A 24 GHz Band FM-CW Radar System
for Detecting Closed Multiple Targets
with Small Displacement
Kazuhiro Yamaguchi∗ , Mitsumasa Saito† , Takuya Akiyama∗ , Tomohiro Kobayashi∗ and Hideaki Matsue∗∗ Tokyo University of Science, Suwa

5000-1, Toyohira, Chino, Nagano, Japan
Email: yamaguchi@rs.tus.ac.jp, matsue@rs.suwa.tus.ac.jp† CQ-S net Inc., Japan
Abstract—In this paper, detection method for 24 GHz band
FM-CW radar system under closed multiple targets with small
displacements environment is proposed, and its performances areanalyzed. The proposed detection method was used a tunable
FIR filter for signal processing, and the distance and small
displacement can be separated for each target correctly fromthe received signal including all of signals from the targets at
the FM-CW radar. Computer simulations were carried out forevaluating the proposed detection method for FM-CW radar andanalyzing the performance according to the parameters underclosed multiple targets environment. The results show that the
proposed detection method can detect both the distance and small
displacement correctly under closed multiple targets environment.

filter in the FM-CW radar system. Furthermore, performance
analysis for FM-CW radar system was shown in computer
simulations.
This paper consists of the following sections. In Section
II, we describe the principle of a FM-CW radar system undersingle target environment. In Section III, we describe theproposed detection method under multiple targets environment.
In Section IV, we show the computer simulations and analysis
with the proposed FM-CW radar system. Finally, in Section
V, we conclude this paper.
II.

I.

I NTRODUCTION

A. Principle of FM-CW radar

Radar systems with 24 GHz band is based on ARIB
standard T73 [1] as sensors for detecting or measuring mobile
objects for specified low power radio station. And the 24 GHz
band radar system can be applied in various field such as
security, medical imaging and so on under indoor and outdoor
environments. Various radar systems were reported [2], [3], [4],[5]. Pulsed radar systems can measure the period between thetransmitted and received signals. The pulsed radar can detectthe distance in far field; however, the target in near field can
not be detected correctly. Doppler radar systems can measure
the frequency difference between the reflected and transmitted
signals. The Doppler radar can detect the moving velocityof the target; however, the distance of the target can not be
detected. FM-CW (Frequency-Modulated Continuous-Wave)
radar systems [6], [7] is the most widely used for detecting
the distance of the target object in near field and the small
displacement of the target.
As previous study, we reported the design, performance
analysis, and applications with 24 GHz band radar systemfor detecting both the distance from the radar and the small
displacement for human breathing [8]. The radar system could
detect both the distance to the human from the radar and thesmall displacement of the human breathing correctly; however,it was difficult for detecting the distances and displacements
for multiple humans at the same time.
In this paper, in order to detect the distances and displacements under closed multiple targets environment, we propose
a detection method for signal processing with a tunable FIR

978-1-4799-8993-5/15/$31.00 ©2015 IEEE

FM-CW R ADAR S YSTEM

268

FM-CW (Frequency-Modulated Continuous-Wave) radar isa radar which is transmitting a continuous carrier modulated
by a periodic function such as a sawtooth wave to provide
range data shown in Fig. 1. Fig. 2 shows the block diagramof a FM-CW radar system [9].
In the FM-CW radar system, frequency modulated signal at
the VCO is transmitted from the transmitter Tx; then, signals
reflected from the targets are received at the receiver Rx.
Transmitted and received signals are multiplied by a mixer, andbeat signals are generated as multiplying the two signals. Thebeat signal pass through a low pass filter; then, an output signal
is obtained. In this process, the frequency of the input signal
is varied with time at the VCO. The modulation waveformwith a linear sawtooth pattern [10] as shown in Fig. 1. This
figure illustrates frequency-time relation in the FM-CW radar,and the red line denotes the transmitted signal and the blueline denotes the received signal. Here, f0 denotes the center
frequency, fw denotes the frequency bandwidth for sweep, andtw denotes the period for sweep.
We define that the transmitting signal VT (f, x) is represented as
2πf

VT (f, x) = Aej c x ,(1)where f denotes a frequency at a time, x denotes a distance
between a target and the transmitter, A denotes an amplitude
value, and c denotes the speed of light.

ICUFN 2015݂of the output signal P (x) is calculated as follow.

