Adv. Radio Sci., 12, 35–41, 2014
www.adv-radio-sci.net/12/35/2014/
doi:10.5194/ars-12-35-2014
© Author(s) 2014. CC Attribution 3.0 License.
Multi-sensor Doppler radar for machine tool collision detection
T. J. Wächter1 , U. Siart1 , T. F. Eibert1 , and S. Bonerz2
1 Technische
2 Ott-Jakob
Universität München, Lehrstuhl für Hochfrequenztechnik, Arcisstr. 21, 80333 Munich, Germany
Spanntechnik GmbH, Industriestr. 3–7, 87663 Lengenwang, Germany
Correspondence to: T. J. Wächter ([email protected])
Received: 26 January 2014 – Revised: 11 July 2014 – Accepted: 16 July 2014 – Published: 10 November 2014
Abstract. Machine damage due to tool collisions is a
widespread issue in milling production. These collisions are
typically caused by human errors. A solution for this problem
is proposed based on a low-complexity 24 GHz continuous
wave (CW) radar system. The developed monitoring system
is able to detect moving objects by evaluating the Doppler
shift. It combines incoherent information from several spatially distributed Doppler sensors and estimates the distance
between an object and the sensors. The specially designed
compact prototype contains up to five radar sensor modules
and amplifiers yet fits into the limited available space. In this
first approach we concentrate on the Doppler-based positioning of a single moving target. The recorded signals are preprocessed in order to remove noise and interference from the
machinery hall. We conducted and processed system measurements with this prototype. The Doppler frequency estimation and the object position obtained after signal conditioning and processing with the developed algorithm were in
good agreement with the reference coordinates provided by
the machine’s control unit.
1 Introduction
Collisions within the operating space of machine tools have
many different causes. Main causes for collisions during human operation are wrong programming (wrong part, compensation or offsets), wrong machine setup (wrong tool,
clamping or raw parts) and inattention or faulty operation by
the operator himself.
The so called technological collisions concern crashes between tool and work piece only. The second group, the geometric collisions, involves further elements of the machine
like the bearings, holder, spindle, axis or the driving shaft.
In the case of tool collisions, tremendous impact forces
cause heavy damage to the work piece, the tool and to other
elements of the drive train. The results are expensive damage,
costs for production downtimes and high rejection rates. The
goal is to guarantee high machine availability to maximize
efficiency and output.
Up to now, no system is known which reliably provides
information in order to avoid collisions with non-moving
components and to actively protect the machine components
against physical damage. There are some promising sensor
based systems that can decouple the inner main motor spindle from the outer spindle stock, hence protecting the components from mechanical overload to reduce damage to a minimum. Other methods, without sensors, monitor the current
flux through the motor and driving chain and activate when
a certain threshold is exceeded. An elaboration on available
safety systems can be found in Abele et al. (2012). All of
these are reactive systems which are activated after a crash.
With these, mitigation of damage is possible, but not their
prevention.
Optical systems like laser scanners or (multi-)camera
based systems are active observers. The disadvantage of
these systems is that they are blinded due to cooling fluid,
drizzle, dust and dirt from the milling treatment which pollute the lens or the sensor space. So their use is limited to
phases where the metal processing is stopped or to other applications with non-cutting manufacture.
In this paper, the implementation of a prototype for a new
possible solution is presented based on an autonomous active radar sensor safety system which operates in the 24 to
24.25 GHz ISM band. The utilized sensors are commercially
available low-cost modules for short-range radar (SRR) applications, containing all front-end parts of a CW radar,
including complex down-conversion. Figure 1 shows the
prototype concept, here equipped with four modules in a
Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.
2
2
36
Wächter, U.
T. T.
F. Eibert
and S.
