2023 13th International Conference on Indoor Positioning and Indoor Navigation (IPIN)
Indoor 3D Positioning Method for a Microphone
using a Single Speaker
2023 13th International Conference on Indoor Positioning and Indoor Navigation (IPIN) | 979-8-3503-2011-4/23/$31.00 ©2023 IEEE | DOI: 10.1109/IPIN57070.2023.10332519
Masanari Nakamura
Yuta Funada
Hokkaido University
Sapporo, Japan
{masanari, funa}@ist.hokudai.ac.jp
Hiroaki Murakami
The University of Tokyo
Tokyo, Japan
murakami@akg.t.u-tokyo.ac.jp
Abstract—This study investigates an indoor 3D positioning
method for a microphone using a single speaker. The proposed
method estimates the distance, azimuth, and elevation of the
microphone from the speaker and calculates the 3D position of
the microphone. Multiple short signals with different frequency
bands were transmitted sequentially at sufficient intervals to
avoid the influence of indoor reflected waves. We extracted these
signals at the receiver side, and their amplitude spectra were
computed. The azimuth and elevation of the microphone were
estimated by matching the obtained amplitude spectrum with
the reference data previously measured at each azimuth and elevation. The distance was estimated from amplitude attenuation.
The 3D positioning performance was evaluated at ten points in a
practical environment. The results show that the 90-th percentile
value of the error was 0.583 m.
Index Terms—Indoor 3D positioning, acoustic localization,
frequency characteristics, and RSSI
I. I NTRODUCTION
Indoor positioning methods have been widely studied as
sensing methods for mobile devices [1]. Among these methods, positioning techniques using acoustic signals have received considerable attention. An advantage of the acoustic
positioning method is that a positioning system can be constructed using commercial off-the-shelf speakers and microphones.
In conventional methods, the 3D positioning of a single
microphone requires multiple speakers. The positions of the
speakers were also required. Therefore, the installation of
multiple speakers costs considerable time and effort.
Nakamura et al. [2] previously proposed a method for
estimating the 2D position of a single microphone using a
single speaker. Based on the concept of this method, we
propose a 3D positioning method for a single microphone
using a single speaker in this paper. This is the first 3D
positioning method for a single microphone using a single
speaker.
The contributions of this study are summarized below.
• We proposed a 3D positioning method for a single
microphone with a single speaker. We devised a novel
method that transmits short signals of different frequency
bands sequentially with sufficient intervals to avoid the
influence of indoor reflected waves.
• To confirm the effectiveness of the proposed method,
3D positioning experiments were conducted in a real
Hiromichi Hashizume Masanori Sugimoto
NIAD-QE
Tokyo, Japan
hasizume@niad.ac.jp
Hokkaido University
Sapporo, Japan
sugi@ist.hokudai.ac.jp
environment. A comprehensive survey of the relationship
between the positioning performance and combinations of
frequency bands is conducted. Performance comparison
for combinations of frequency bands shows that the best
performance is obtained when the bandwidth is set to
3 kHz. Here, 90 % of the measurement errors were below
0.583 m.
The remainder of this paper is structured as follows. Section
2 describes related research focusing on positioning methods
that use acoustic signals. Section 3 describes the proposed
method in detail. Section 4 evaluates the performance of
the proposed method using real-environment experiments. We
comprehensively studied the relationship between the combinations of frequency bands and positioning performance.
Section 5 discusses the experimental results in section 4, and
section 6 concludes the study.
II. R ELATED WORK
For positioning using acoustic signals, if time synchronization between the speaker and microphone is established,
the propagation time can be determined, and the distance
can be estimated by multiplying the propagation time by
the speed of sound. Likewise, the microphone’s position can
be estimated using the distance between multiple speakers
and the microphone. However, the built-in microphone of
a mobile device cannot synchronize the time with speakers
with sufficient precision. Therefore, it is difficult to estimate
the position of a built-in microphone in a mobile device by
measuring the propagation time of multiple speakers.
Without time synchronization, differences in propagation
times between multiple speakers and microphones can be
measured, and the microphone position can have calculated
using these differences. This method is called TDoA (time
difference of arrival). Various methods have been widely
studied [3]–[13].
In acoustic positioning, the position can also be estimated
without differences in the propagation times. In the method
of Zexing et al. [14], the fingerprints of multiple speakers
were previously measured at multiple locations. The positions
are then estimated by matching the observed signal with the
fingerprints.
The distance between the speaker and microphone can be
estimated using only the amplitude of the received signal.