Frequency

݂௪
݂଴ ൅
ʹ

Transmitted signal

Received signal

P (x) =

݂଴ ݂௪

݂௪
݂଴ െ
ʹ

=
‫ݐ‬௪
‫ݐ‬

Time

∫ f0 + f2w∫

f0 − f2w
f0 + f2w
f0 − f2w

=A

2

K
∑

4πf

Vout e−j c df
K∑

A2 αk γk ejφk ej

k=1

αk γ k e

jφk

k=1

Fig. 1.

Sawtooth frequency modulation

= A2
D/A

VCO

BPF

ܸ୘

Target 1

Tx

‫ݔ‬ଵ

FFT

A/D

BPF

ܸ୭୳୲

ܸୖ

Rx

Target ‫ܭ‬‫ݔ‬௄distance from the radar

Fig. 2.

‫ݔ‬

Block diagram of a FM-CW radar system

The reflected signal VR (f, x) is represented as

VR (f, x) =

K
∑

2πf

Aαk γk ejφk ej c (2dk −x) ,

(2)

k=1

where γk and φk are the reflectivity coefficients for amplitude
and phase on kth target, respectively. αk denotes an amplitude
coefficient for transmission loss from the kth target, and dk isthe distance between the transmitter and the kth target.
Here, at the receiver whose position is x = 0, Eq. (2) isrewritten as

VR (f, 0) =

K
∑

2πf

Aαk γk ejφk ej c (2dk ) .

(3)

k=1

The beat signal is generated as multiplying the transmitted
signal in Eq. (1) and the received signal in Eq. (3) at theposition x = 0. After through LPF, the output signal Vout (f, 0)
is generated by

Vout (f, 0) =K∑

A2 αk γk ejφk e

4πf d
j c k

.

ej

4πf0 (dk −x)
j
c

e−j

4πf x
c

4πf (dk −x)
c

sin
fw

{

df

df
2πfw (dk −x)c2πfw (dk −x)
c

}

.

(5)

The amplitude value of the distance spectrum |P (x)| in Eq. (5)is given as
}�
{
�
�K
�
k −x)
sin 2πfw (d∑4πf0 (dk −x)
�
�
c
�
c
αk γk ejφk ej
fw|P (x)| = A2 ���
2πfw (dk −x)
�k=1
�
c
{
}
�
�
� sin 2πfw (dk −x) �
K
∑
�
�
c
2
� ,
(6)
≤ A fw
αk γk ���
2πfw (dk −x)
�
�
k=1
c

Target ݇‫ݔ‬௞

f0 − f2w

αk γk ejφk e

k=1

Signal processing

SignalK∑∫ f0 + f2w

4πf dkc(4)

k=1

and we have equality if and only if the phase components
ϕk + 4πf0 (dc k −x) about all of k are equal.
Here, we assumed that the number of target is 1. The
distance spectrum in Eq. (5) is rewritten as
}
{
1 −x)
sin 2πfw (d4πf0 (d1 −x)ccfw,
P (x) = A2 α1 γ1 ejφ1 ej
2πf (d −x)
w

269

(7)

and the amplitude value of distance spectrum is given as{}��� sin 2πfw (d1 −x) �
�
�
c
� .
(8)
|P (x)| = A2 α1 γ1 fw ���
2πfw (d1 −x)��cThis equation indicates that the distance for the target isgenerated by the amplitude value of distance spectrum.
as

The phase value of distance spectrum ̸ P (x) is represented̸

P (x) = φ1 +4πf0 (d1 − x)
= θ1 (x) .
c(9)Here, θ1 (x) satisfy −π ≤ θ1 (x) ≤ π, then the displacement
for the target is−

By using signal processing, a distance and a displacement
for the target are given from the generated output signal in
Eq. (4). By using the Fourier transform, the distance spectrum

1cc (−π − φ1 )c (π − φ1 )≤ d1 ≤
.
4πf0
4πf0

(10)

If the phase value satisfies ϕ1 = 0, Eq. (10) is rewritten as−3.11 [mm] ≤ d1 ≤ +3.11 [mm] with f0 = 24.15 [GHz].
That is, the small displacement of the target within ±3.11[mm] is generated by the phase value of distance spectrum.