Bonerz:
Multi-Sensor
Doppler Radar
for Machine for
Tools
T.T.J.J.Wächter,
U.Siart,
Siart,
F. Eibert
and
S.etBonerz:
Multi-Sensor
Machine Too
T. J. Wächter
al.: Multi-sensor
DopplerDoppler
radar for Radar
machine tools
z
z
sensor
sensor
platform
platform
metal
sphere
metal
sphere
x
x
y
y
Fig. 1. Concept of the toroidal holder with four modules in a symmetric arrangement and the internal coordinate system. A metal
Figure
1. Concept
of the toroidal
holder with four modules in a
sphere serves
as a measurement
target.
symmetric
arrangement
and
the
internal
coordinate
A metal
Fig. 1. Concept of the toroidal holder with
four system.
modules
in a symsphere
serves
as
a
measurement
target.
metric arrangement and the internal coordinate system. A metalFigure 2. The implemented toroidal sensor platform equipped with
Fig. 2.
The and
implemented
sensor
platform
with
four
radars
integratedtoroidal
amplifiers
embedded
in equipped
an accessible,
sphere serves as a measurement target.
four radars and
amplifiers
embedded
in an
accessible,
milling machine tool to provide complete coverage of the
maneuverable
testintegrated
environment.
Obtained
signals are
conducted
via
maneuverable
Obtained
signals
are conducted via
three-dimensional surrounding space.
coaxial
lines totest
theenvironment.
data storage and
processing
system.
symmetrical, perpendicular arrangement. The origin of the
coaxial lines to the data storage and processing system.
We designed a toroidal holder with integrated low-noise
internal coordinate system is at the center point of the holder
amplifiers (LNAs) which allows test scenarios with differ-
Fig. 2. The implemented toroidal sensor platform equipped wi
(sensor
platform).
Several
modulescomplete
are arranged
around the
fourthe
radars
integrated
amplifiers
in an accessibl
milling
machine
tool
to provide
coverage
of thethermore,
large and
operating
temperature
rangeembedded
and the rapid
ent antenna
configurations
involving up to five
radar moddistance
information.
Alsoenvironment.
the use
of
the
24 GHz
wideband
milling machine surrounding
tool to provide
complete coverage of the
maneuverable
test
Obtained
signals
are
conducted v
three-dimensional
space.
fluctuation
of
temperature
must
be
dealt
with
by
the
equipules with variable radial distance, angle and positions in xtechnology
with
5 GHz
bandwidth
as inlinearity
automotive
SRR system.
was
three-dimensional surrounding space.
coaxial
lines
to
the
data
storage
and
processing
ment
to
meet
the
high
demands
on
of
frequency
Wedirection.
designed
a toroidal
holder
with integrated
Figure
2 shows the
implementation
with fourlow-noise
radar
ceasedinasfrequency
of June 2013
(StrohmCW
et al.,
2005).
The necessary
We designed a toroidal holder with integrated low-noise
modulated
radar
(FMCW)
or pulsed
modules(LNAs)
and the corresponding
integrated
LNAs embedded
amplifiers
which
allows
test
scenarios
with
differ-ramps
bandwidth
for
a
specific
range
resolution
∆r
can
be
derived
amplifiers (LNAs) which allows test scenarios with differradar
to
provide
proper
distance
information.
Also
the
use of
in an open
test environment.
Some important five
properties
of
ent antenna
configurations
radar
from24∆r
=
c
/(2∆f
),
where
c
is
the
speed
of
light
and
∆f
ent antenna
configurations involving
involving upupto to
five radar
mod-mod-the
0
0
GHz
wideband
technology
with
5
GHz
bandwidth
as
distance information. Also the use of the 24
GHz wideban
this additional system and the CW concept are its indepenis the
absolute
bandwidth.
With
the
automotive
SRR,
a
suffiules ules
with
variable
angle
and
positions
with
variableradial
radialdistance,
distance, angle
and
positions
in xin x-in
automotive
SRR
was
ceased
as
of
June
2013
(Strohm
et
dence from the acting machine tool, robustness against envitechnology
with
5
GHz
bandwidth
as
in
automotive
SRR wa
cient
resolution
of 3 cm isbandwidth
achievablefor
if the
full bandwidth
of
showsthe
the implementation
with
fourfour
radarradaral.,
direction.
Figure
direction.
