Proceedings of 2022 APSIPA Annual Summit and Conference

7-10 November 2022, Chiang Mai, Thailand

Heart Rate Estimation of Car Driver Using
Radar Sensors and Blind Source Separation
Keito Murata∗ , Daichi Kitamura∗ , Ryo Saito† , and Daichi Ueki†∗ National Institute of Technology, Kagawa College, Kagawa, Japan† Murata Manufacturing Co., Ltd., Kyoto, Japan

Abstract—Monitoring a driver’s health condition is essential
for advanced driver assistance systems. To detect the driver’s
health condition, we propose a new system using a contactlessbiometric radar sensor to monitor the driver’s heart rate. The
radar sensor measures a microdisplacement of the driver’s bodysurface, and heartbeat signals can be obtained. However, theobserved signals are contaminated by noise signals such as body
movement and car vibration. The proposed system utilizes blindsource separation algorithms and extracts the driver’s heartbeat
signal from the noisy observation. Furthermore, the estimatedheartbeat signal is input to a heart rate estimation algorithm. In
experiments, we built a vibration measurement system to simulatea moving car, and an actual noisy heartbeat signal from a subject
sitting on a driver’s seat was measured. The results show thatthe proposed system can accurately estimate the subject’s heart
rate by removing the noise signals.

I. I NTRODUCTION
It is fatal for a driver to have a seizure or lose consciousness
while driving a car. Thus, monitoring the driver’s condition ina car is a crucial issue. In this paper, to address this problem,
we propose a new system for measuring and estimating thedriver’s heart rate while driving a car. The proposed system
uses a contactless biometric radar sensor [1] (hereafter referred
to as a radar sensor), as shown in Fig. 1 (a). This radar sensor
can measure a microdisplacement of the driver’s body surface,and signals originating from the heartbeat can be obtained.
To simulate a moving car condition, we built a vibration
measurement system depicted in Fig. 1 (b). The radar sensor
is embedded in the back of the driver’s seat so that the microdisplacement of the driver’s back is measured. Our objective
is to estimate the heart rate from the microdisplacement of the
body surface. However, the observed signal is contaminated byenormous noise, mainly a car vibration. A vibration plate simulates this noise signal in our vibration measurement system,
where the plate vibrates in the vertical direction. In addition,
the driver’s breathing also causes a significant movement of
the body surface and appears in the observed signal.
This paper aims to improve the accuracy of heart rateestimation using blind source separation (BSS) [2], [3]. BSS isapplied to the observed signals measured by the radar sensor
in the vibration measurement system and extracts the displacement of the body surface derived from the driver’s heartbeat.
In particular, we apply independent vector analysis (IVA) [4],[5], independent low-rank matrix analysis (ILRMA) [6], [7],and ILRMA based on the complex Student’s t distribution (tILRMA) [8], [9]. These algorithms have been well investigated978-616-590-477-3 ©2022 APSIPA(a) Beams from radar sensor(b) Vibration system

Fig. 1. Vibration measurement system with the radar sensor
embedded in a back of seat.

in the field of audio BSS. We compare the precision of heart
rate estimation with these BSS algorithms.
II. OVERVIEWS OF V IBRATION M EASUREMENT S YSTEMAND O BSERVED S IGNAL
A. Conditions for Vibration Measurement System
The vibration measurement system built for an experimentis shown in Fig. 1 (b). In this system, the radar sensor isembedded in the back of the seat, and the microdisplacementof the subject’s back surface can be measured. We measured
for 420 s in total, and the vibration plate was operated onlyin 60–360 s. The input signal to the vibration plate was asinusoidal wave with a 10 mm amplitude and 1.2 Hz frequency
towards the vertical direction, which simulates car movementsof idling or driving. The radar sensor emits millimeter waves
with four different directivities, as shown in Fig. 1 (a), andreceives the reflected waves. Thus, the microdisplacements offour points can be simultaneously measured as a four-channel
signal. The sampling frequency of this radar sensor is 40 Hz.
In addition, a contact-type electrocardiograph (ECG) sensor(hereafter referred to as an ECG sensor) is attached to thesubject’s chest and is operated on during the measurement. A
reference heart rate can be obtained by analyzing the ECG
sensor signal, which is used in the evaluation.
B. Observed Spectrograms of Radar and ECG Sensors
The spectrograms of the observed signals obtained by theradar sensor (ch. 1) and the ECG sensor are shown in Fig. 2.
We can confirm that the observed signal of the radar sensor
contains components of not only heartbeat but also the vibration plate noise, breathing motion, and background noise.
On the other hand, the ECG sensor captures the components of1157