FM-CW radar

1m

Distance

Amplitude
2.5mm

Target 1

Small displacement

An example of FM-CW Radar for detecting human breathing

2mTarget 2

FM-CW radar2m
1m

Fig. 4.

7.5s

DistanceTime

Amplitude

Target 2

Fig. 5.

Phase

Results of individual detections for single moving target

Small displacement:
Amplitude: 2.0 mm
Period:7.5 sec

Target 1+
Target 2

Setup conditions with 2 targets

ܸ୘On the other hands, the maximum distance for measuringdmax isfw[Hz] ,
tw /tsc[m] ,dmax =
4∆f

Amplitude

Fig. 6.

∆f =B. Detection for single target

‫ݔ‬ଵ

݇

Phase

‫ݔ‬௞
‫ݔ‬

௄
ܸୖ
୭୳୲ multiple
Results of detection ܸformoving targets

‫ܭ‬
‫ݔ‬

Signal processing(11)

where tw denotes the sweep time, ts denotes the interval time
for sampling. For example, in the case with tw = 1024 µs andts = 1 µs, the maximum distance is dmax = 384 [m].

Signal after
A/D process

Peak position
detection
FFT

Tunable band-path
FIR filter

Display
amplitude value
Displayphase value

Fig. 7. Block diagram of the proposed detection method in signal processing

In this section, an example of detection using the FMCW radar system is demonstrated by using the computer
simulation. The setup condition in the computer simulationis shown in Fig. 3, and the condition was corresponding to
the experiment in [8]. We assumed that the FM-CW radar was
located on the ceiling, and the target was the human who lie
in bed. If there was only single target within the range of the
FM-CW radar, the individual distance and small displacement
was detected correctly shown in Fig. 5.
III.

Amplitude
2.0mm

Time

Target 1
Small displacement:
Amplitude: 2.5 mm
Period:10.0 sec

Small displacement

Fig. 3.

Power

10s

P ROPOSED D ETECTION M ETHOD

As mentioned in the above section, the FM-CW radar system could detect both the distance and displacement correctly
under single target environments; however, the FM-CW radar
could not detect both the distance and displacement correctly
under closed multiple targets environments. In order to realize
detections for closed multiple targets, we propose the detection
method by using the signal processing with a tunable FIR filter.
The procedures of the proposed detection method is asfollow. We assumed that the FM-CW radar is located a shortdistance from a bed as shown in Fig. 4. The radio waves areradiated from the FM-CW radar, and 2 targets lie on the bed.

270

The distances from the radar to each target are different, sothat the peaks of distance spectrum are detected at different
frequency. In this case, the detected result shown in Fig. 6 issum of these 2 targets, and it is difficult for detecting both the
distance and phase values for each user correctly.
In order to solve this problem, signal processing with thetunable FIR filter is used in the proposed detection method.
Figure 7 shows the block diagram of the proposed detection
method. At first, the A/D converted signal is carried out theFFT operation, and the distance spectrum is obtained. After
processing the FFT operation, the peaks of amplitude valueof the distance spectrum are calculated. In the peak position
detection processing, the two frequency value according to thetargets is obtained; then, FIR filters are designed according to
the peak positions. The tunable FIR filter has the center frequency corresponding to the calculated frequency in the peak
position detections, and the linear property for the phase value.
By using the designed FIR filter, band-path filtering operation
is carried out for the distance spectrum. After through bandpath filter, the amplitude and phase value for each target aredetected correctly.

TABLE I.

PARAMETERS IN COMPUTER SIMULATIONSParameters

Value

Center frequency f0
Bandwidth of sweep frequency fw
Sweep time tw
Bandwidth for FIR filter
Number of FFT points
Window function

24.15 GHz
100, 200, 400, 800 MHz
256, 512, 1024, 2048 µs
200, 400, 800, 1600, 3200 Hz
4096
hamming

S ETUP CONDITIONS FOR TARGETS

Parameters

Target 1

Target 2

Distance
Amplitude of Displacement
Period of displacement

1.0 m
2.5 mm
10.0 s2.0 m
2.0 mm
7.5 s

Maximal value for target 1:ܲଵ ൌ ܲ ݂ଵ

Small displacement [mm]Amplitude [A.U.]

