (-3.0, 1.5). nal length and the reverberation time of multipath. Regarding the signal length, a
̇
short one with large amplitude is preferable for the precision and the updating rate of
localization. However, the amplitude is generally restricted due to speaker’s
inaudibility. To obtain the desired signal-to-noise ratio (SNR) with the restricted amplitude, a
longer signal can be utilized. A reverberation time of 100 ms is sufficient to attenuate
the multipath [
The observation noise of the received time depends on the bandwidth and SNR.
The bandwidth and SNR herein are set to 1 kHz and 30 dB, respectively. These
parameters were determined in consideration of the characteristic of microphones
emHence, the observation noise of TDoA is 2 × 1.58 × 10−5 = 3.16 × 10−5 sec.
bedded in smartphones [
The conventional method numerically solves equation (2) using the current and
previous measurements. The observation noise, process noise, and number of particles
ly. The range of uniform random numbers to generate these particles
of the proposed method were set to 3.16 × 10−5 sec, 0.5 m/sec, and 5000,
respectiveat = 1 were [
Root mean square error (RMSE) was used for evaluating each trial with the number of trials set to 100. The starting position = 1 was excluded from this evaluation 4.2
intersections of hyperbolic curves, far from true positions, which represent the bias errors. Figure 4-(b) indicates that the proposed method can reduce these errors using the asynchronous tracking filter.
In Figures 3-(a) and 3-(b), RMSE of the proposed method was minimum around = 0 m, turning slightly worse in > 0 m. For clarification, predicted particles at = 0 m and 2.5 m were plotted in Figures 5-(a) and 5-(b). The transmission interval was set to 300 ms. In these figures, the particles are scattered in an ellipse, and the major axis was roughly parallel to the previously plotted hyperbolic curve. This is because these particles were generated by extrapolating the resampled particles based on the previously obtained hyperbolic curve.
When the microphone’s position was = 0 m (Figure 5-(a)), current hyperbolic curve crossed the major axis of the ellipse nearly at right angles. In this case, the area of resampled particles was narrow, leading to high precision. When the microphone’s position was = 2.5 m (Figure 5-(b)), the minor axis of the ellipse crossed the current hyperbolic curve at roughly right angles, and the area of resampled particles was relatively broad, leading to reduction in precision.
In this paper, we described an acoustic indoor localization system with multiple COTS stereo speakers. We proposed the asynchronous tracking filter to reduce the bias error caused by the asynchrony of speakers that do not produce stereo sound when the smartphone is moving. The simulation experiments showed that the proposed method can effectively reduce the bias error.