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2023 13th International Conference on Indoor Positioning and Indoor Navigation (IPIN)
Richards et al. [15] proposed a method for 3D positioning
based on this method using multiple speakers.
In these methods, multiple speakers are required. Here, the
installation cost was proportional to the number of speakers.
To reduce the installation cost, positioning methods were
proposed with a single speaker [2], [16]–[18]. Murakami
et al. [16] proposed a 3D positioning method using stereo
microphones of a smartphone, a single speaker, and a floor
map. Zhang et al. [17] proposed a 2D positioning method
using a neural network. The microphone region was estimated
using the distance and amplitudes of several frequencies.
This distance was estimated by the given initial position, and
the change in distance due to microphone movement was
measured. Cheng et al. [18] estimated the 2D position of a microphone using a simple model that represents the relationship
between distance, azimuth, frequency, and amplitude. This
model is left-right symmetrical from the speaker’s perspective.
Therefore, determining whether the microphone was on the
right or left side of the speaker was impossible.
Nakamura et al. [2] have previously proposed a 2D positioning method for a single microphone with a single speaker.
The azimuth is estimated by comparing the amplitude spectra
with the reference data, which was previously constructed
using measurements at multiple azimuths. The distance was
estimated using the received amplitude. The 2D position was
calculated using the azimuths and distances. This method
is characterized by not requiring information, such as floor
maps, the initial position of the microphone, or the second
microphone, which are required by conventional methods.
It also identifies the left or right side from the speaker’s
perspective.
The above method [2] uses a chirp signal swept from 6 to
24 kHz in 1 s. In an indoor environment, the reverberation
time was approximately 100 ms. Therefore, the results of the
above method may include the speaker’s characteristics and
the influence of reflected signals caused by indoor objects. In
addition, because it uses continuous wideband chirp signals,
the effective frequency bands for positioning are unclear.
A 3D positioning method for a microphone using a single
speaker is proposed in this paper based on the concept of the
method discussed above [2]. The proposed method contains
a new signal transmission and reception method to avoid
reflected waves, which was an issue with the previous method.
This study also examined the effectiveness of combinations of
frequency bands.
III. P ROPOSED METHOD
This section proposes a 3D positioning method that uses
the difference in amplitude spectra at each azimuth and
elevation. Section III-A describes the transmission and reception methods used to avoid the influence of reflected waves.
Section III-B explains the construction of reference data for
3D positioning. In section III-C, we describe the positioning
method using the reference data.
Fig. 1: Overview of the proposed method. (a) Transmission
of multiple chirp signals with different frequency bands. (b)
Examples of amplitude spectra. (c) Relationship between xyz
and rθϕ coordinates.
A. Transmission and reception method
In the proposed method, chirp signals with different frequency bands are sequentially transmitted from the speaker.
m (m = 1, 2, . . . , M )-th chirp signal is expressed as follows:
(
t2
0≤t<T
sin 2π fm t + ∆f
2T
, (1)
sm (t) =
0
otherwise
where fm = f1 +(m−1)∆f . T is the signal length. Hereafter,
the signal with a sweep start frequency of fm kHz is referred
to as the fm kHz signal. Figure 1a presents an overview of
this transmission scheme.
As shown in [2], a transmitted signal varies with the
frequency response depending on the radiation direction of
the speaker. Ignoring noise and multipath, the received signal
r(t) can be expressed as follows:
r(t) =
M
X
(Θm ∗ sm )(t − (∆t + (m − 1)(T + Td )),
(2)
m=1
where Θm (t) is the impulse response of the speaker’s radiation
characteristics at the azimuth θ and elevation ϕ. ∗ denotes
convolution. ∆t denotes the propagation delay. Let rn be a
sampled discrete series of r(t). In the following, we assume
that T and Td are integer multiples of sampling period Ts . Let
N and Nd be the numbers of samples corresponding to T and
Td , respectively.
Next, part of the received signal rn corresponding to the
m-th signal is extracted. The positive frequency component
of the m-th signal is expressed as
em
emn
= (em0 , em1 , . . . , em(N −1) ),
∆f
2
= exp j2π fm nTs +
(nTs )
.
2T
(3)
(4)
Let e0 be (e1 , 0, e2 , 0, . . . , eM ) where 0 denotes a zero vector
of length Nd . The convolution of e0 and rn is represented as
follows:
N
−1
X
cn =
rn+q eq ,
(5)
q=0
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2023 13th International Conference on Indoor Positioning and Indoor Navigation (IPIN)
where eq denotes the q-th element of e0 . This process is known
as matched filtering [19]. The initial time of signal sequence
s1 (t), s2 (t), . . . , sm (t) can be estimated as follows:
p0 = arg max |cn |.