0.8
0.7
0.6

ܵଵ

Maximal value for target 2:ܲଶ ൌ ܲ ݂ଶ

0.5
0.4

ܵଶ

0.3
0.2

Minimal value:ܲ௠௜௡ ൌ ܲ ݂௠௜௡

0.1

0

0

1

݂ଵ

2

݂௠௜௡

3

݂ଶ

4

5

2

-12
-14
-16
-18
-20

‫ݐ‬௪ ൌ ͳͲʹͶ ߤ‫ݏ‬‫ ܤ‬ൌ ʹͲͲ Hz-220݀௜ െ ݀௜ᇱ

-1

10

15

400

500

600

‫ݐ‬௪ ൌ ͳͲʹͶ ߤ‫ݏ‬‫ ܤ‬ൌ ʹͲͲ Hz

6.0%

-2

5

300

700

800

7.0%

݀௜ᇱ

0

200

݂௪ ǣ Bandwidth of sweep frewuency [MHz](a): Amplitude

0

-3

100

Setuped value

Beat frequency [kHz]20

25

Target 1
Target 2

5.0%

30Time [s](b) Phase value

Definitions of evaluation values for computer simulation

IV.

-8
-10

݀௜

1

(a) Amplitude value

Fig. 8.

Target 2-6

Detected value

Phase value for target 1
3

0.9

Target 1

-4

-24

NMSE

1

Degree of amplitude separation [dB]TABLE II.

0
-2

4.0%
3.0%
2.0%

C OMPUTER S IMULATION‫ݐ‬௪ ൌ ͳͲʹͶ ߤ‫ݏ‬
A. Setup condition

1.0%‫ ܤ‬ൌ ʹͲͲIn order to evaluate the performance for FM-CW radarsystem with the proposed method under multiple targets envi݂௪ ǣronment, we carriedout computer simulations. Parameters forcomputer simulations are listed in Table I, and the parameters
are based on ARIB standard T73 [1]. Center frequency was
24.15 GHz, and frequency bandwidths were 100, 200, 400, and
800 MHz. Note that the 400 and 800 MHz bandwidth were
only used for the computer simulation because of standards inthe Radio Law in Japan. Sweep times were 256, 512, 1024,
and 2048 µs, sampling time of sweep was 0.1 µs, number of
FFT points was 4096, and the hamming windows was adapted
as the window function in signal processing. The bandwidths
for FIR filter were 200, 400, 800, 1600, and 3200 Hz.

0.0%

0

100

200

300

400

500

600

݂௪ ǣ Bandwidth of sweep frequency [MHz]

700

800

(b): Phase
Fig. 9.

Evaluation values versus bandwidth of sweep frequency

tude whose frequency is fmin , and Pk denotes the peak value
for k-th target with frequency of fk .
The NMSE for phase value is represented by
NMSE =

N2∑|d′ − di |
i

,

(13)

In the following sections, we describe the evaluation values
for analyzing the results of multiple targets detections, andthe performance analysis according to bandwidth for sweep
frequency, sweep time, bandwidth for FIR filter, and positionof target 2 are described.

where N denotes the number of sampling points, di and d′idenote the sampled signals of detected and setuped values fora target, respectively.

B. Evaluation values for amplitude and phase values

C. Performance for Bandwidth of sweep frequency

Figure 8 shows the evaluation value for detecting the amplitude and phase values of the distance spectrum of multiple
targets. We defined the degree of amplitude separation for
amplitude value and NMSE for phase value.

Figure 9 shows the evaluation values versus the bandwidthof sweep frequency fw for amplitude value in (a) and phasevalue in (b). As shown in (a), the degrees of amplitude
separation were about -2.5 dB and -19 dB with fw = 100
MHz and fw = 800 MHz, respectively. Because the resolutionof the distance spectrum was increased as an increasing the
bandwidth of sweep frequency, the separation of targets for
amplitude value become easily.