Figure
2 2shows
implementation
with
2005).
The necessary
a specific
range resronmental
influences
and reliability
due to its simplicity.
as of June 2013 (Strohm et al., 2005). The necessar
5 GHzceased
is1r
becan
used.
modules
corresponding integrated
LNAs
embedded
be derived from 1r = c0 /(21f ), where c0 is
modules
andand
thethe
corresponding
LNAs
embeddedolution
Microwave
sensorics
is more integrated
suited for this
application
bandwidth
for
a specific
range
resolution
∆r
A
second
figure
of1f
merit
is the
accuracy
δr which
is
dein
an
open
test
environment.
Some
important
properties
of
the
speed
of
light
and
is the
absolute
bandwidth.
With
thecan be derive
cameras
and optical sensors.
is due to
the su- of
in anthan
open
test environment.
SomeThis
important
properties
fined
as
(e.g.,
Skolnik,
1960;
Barton,
1964),
this
additional
system
and
the
CW
concept
are
its
indepenfrom ∆r = c0 /(2∆fresolution
), whereofc03 cm
is the
speed of light and ∆
is achievable
perior properties
of microwaves
withconcept
the above-mentioned
this dence
additional
system
and
the tool,
CW
are
its enviindepen-automotive SRR, a sufficient
from
the
acting
machine
robustness
against
is
the
absolute
bandwidth.
With
the
automotive
SRR, a suffi
c
if
the
full
bandwidth
of
5
GHz
is
be
used.
problems
with
dirt and
moisturetool,
in the
operating space.
Mi-envi-δr = τ √ 0 ,
dence
from the
acting
machine
robustness
against
(1)
p
ronmental
influences
and
reliability
due
to
its
simplicity.
A
second
figure
of
merit
is
the
accuracy
δr
which
is
decient
resolution of 3 cm is achievable if the full bandwidth o
crowave sensorics is also more suited than acoustical and
2SNR
ronmental
influences
and isreliability
due(300
to this
its simplicity.
Microwave
sensorics
more
suited
for
application
fined as
(e.g., Skolnik,
1960; Barton, 1964),
ultrasonic
sensors.
The speed
of sound
mm/ms)
causes
5
GHz
used.
with the pulse is
risebetime
τp and the signal-to-noise ratio SNR.
than
cameras
and
optical
sensors.
This
is
due
to
the
suMicrowave
sensorics
is
more
suited
for
this
application
long signal delays compared to electromagnetic wave propac0second
A
figure
of meritdepends
is the accuracy
δr which is d
Just
like
the
resolution,
the accuracy
on the bandperior
properties
of
microwaves
with
the
above-mentioned
,
(1)
than gation.
cameras and optical sensors. This is due to the su-δr = τp √
asdetermines
(e.g., Skolnik,
1960; Barton,
1964),
width fined
which
τp ≈ 0.35/∆f
. Both conditions,
2SNR
problems
with
dirt
and
moisture
in
the
operating
space.
Miinside
the enclosure ofwith
the machine
and processperior Operation
properties
of microwaves
the above-mentioned
sufficient range resolution and accuracy, cannot be met in the
crowave
sensorics
is also
morefrom
suited
thanisacoustical
and
uling thewith
diverse
radar
returns
there
one of−1the
chalc0 τp and the signal-to-noise ratio SNR.
the to
pulse
rise time
problems
dirt
and
moisture
in
the
operating
space.
Mi-with
24 GHz
trasonic
sensors.
The
speed
of
sound
(300
mm
ms
)
causes
,
(1
δr the
=24.25
τresolution,
p √GHz ISM-band.
lenges for the signal processing. Multiple reflexions at the
Just
like
crowave
sensorics
also more
suited than wave
acoustical
2SNRthe accuracy depends on the bandlong
delaysis
compared
to electromagnetic
propa- and
wallssignal
at arbitrary
distances
cause
clutter effects and
increase
ultrasonic
sensors.