(6)
n
Each part of the received signal around the m-th signal is
extracted using p0 as follows:
rm
=
(rp0 +(m−1)(N +Nd )−Nc , rp0 +(m−1)(N +Nd )−Nc +1 ,
. . . , rp0 +mN +(m−1)Nd +Nc ).
(7)
To cut out the m-th signal accurately, the index pm corresponding to the received time of m-th signal is calculated using the
matched filter as follows:
pm = arg max |cmn |,
(8)
n
cmn =
N
−1
X
rm(n+q) emq ,
(9)
q=0
′
where rmb is the b-th element of rm . Let rm
be the signal
extracted from the received series rmn corresponding to the
m-th signal of length N
′
rm
= [rm(pm ) , rm(pm +1) , . . . , rm(pm +N −1) ].
(10)
The amplitude at each frequency is expressed as follows:
u(m,i)
=
N
X
′
rmq
exp(−j2πiF (q − 1)Ts ) ,
(11)
To improve the estimation performance of the azimuth and
elevation, the amplitude spectrum at the unmeasured azimuth
and elevation are generated by interpolation. We use Akima’s
method [20] for this interpolation. In the following, let u(e,d)
be the amplitude spectrum at azimuth θe (e = 1, 2, . . . , E)
and elevation ϕd (d = 1, 2, . . . , D).
2) Reference data for distance estimation: Let R be the
distance between the speaker and microphone. The received
amplitude a approximately follows the model shown below
Rref
.
(13)
a = aref
R
This formula indicates that if the reference amplitude aref at
the reference distance Rref is known, then the distance R can
be estimated from the observed received amplitude a.
From the results of a previous study [2], the value of the
received amplitude varies in each direction. Therefore, the
amplitudes are measured at multiple azimuths and elevations.
During the measurements, the reference distance was kept
constant. Furthermore, interpolation of the reference amplitude
was performed as described in the previous section. Let a(e,d)
be the reference amplitude value at azimuth θe and elevation
ϕd .
The maximum value of the matched filter output is used as
the reference amplitude. Unlike the conventional method [2],
the proposed method sequentially transmits multiple frequency
band signals; therefore, we must decide which matched filter
output of the frequency band to use. This is discussed in
section IV-B.
q=1
′
′
and F = 1/T . i is an
where rmb
is the b-th element of rm
index ranging from 1 to N .
For each signal, we use only u(m,i) ranging from fm to
fm+1 . Let αm and βm be indices representing this range. We
denote the sequence of u(m,i) by u as follows:
u =(u(1,α1 ) , u(1,α1 +1) , . . . , u(1,β1 ) , u(2,α2 ) , u(2,α2 +1) ,
. . . , u(2,β2 ) , . . . , u(M,βM ) ).
(12)
Hereafter, we refer to u as the amplitude spectrum. u contains
the radiation characteristics of the speaker and is used to
estimate azimuth and elevation. Examples of amplitude spectra
are presented in Figure 1b.
In the indoor measurements, the reflected waves were
superimposed on the direct wave. The main sources of the
reflected signals were ceilings, floors, and walls. These signals
arrived at the microphone with a greater delay than the direct
wave. Therefore, if the signal length is sufficiently short, the
influence of reflected signals can be avoided.
B. Construction of a reference data
1) Reference data for azimuth and elevation estimation:
We describe the construction of the reference data for azimuth
and elevation estimations. First, the amplitude spectrum was
calculated from the measurement at each azimuth and elevation. Then, normalization u/ max(u) was applied to eliminate
the influence of the sound level depending on the distance.
C. Positioning
First, azimuth and elevation were estimated. The observation
vector uobs was obtained by estimating and normalizing the
amplitude spectrum u using the same procedure as in section
III-B
uobs = u/ max(u).
(14)
We calculate the differences between the observed vector and
all vectors in the reference data for azimuth and elevation
estimation and find pe and pd as follows:
(pe , pd ) = arg min
i,j
Nu
X
(i,j)
|uobs
|.
n − un
(15)
n=1
(i,j)
uobs
and un are n-th element of uobs and u(i,j) , respecn
tively. Nu denotes the length of u. The estimated azimuth and
elevation values were determined as θ̂ = θpe and ϕ̂ = ϕpd .
Next, we explain the estimation of the distance. Let â be the
estimated amplitude using a matched filter, and let the distance
R̂ be calculated using Equation (13) as follows:
R̂ = Rref a(pe ,pd ) /â.