APSIPA ASC 2022

Proceedings of 2022 APSIPA Annual Summit and Conference

7-10 November 2022, Chiang Mai, Thailand(a) Mixing model(b)Demixing modelFig. 3. Mixing and demixing models (M = N = 2)
Fig. 2. Spectrograms of the observed signals obtained by theradar sensor (left) and the ECG sensor (right).

The source, observed, and estimated signals in the timefrequency domain are defined as
sij = [sij1 , sij2 , · · · , sijn , · · · , sijN ]T ∈ CN ,the heartbeats with a high signal-to-noise ratio. This is because
the ECG sensor is a contact-type device and is attached to thechest.
To extract only the heartbeat components from the radar
sensor signal, we apply a BSS technique and a heart rateestimation algorithm. The accuracy of the estimated heart rates
is evaluated by comparing the reference heart rates calculated
from the ECG sensor signal.
III. BSS AND H EART R ATE E STIMATION A LGORITHM
This section presents BSS formulation in the time-frequency
domain and the algorithms of IVA, ILRMA, and t-ILRMA.
Also, an algorithm for estimating heart rate is described.
A. Formulation of BSS
As described in Sects. II-A and II-B, we assume that theobserved radar sensor signal consists of a four-channel timedomain signal and is contaminated by some noise sources. Lets̃ be the N source signals that include heartbeat and the otherN − 1 noise signals:s̃[l] = [s̃1 [l], s̃2 [l], · · · , s̃n [l], · · · , s̃N [l]]T ∈ RN ,(1)

where l = 1, 2, · · · , L and n = 1, 2, · · · , N are the indices ofthe discrete-time samples and the source signals, respectively,
and ·T denotes the transpose. These source signals are mixed
and observed as an M channel signal x̃:T(5)yij = [yij1 , yij2 , · · · , yijn , · · · , yijN ] ∈ C ,(6)

xij = [xij1 , xij2 , · · · , xijm , · · · , xijM ] ∈ C ,T

Nrespectively, where i = 1, 2, · · · , I and j = 1, 2, · · · , J are
the indices of frequency bins and time frames. Note that sij
and yij are “multisource” signals, and xij is a “multichannel”
signal in each time-frequency slot. We also define the timefrequency matrices (spectrograms) of (4)–(6) as Sn ∈ CI×J ,Xm ∈ CI×J , and Yn ∈ CI×J , respectively.
In time-frequency domain BSS, the mixing system of thesources is modeled by a time-invariant instantaneous mixture
in each frequency bin. This model can be represented as
xij = Ai sij ,(7)

where Ai ∈ CM ×N is a frequency-wise mixing matrix. Then,
BSS estimates the inverse system of (7):yij = Wi xij ,(8)

where Wi = [wi1 wi2 · · · wiN ]H ∈ CN ×M is a frequencywise demixing matrix, which ideally coincides with Wi =A−1
under the determined condition, and ·H denotes theiHermitian transpose.
The mixing and demixing systems (7) and (8) are depicted
in Fig. 3, where sjn , xjn , and y jn in this figure are the vectorsthat consist of all the frequency components as
sjn = [s1jn , s2jn , · · · , sijn , · · · , sIjn ]T ∈ CI ,Tx̃[l] = [x̃1 [l], x̃2 [l], · · · , x̃m [l], · · · , x̃M [l]]T ∈ RM ,ỹ[l] = [ỹ1 [l], ỹ2 [l], · · · , ỹn [l], · · · , ỹN [l]]T ∈ RN .