The degree of amplitude separation is represented by
Sk = 10 log|P (fmin )||Pmin |
= 10 log|Pk ||P (fk )|[dB], (12)

where k denotes the number of target, Sk denotes the degree of
amplitude separation, Pmin denotes minimal value of ampli-

271

i=1

|d′i |

2

As shown in (b), NMSE was about 2 % with the bandwidthof sweep frequency fw = 100 MHz, and NMSE was also0-2

Degree of amplitude seperation [dB]

Degree of amplitude separation [dB]

0
-2
-4
-6
-8
-10
-12

Target 1-14

Target 2

-16

-18
-20

݂௪ ൌ ʹͲͲ MHz‫ ܤ‬ൌ ʹͲͲ Hz

-22
-24

0

200

400

600

800

݂௪
‫ݐ‬

-6

-8

Target 1-10

Target 2

-12
-14
-16
-18
-20

݂௪ ൌ ʹͲͲ MHz‫ݐ‬௪ ൌ ʹͷ͸ ߤ‫ݏ‬

-22
-24

1000 1200 1400 1600 1800 2000 2200

݂௪ ൌ ʹͲͲ‫ ܤ‬ൌ ʹͲͲ-4‫ݐ‬௪ ǣ Sweep time [us]

0

500

1000

(a): Amplitude

Target 1

3000

3500

2500

3000

3500

݂௪ ൌ ʹͲͲ MHz‫ݐ‬௪ ൌ ʹͷ͸ ߤ‫ݏ‬

6.0%

Target 2

5.0%

5.0%

4.0%

4.0%

NMSE

NMSE

2500

7.0%

݂௪ ൌ ʹͲͲ MHz‫ ܤ‬ൌ ʹͲͲ Hz

6.0%

3.0%

Target 1
Target 2

3.0%
2.0%

2.0%

݂௪ ൌ ʹͲͲ‫ݐ‬௪ ൌ ʹͷ͸ ߤ‫ݏ‬

1.0%

0

200

400

1.0%

600

‫ܤ‬ǣ

800

0.0%

1000 1200 1400 1600 1800 2000 2200

‫ݐ‬௪ ǣ Sweep time [us](b): Phase

Fig. 10.

2000(a): Amplitude

7.0%

0.0%

1500

‫ݐ‬௪ ǣ
‫ܤ‬ǣ Bnadwidthof FIR filter [Hz]

0

500

1000

1500

2000

‫ܤ‬ǣ Bandwidth of FIR filter [Hz](b): Phase

Evaluation values versus sweep time

Fig. 11.

improved as an increasing the bandwidth of sweep frequency.
Although there was a few disadvantage for NMSE of target
2, the multiple targets detections could correctly achieved
because the degree of amplitude separation with -1 dB and
NMSE with 6 % were enough values for detecting multiple
targets in practical use.

D. Performance for Sweep time
Figure 10 shows the evaluation values versus the sweep
time tw for amplitude value in (a) and phase value in (b). As
shown in (a), the degree of amplitude separation for target 1
kept about -4 dB in accordance not to the sweep time. The
degree of separation for target 2 had -1 dB during the sweep
time tw = 256 ∼ 1024 µs. In the case with tw = 2014µs,
the degree of amplitude separation was almost 0 dB. Thatis, it was difficult to detect the peak value of amplitude fortarget 2. Moreover, compared to the result in (b), the worst
NMSE for target 2 was about 4 % with tw = 2048 µs.
Because the resolution for distance spectrum was decreased
as an increasing the sweep time, the sweep time should beless than 1024 µs.

272

Evaluation values versus bandwidth of FIR filter

E. Performance for Bandwidth of FIR filter
Figure 11 shows the evaluation values versus the bandwidthof FIR filter B for amplitude value in (a) and phase value in(b). As shown in (a), the degree of amplitude separation fortarget 1 kept -2 dB in accordance not to the bandwidth of FIR
filter B. When B was more than 1600 Hz, the degree wasmore than -1 dB, therefore, it was difficult to detect the peakvalue.
As shown in (b), NMSE for target 1 was less than 3 %,but NMSE for target 2 was more than 5 % with B = 1600
and 3200 Hz. Because the widely bandwidth of FIR filter wasenough not to cut the signal of the other target completely, thebandwidth of FIR filter should be less than 1600 Hz.
F. Performance for distance between targets
Finally, we show the result for detecting multiple targets
when the target 2 comes close to the target 1 from 2 m to 1.5
m. Figure 12 shows the evaluation values versus the positionof target 2 from the radar for amplitude value in (a) and phasevalue in (b). The position of the target 1 was 1 m from theradar.

V.