(16)
The 3D position (x̂, ŷ, ẑ) was transformed from the estimated
distance, azimuth, and elevation
x̂
=
R̂ cos ϕ̂ sin θ̂,
(17)
ŷ
=
R̂ cos ϕ̂ cos θ̂,
(18)
ẑ
=
R̂ sin ϕ̂.
(19)
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2023 13th International Conference on Indoor Positioning and Indoor Navigation (IPIN)
Fig. 2: Experimental setup for the real environment. (a)
Measurement system. (b) Experimental environment.
Fig. 3: Measurement positions (▲: measurement point for
reference data construction, ⃝: measurement point for evaluation, □: speaker).
Figure 1c indicates the relationship between xyz and rθϕ
coordinates.
IV. E VALUATION EXPERIMENTS OF POSITIONING
PERFORMANCE
Positioning experiments were conducted in a real environment to evaluate the positioning performance of the proposed
method. Additionally, we evaluated the performance of each
combination of frequency bands.
Fig. 4: Speaker location in the experimental environment
set from 0 to 50 degrees in 10-degree increments. Thus, the
number of measurement points is 9 × 6 = 54. Interpolation in
azimuth and elevation was performed in 1-degree increments.
Hence, the number of azimuths E and elevations D after
interpolation were 81 and 51, respectively.
We conducted measurements to evaluate the positioning
performance at the ten points. The positions of the microphone
in the xyz coordinates are shown in Figure 3b. Ten positions
were selected within the measurement range of the reference
data. In addition, these positions were different from the 54
measurement points that constructed the reference data.
The locations of the speaker and walls are shown in Figure
4. The speaker position was set to (0.0, 0.0, 1.0) m. The height
of the ceiling is 2.5 m.
We calculated the difference between the received times
of the direct wave and reflected waves of the ceiling, floor,
and wall at each measurement point. The smallest value was
approximately 3.63 ms. To avoid the overlapping of direct and
reflected waves, the signal length was set to 3 ms. Thus, N
in Equation (10) is 48000 × 0.003 = 144. Nc was set to 48.
This value corresponded to 1 ms. Nd was set to 4800. This
experiment sets the number of signals M to nine. f1 and ∆f
were set to 4 kHz and 1 kHz, respectively.
B. Preliminary experiment
A. Experimental settting
1) Measurement system: The configuration of the measurement system is illustrated in Figure 2a. In the transmission system, the NF circuit design block WF1948 and Fostex AP20d
were used as the signal generator and amplifier, respectively.
The speaker was a ToA BS-320. The speaker has a diameter
of 12 cm. A booster transformer was inserted between the
amplifier and the speaker. In the reception system, Rion
UC-31, NH-05A, and UN-14 were used as the microphone,
preamplifier, and amplifier, respectively. In addition, we used
ROLAND UA-4FX2 as the audio interface. The sampling
frequency was set at 48 kHz. Measurements were conducted
in a sufficiently silent environment. The actual measurement
environment is illustrated in Figure 2b.
2) Measurement positions and transmission signals: The
measurement points for reference data construction are shown
in Figure 3a. At these measurement positions, the distance
from the speaker is set to 1.0 m. The azimuth directions from
the speaker were set from −40 to 40 degrees in 10-degree
increments. The directions of elevation from the speaker were
As mentioned in section III-B2, distance estimation was
performed using the azimuth and elevation estimation results.
Therefore, errors in the azimuth and elevation estimations can
propagate to the distance estimation. Therefore, the rate of
change at each point in the reference amplitude data must be
low.
Generally, the directivity of an acoustic signal is weaker
at lower frequencies. Therefore, the reference amplitude data
of the lower-frequency signal are preferable for distance
estimation. Figures 5a and 5b show the reference amplitude
data interpolated from the measured values of the 4 kHz and
12 kHz signals, respectively. These figures also indicate that
the 4 kHz signal should be used.
C. Performance evaluation
During the measurement, the nine signals shown in Figure 1
were transmitted 100 times at each position. We can estimate
the azimuth and elevation using only a subset of nine signals.
Therefore, we evaluated the positioning performance of each
subset. As shown in Figure 1a, each signal had a different
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2023 13th International Conference on Indoor Positioning and Indoor Navigation (IPIN)
(a) 4 kHz signal
(b) 12 kHz signal
Fig. 5: Amplitude distribution of 4 and 12 kHz signals
frequency band. Therefore, the results of this evaluation show
the relationship between combinations of frequency bands and
positioning performance.