(3)

In this paper, we assume N = M = 4. The assumption of
N = M is often called the determined condition [3], which isnecessary for the BSS techniques used in this paper.
To model the convolutive mixture in the time domain, we
transform the signals (1)–(3) into the time-frequency (spectrogram) domain via the short-time Fourier transform (STFT).

(9)I

xjm = [x1jm , x2jm , · · · , xijm , · · · , xIjm ] ∈ C ,(2)

where m = 1, 2, · · · , M is the index of the channels. Estimated(separated) signals are also defined as

(4)

M

T

I

y jn = [y1jn , y2jn , · · · , yijn , · · · , yIjn ] ∈ C .

(10)
(11)

The algorithms of time-frequency domain BSS aim to estimate
the frequency-wise demixing matrix Wi from the multichannel
observed signal (X1 , X2 , · · · , XM ) without any assumptions
about the mixing system Ai , e.g., positions of the sensors orsources.
Since the radar sensor has four-channel directivities(M = 4), the BSS algorithm outputs four estimated signals(Y1 , · · · , Y4 ) that ideally correspond to one heartbeat signal
and three other noise sources. However, the order of the estimated sources depends on the initial values of BSS parameters

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C. ILRMA(a) IVA(b) ILRMA

Fig. 4. Source models assumed in IVA and ILRMA.

and an optimization algorithm. This paper treats the method forselecting the estimated heartbeat signal from the four estimatedsignals as future work. In all the experiments, we manually
select the estimated heartbeat signal by comparing BSS outputs
with the reference heartbeat signal obtained by the ECG sensor.
B. IVAThe first BSS algorithm applied in this paper is called
IVA [4], [5]. To estimate the demixing matrix Wi , IVA
assumes both “statistical independence between sources” and“co-occurrence of all the frequency components in eachsource” [4]. The co-occurrence assumption means that all thecomponents in sjn or y jn are assumed to have large powers
at the same time j, as depicted in Fig. 4 (a). This sourcewise
time-frequency model is valid in many sources to some extent.
For example, clear harmonic structures can be confirmed in theheartbeat and vibration plate components in Fig. 2, resulting in
the co-occurrence of fundamental and harmonic frequencies.
In IVA, the estimation of Wi is formulated as the following
minimization problem [4]:X
X
Minimize −2J
log | det Wi | +∥y jn ∥2 ,
(12)
W

i

j,n

where W = {Wi }Ii=1 is the set of optimization
parameterspP2and ∥ · ∥2 is the L2 norm, namely, ∥y jn ∥2 =i |yijn | .
Although the closed-form solution of (12) has not been found,an efficient iterative optimization algorithm was proposed,
which is called auxiliary-function-based IVA (AuxIVA) [5].
In AuxIVA, the following update rule for W is iteratively
calculated:
1X
1
qP
Gin =
xij xH
(13)
ij ,
J j
H x |2|win ij
iwin ← (Wi Gin )−1 en ,

(14)

1
H
win ← win (win
Gin win )− 2 ,(15)where en ∈ {0, 1}N denotes the unit vector with the nthelement equal to unity. The update rule (13)–(15) is called
iterative projection (IP) and guarantees a monotonic decrease(or non-increasing) of the cost function (12). Thus, we canobtain the estimated demixing matrix Wi by iterating (13)–(15) until the value of (12) is converged.