Degree of amplitude seperation [dB]

0
-2

⣔ิ5
Target 1 (݂௪ ൌ ʹͲͲ MHz)

-4

⣔ิ6
Target 2 (݂௪ ൌ ʹͲͲ MHz)

-6

⣔ิ3
Target 1 (݂௪ ൌ ͶͲͲ MHz)

-8

Target 2 (݂௪ ൌ ͶͲͲ MHz)
⣔ิ4

In this paper,a ݂FM-CW
radar system with 24 GHz band䝍䞊䝀䝑䝖௪ ൌ ʹͲͲ
with tunable 䝍䞊䝀䝑䝖䠍FIR filter
for detecting closed multiple moving݂௪ ൌ ͶͲͲtargets with small
displacements was described. The proposed䝍䞊䝀䝑䝖 ݂௪ ൌ ͶͲͲ
detecting method
generates
tunable FIR filter whose center݂௪ ൌ ͺͲͲ䝍䞊䝀䝑䝖䠍
frequency is 䝍䞊䝀䝑䝖correspondingtothe peak positions of distance݂௪ ൌ ͺͲͲ
spectrum of each target. The tunable FIR filtered signal canbe detected the distance and displacement for each target
correctly. In computer simulations, performances of FM-CW
radar system under closed multiple moving targets environment was ‫ݐ‬௪analyzedൌ ʹͷ͸ ߤ‫ ݏ‬in accordance with the bandwidth of‫ ܤ‬ൌ ʹͲͲ sweep time, bandwidth of FIR filter, and thesweep frequency,
distance between targets. As the result, the 24 GHz FM-CW
radar with the proposed detection method could effectively
detect both the distance and the small displacement for eachtarget under the multiple moving targets environments. And it
was confirmed that the proposed detection method can detectboth the distance and small displacement correctly when the
distance between targets was 0.5 m.

Target 1 (݂௪ ൌ ͺͲͲ MHz)
⣔ิ1

-10

Target 2 (݂௪ ൌ ͺͲͲ MHz)
⣔ิ2

-12
-14

-16
-18
-20

‫ݐ‬௪ ൌ ʹͷ͸ ߤ‫ݏ‬‫ ܤ‬ൌ ʹͲͲ Hz

-22
-24

1

1.2

1.4

1.6

1.8

2

Position of target 2 [m](a): Amplitude
7.0%
Target 1 (݂௪ ൌ ʹͲͲ MHz)䝍䞊䝀䝑䝖䠍

6.0%

Target 2 (݂௪ ൌ ʹͲͲ MHz)䝍䞊䝀䝑䝖2NMSE

R EFERENCES

Target 1 (݂௪ ൌ ͶͲͲ MHz)䝍䞊䝀䝑䝖䠍

5.0%

Target 2 (݂௪ ൌ ͶͲͲ MHz)䝍䞊䝀䝑䝖2[1]

Target 1 (݂௪ ൌ ͺͲͲ MHz)䝍䞊䝀䝑䝖䠍

4.0%

Target 2 (݂௪ ൌ ͺͲͲ MHz)䝍䞊䝀䝑䝖2

[2]

3.0%
2.0%

[3]
[4]

‫ݐ‬௪ ൌ ʹͷ͸ ߤ‫ݏ‬‫ ܤ‬ൌ ʹͲͲ Hz

1.0%
0.0%

1

1.2

1.4

1.6

1.8

2

Position of target 2 [m][5](b): Phase
Fig. 12.

C ONCLUSION݂௪ ൌ ʹͲͲ䝍䞊䝀䝑䝖䠍

Evaluation values versus position of target 2[6]Compared to the results, the degree of amplitude separation
and NMSE become depleted as the target 2 approaches tothe target 1. As shown in (a), when the bandwidth of sweep
frequency was more than 400 MHz, the degree of amplitude
separation had good property which enough to detect thepeaks. However, in the case with fw = 200 MHz, the degree
for target 2 was about -0.3 dB, and it was difficult to detect
the peaks.

[7]

[8]

[9]
[10]

As shown in (b), when fw was less than 400 MHz, NMSE
could be kept about less than 5 %. However, in the case with
fw = 800 MHz, NMSE become depleted. It was difficult to
detect peaks of amplitude for targets as decreasing distance
between targets. Therefore, the center frequency of FIR filter
was not enough to cut the other target’s signal, and theimperfect FIR filter influenced NMSE values. Although there
were a few difficulty for determining the parameters of the
proposed detecting method for FM-CW radar, the proposed
detecting method could be effective for detecting the distanceand the small displacement at the same time under multiple
targets environments.

273

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