Nine different results can be obtained for each signal when
only one signal out of the nine is used. The results are shown
in Figure 6a. Similarly, Figures 6b, 7a, 7b, 8a, and 8b show
the results when the number of signals was increased. These
figures show the cumulative distribution functions (CDFs) of
the 3D positioning errors of all 10 locations for each signal
combination. The range of the x-axis in these figures was set
from 0 m to 2 m for ease of comparison.
Figure 6a shows that the 90-th percentile error is greater
than 1 m for any signal. From Figures 6b, 7a, and 7b which
show positioning using two, three, or four signals, there are
four combinations of signals that have a maximum error of
less than 1 m. There combinations are the {6,7}, {5,6,7},
{6,7,8}, and {4,5,6,7} kHz signals. The maximum error was
smallest for the {6,7,8} kHz signals. In this case, the 90-th
percentile error was 0.583 m. The positioning results of this
case in the xy and xz coordinates are shown in Figures 9a
and 9b, respectively. In Figure 9a, true positions of #2 and #3
are superimposed. In Figure 9b, true positions of #8 and #9
overlap.
In Figures 6a, 6b, 7a, 7b, 8a, and 8b by focusing on
the 50-th percentile values, we can see that the differences
between the combinations become smaller as the number of
signals increases. This means that, as the number of signals
increases, the impact of the signal selection on the positioning
performance decreases.
Figure 10a showed the results at each position when all
nine signals were used. The results at each position using
the {6,7,8} kHz signals, where the maximum error was the
minimum, are shown in Figure 10b. Figure 10a shows a large
error at #9. However, this error did not occur in Figure 10b.
This difference is discussed in section V-A.
V. D ISCUSSION
A. Outlier at #9
We discuss the outlier at #9 in Figure 10a. Figures 11a
and 11b show the residuals for each azimuth and elevation
when positioning at #9 using all nine and {6,7,8} kHz signals,
respectively. These figures show the summation values of
Equation (15). ◦ and ⋄ denote the true and estimated indices,
(a) With 1 signal
(b) With 2 signals
Fig. 6: Positioning performance with 1 and 2 signals
(a) With 3 signals
(b) With 4 signals
Fig. 7: Positioning performance with 3 and 4 signals
respectively. Areas with residuals larger than the residuals of
the true indices are indicated in white.
In Figure 11b, the estimated indices are close to the true
indices. However, in Figure 11a, although local minima are
found near the true indices, the estimated indices are far from
the true indices. This difference might be caused by significant
interpolation errors of signals other than 6, 7, and 8 kHz at #9.
This interpolation error could be caused by the interpolation
method used in this study or by insufficient measurement
points to construct the reference data. A detailed study of this
point will be conducted in future work.
B. Limitations
1) Audibility: This study used the frequency bands where
the speaker output was large to investigate the feasibility of 3D
positioning. These signals are audible and annoying to human
beings. In addition, sounds in this band are often generated
in real-world environment. Thus, position performance can be
degraded.
Using inaudible signals above 15 kHz is one solution to
these problems. However, the output in these bands may be
small for certain types of speakers. This issue will be discussed
in future studies.
2) Dependency on devices: Although the proposed method
assumes that the amplitude spectra for each azimuth and
elevation are different from each other, it is still unclear
what kind of speakers and microphones are sufficient for
this assumption. We would like to clarify this point through
theoretical investigations based on acoustics and analysis of a
large amount of measurement data in future work.
3) 3D positioning for moving microphone: In the evaluation
experiments, the 3D positioning performance was evaluated
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2023 13th International Conference on Indoor Positioning and Indoor Navigation (IPIN)
(a) With 5 signals
(b) With 6, 7, 8, and 9 signals
Fig. 8: Positioning performance with 5, 6, 7, 8, and 9 signals
(a) All signals
Fig. 10: Positioning performance at each measurement points
using all and {6, 7, 8} kHz signals
(a) All signals
Fig. 9: The true and estimated positions (⃝: true position, ◦:
estimated position). (a) xy coordinates. (b) xz coordinate.
under stationary conditions. For practical applications, a microphone can move. Here, the Doppler effect changes the
amplitude spectrum and the matched filter output. Therefore,
an adaptive correction process might be required.
VI. C ONCLUSION
This paper proposes a 3D positioning method for a single
microphone using a single speaker. We conducted a positioning experiment at 10 points in a real environment and studied
the relationship between the combinations of frequency bands
and the positioning performance. The results show that 90 %
of the errors are below 0.583 m when {6, 7, 8} kHz signals
were used.
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ACKNOWLEDGMENT
This work was supported by JSPS KAKENHI Grant Numbers 20K23313 and 21K17797.
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