The second BSS algorithm, ILRMA [6], [7], assumes theindependence and “low-rank time-frequency structure of eachsource” instead of the co-occurrence assumption in IVA. This
assumption is depicted in Fig. 4 (b). The power spectrogramof source signals, |Sn |.2 or |Yn |.2 , is assumed to be wellapproximated by a low-rank matrix, where the absolute anddotted exponent for matrices represent entry-wise absoluteand exponent, respectively. Namely, the power spectrogram ofthe same source includes many repetitions of similar spectral
patterns. For this low-rank modeling, ILRMA uses nonnegative
matrix factorization (NMF) [10].
Fig. 5 illustrates the BSS principle of ILRMA. The demixing
matrix Wi is updated so that the estimated power spectrograms |Yn |.2 have a low-rank time-frequency structure andare modeled by NMF. During the low-rank modeling, NMF
enhances the components of one source and reduces the othersource components, which facilitates the separation in the
optimization of Wi .
As shown in Fig. 2, the components of both the heartbeat
and the vibration plate have repetitions of harmonic spectral
patterns along with the time frames. Thus, the low-rank source
model in ILRMA (Fig. 4 (b)) has the potential to precisely
represent the time-frequency structures of each source, andmore accurate BSS can be achieved compared with IVA in
many cases.
In ILRMA, the optimization of parameters is formulated as
XXMinimize − 2J
log | det Wi | +D |Yn |.2 |Tn Vn ,
W,T,V

i

n

(16)
N
where T = {Tn }N
n=1 and V = {Vn }n=1 are the sets of
I×K
K×J
NMF variables Tn ∈ R≥0
and Vn ∈ R≥0, respectively,
which are often called basis and activation matrices in thecontext of NMF [6], [7]. They model the power spectrogramof the estimated signals as |Yn |.2 ≈ Tn Vn (see Fig. 5).
Furthermore, D(·|·) is the sum of the entrywise Itakura–Saito
divergence [10] between the input matrices, and K ∈ N is thenumber of NMF basis vectors. The parameters in ILRMA, W,
T, and V, can be optimized by iterating the following update
rules:v
PuP−2
H x |2 v
u j |win
′
′
ij
kjn (
k′ tik n vk jn )t
, (17)
tikn ← tikn
P
P
−1
′
′
j vkjn (k′ tik n vk jn )
sP
P
−2
H
2
′
′
i |win xij | tikn (k′ tik n vk jn )vkjn ← vkjn
, (18)
PP−1′′
i tikn (k′ tik n vk jn )
1X
1
P
Uin =
xij xH
(19)
ij ,
J j
k tikn vkjn

win ← (Wi Uin )−1 en ,

(20)

1
H
win ← win (win
Uin win )− 2 ,(21)

where tikn and vkjn are the elements of Tn and Vn , respectively, and k = 1, 2, · · · , K is the index of the basis vectors.

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Fig. 5. BSS principle of ILRMA.

Similar to IP in AuxIVA, this iterative optimization algorithm
also guarantees a monotonic decrease of the cost function (16).
D. t-ILRMA
The third BSS is an extension of ILRMA, which is called
t-ILRMA [8], [9]. ILRMA uses NMF based on the Itakura–
Saito divergence (ISNMF). In ISNMF, the time-frequency
components of source signals are assumed to follow the zeromean isotropic complex Gaussian distribution [10], namely,
2yijn ∼ NC (yijn ; 0, σijn
),


|c
−
µ|2
1
exp
−
,
NC (c; µ, σ 2 ) =
πσ 2
σ2
X
2
σijn
=
tikn vkjn ,are contaminated by background noise), t-ILRMA provides
better separation performance than standard ILRMA.
The parameter optimization in t-ILRMA is formulated as
X
Minimize − 2J
log |det Wi |
W,T,V

i



H
2 |winxij |2νlog 1 ++
1+
2
ν zijn
i,j,n
#
X
2
+ log
tikn vkjn ,
(28)
p
X 

(22)
(23)
(24)

k

where µ ∈ C and σ 2 > 0 are the mean and variance of theisotropic complex Gaussian distribution NC (c; µ, σ 2 ) and c ∈C is a random variable. ISNMF in ILRMA decomposes the2
power spectrogram (time-frequency variance σijn
) based on
the generative model (22).
The generative model (22) can be extended by using theisotropic complex Student’s t distribution, which is called tNMF [11], [12], askSimilar to ILRMA, the minimization problem (28) can besolved by iterating the following update rules:
p
P
 p+2
H
|win
xij |2Pv
j bijn k′ tik′ n vk′ jn kjn
,(29)
tikn ← tikn  P
1
P
v
kjn
j
t
v
′
′
′
k

ik n k jn

H|win
xij |2P
i bijn k′ tik′ n vk′ jn

Pvkjn ← vkjn  P
1
Uin =
J



2
1+
ν

1
i

P

k′ tik′ n vk′ jn

X
j

tikn

tikn

p
 p+2



,

1
H
(31)
2 xij xij ,Pzijn ( k tikn vkjn ) p−1

2
yijn ∼ TC (yijn ; 0, σijn, ν),− 2+ν
2
1
2 |c − µ|22
TC (c; µ, σ , ν) =
1+
,
2
2
πσ
ν σ
X
p
σijn
=
tikn vkjn ,win ← (Wi Uin ) en ,win
win ← p,H
win Uin win

(25)
(26)

(30)

(32)
(33)

where
(27)

k

where ν > 0 is a degree-of-freedom parameter. Note that (24)is also generalized to (27) by introducing the domain parameterp > 0, i.e., |Yn |.p ≈ Tn Vn . If we set ν → ∞ and p =2, (25) converges to (22). Thus, t-NMF is interpreted as a
generalization of ISNMF.
It has been reported that t-NMF performs better than
ISNMF in specific NMF-based tasks, such as sparse noise
reduction [12] and multichannel audio BSS [13]. t-NMF tends
to ignore components that do not contribute to low-rank modeling, such as sparse outliers, and focuses on capturing truly
low-rank structures in the mixture. This property is enhanced
when we set ν to a small value. t-ILRMA utilizes this nature by
replacing ISNMF in ILRMA with t-NMF [8], [9]. Therefore, if
the sources in Fig. 2 (left) have a truly low-rank structure (butνbijn =
ν+2zijn = 1 +! p2
Xtik′ n vk′ jn

k′

+

2
|wH xij |2 ,
ν + 2 inH2
|winxij |22 .
Pν(pk tikn vkjn )

(34)
(35)

The monotonic decrease of the cost function (28) is guaranteed.
E. Algorithm of Heart Rate Estimation
After applying BSS to the observed radar sensor signal, we
obtain the spectrogram of the estimated heartbeat signal. LetỹHB [l] be the estimated heartbeat signal in the time domain,
calculated via an inverse STFT.
A popular method to calculate heart rates from the heartbeat
signal is to detect a QRS peak (a spiky waveform that1160

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Emphasize
heartbeatBand passfilterContourtracking ofspectral peaks

Heart rateestimates

7-10 November 2022, Chiang Mai, Thailand

Fig. 6. Process flow of the heart rate estimation algorithm.
appears in the heartbeat signal) using, e.g., the Pan–Tompkins
algorithm [14]. Since an interbeat interval corresponds toa fundamental period of the heartbeat, the heart rate canbe estimated. However, this approach is designed for ECG
sensor signals that clearly include the QRS peak. Since theheartbeat signal estimated by BSS, ỹHB [l], does not include
clear QRS peaks, in this paper, we apply a heart rate estimation
algorithm summarized in Fig. 6. In this algorithm, a bandpass filter enhances the harmonic structure in ỹHB [l] while thelow-frequency components are removed. The signal is thenconverted to a spectrogram using STFT, and the contours of
the spectral peaks are estimated. Finally, the heart rate for eachtime frame is obtained from the estimated contours.
IV. E XPERIMENTS
A. Preprocess for Eliminating Breathing Components
As shown in Fig. 2 (left), the components of the breathing
motion tend to be strongly measured by the radar sensor.
These components often degrade the accuracy of heart rateestimation.
To solve this problem, we reduced the low-frequency energy
using a high-pass filter before applying the BSS algorithm.
The amplitude and phase responses of the high-pass filter are
shown in Fig. 7. The filter was designed as 170th-order finite
impulse response, and its cutoff frequency was set to 1.5 Hz.
After applying this filter to all channels, x̃1 [l], · · · , x̃4 [l], we
input them to BSS. Although the fundamental frequency ofthe heartbeat may also be reduced by the high-pass filter, thealgorithm described in Sect. III-E can predict accurate heart
rates due to the processes shown in Fig. 6.
B. Experimental Conditions of BSS algorithms
To confirm the best BSS algorithm for radar sensor signals,
we applied three BSS algorithms, IVA, ILRMA, and t-ILRMA,
to reduce the noise components. The spectrograms of the highpass-filtered signals were calculated via STFT, where a 1.6-slong hamming window with 0.1-s-long shifting was used1 .
The number of iterations of each BSS algorithm was set to100. The initial values of the demixing matrix Wi were set tothe identity matrix for all frequencies. Also, the initial values
1 This STFT setting is different from that showing Figs. 2 and 8–11. The
spectrograms of Figs. 2 and 8–11 are calculated by STFT with a 25.6-s-longhamming window with 0.8-s-long shifting for the visibility of components inthe signal.

Fig. 7. Amplitude response (left axis) and phase response(right axis) of the high-pass filter used in the preprocessingof observed signals.

of the NMF matrices Tn and Vn in ILRMA and t-ILRMA
were set to uniformly random values in the range (0, 1), andthe number of NMF bases was set to K = 3. For t-ILRMA,
we set p = 1 (amplitude domain) and ν = 5.
C. Experimental Results
Fig. 8 shows the spectrograms of the observed radar sensor
signals, where the high-pass filter is applied. As we discussed
in Sect. II-B, the heartbeat components are contaminated bynoise. The spectrograms of the signals estimated by IVA,ILRMA, and t-ILRMA are shown in Figs. 9, 10, and 11,
respectively. In all cases, the third estimated signal corresponds
to the heartbeat signal. From these results, we can confirm thefollowing points:• The vibration plate and background noise components
tend to split into several estimated signals (the first,
second, and fourth signals in Figs. 9, 10, and 11).
• All BSS algorithms can extract only the heartbeat components from the observed signal, although their accuracy
is different.
• In the IVA results (Fig. 9), some residual componentsof the vibration plate can be confirmed at around 3.6 Hz.
This estimation error is mitigated in the results of ILRMA
and t-ILRMA (Figs. 10 and 11).
• In the ILRMA results (Fig. 10), some components of theheartbeat at 200–400 s are split into the second signal,
which is not confirmed in the result of t-ILRMA (Fig. 11).
This difference will affect to the estimation accuracy ofheart rates.
From these results, we expect that t-ILRMA will provide thebest performance for the heart rate estimation.
Fig. 12 shows the results of the heart rate estimation algorithm, where the estimated heartbeat signals obtained by eachof IVA, ILRMA, and t-ILRMA (the third signals in Figs. 9, 10,
and 11) were input, respectively. In addition, estimated heart
rates using the ECG sensor signal are shown as a reference for
estimation. The IVA-based result (Fig. 12 (a)) includes someerrors, particularly at 60–160 s. The results of ILRMA andt-ILRMA show a comparable accuracy of estimation, but theresult of t-ILRMA is slightly better. These results show the1161Proceedings of 2022 APSIPA Annual Summit and Conference

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Fig. 8. Four-channel spectrograms of the observed radar sensor signal after applying the high-pass filter.

Fig. 9. Spectrograms of the estimated signals obtained by IVA.

Fig. 10. Spectrograms of the estimated signals obtained by ILRMA.

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Fig. 11. Spectrograms of the estimated signals obtained by t-ILRMA.

Fig. 12. Estimated (red) and reference (blue) heart rates obtained by BSS algorithms.

validity of the proposed unification of the radar sensor and the
BSS algorithms to estimate the driver’s heart rate.
V. C ONCLUSION
This paper proposed a new system to monitor the driver’s
heart rate. The unification of radar sensors and BSS algorithms
was proposed. We conducted a car-simulated experiment using
the vibration plate, and the actually observed signals wereanalyzed using the proposed system. The experimental result
confirmed that ILRMA and t-ILRMA could improve theaccuracy of estimating the driver’s heart rate by reducing thenoise components.
In future work, we will evaluate heart rate estimation
accuracy using a quantitative criterion and various conditionsof observed signals. In addition, actual car-driving noise ismeasured and used to simulate more realistic observed signals.

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