The speed
of sound
mm/ms) causeswidth which determines τp ≈ 0.35/1f . Both conditions,
gation.
the noise
level. Further
challenges
are (300
the non-stationary
sufficient
range
resolution
accuracy,
cannot
be met in the ratio SNR
2 Designed
Doppler
Radar
with
theMulti-Sensor
pulse riseand
time
τp and
theNetwork
signal-to-noise
Operation
inside
the shapes
enclosure
ofgeometries
the machineofand
processlongenvironment,
signal
delays
compared
toand
electromagnetic
propa-24 to 24.25 GHz ISM-band.
varying
thewave
milling
Just like the resolution, the accuracy depends on the band
ing
from there
is operating
one of thezone.
chalgation.
toolsthe
as diverse
well as radar
swarf returns
from treatment
in the
From the viewpoint of hardware one of the limiting factors in
width which determines τp ≈ 0.35/∆f
. Both condition
lenges
for
the
signal
processing.
Multiple
reflexions
at
the
The system
development
concentrated
on using CW
space in the maOperation
inside
the enclosure
of the machine
andradar
process-this application is the available installation
walls
at
arbitrary
distances
cause
clutter
effects
and
increase
sufficient
range
resolution
accuracy,
cannot
Designed
multi-sensor
Doppler
radar
network
only.diverse
This, onradar
the one
hand, is
due there
to the robustness
tool.
A block
diagram
of
a singleand
sensor
module and
the be met in th
ing the
returns
from
is non-stationary
one of of
thethechal-2chine
the
noise level.
Further
challenges
the
GHz tocomponents
24.25 GHzisISM-band.
technology
and the
low cost
argumentsare
of the
electronic hardsignal24
processing
given in Fig. 3 showing the
lenges
for the signal
processing.
Multiple reflexions
at theFrom the viewpoint of hardware one of the limiting factors in
environment,
varying
shapes
and geometries
themachine
milling
ware. On the other
hand,
the available
space inofany
RF front-end, which includes the 24 GHz voltage controlled
wallstools
at
arbitrary
distances
cause
clutter
effects
and
increase
as
well
as
swarf
from
treatment
in
the
operating
zone.
this
application
is athe
installation
space in the(Tx)
matool is limited. This only permits additional components of
oscillator
(VCO),
90°available
hybrid coupler,
the transmitting
In
this
first
approach
the
system
development
concentrated
chine
tool.
A
block
diagram
of
a
single
sensor
module
andNetwork
the noise
level.
challenges
are the
small size
and Further
low complexity.
Furthermore,
thenon-stationary
large operand receiving
(Rx) 4-patch
antenna array
and the IQ
mixing
2 Designed
Multi-Sensor
Doppler
Radar
on
using
CW
radar
only.
This,
on
the
one
hand,
is
due
to
the
signal
processing
components
is
given
in
Fig.
3
showing
environment,
varying
shapes
andrapid
geometries
millingelement. Due to the homodyne mixing process the output of
ating temperature
range
and the
fluctuationof
of the
temperthe
robustness
of thewith
technology
and the lowtocost
arguments
the RF front-end,
which includescomplex
the 24 GHz voltage
conature
must
be
dealt
by
the
equipment
meet
the
high
the viewpoint
downconverted
A
tools as well as swarf from treatment in the operating zone. the module
Fromisthe
of
hardwareDoppler
one of signal.
the limiting
factors
◦ hybrid
of
the
electronic
hardware.
On
the
other
hand,
the
available
trolled
oscillator
(VCO),
a
90
coupler,
the
transmitdemands
on
linearity
of
frequency
ramps
in
frequency
modfrequency
gap
of
30
MHz
between
the
carrier
frequencies
is
The
system
development
concentrated
on
using
CW
radar
this
application
is
the
available
installation
space
in
the m
space
anyradar
machine
tool is
This to
only
permits
adting
(Tx) and
4-patch
antenna
arraybetween
and the
ulatedinCW
(FMCW)
or limited.
pulsed radar
provide
proper
introduced
by receiving
tuning the(Rx)
VCOs
to avoid
crosstalk
only.ditional
This, components
on the oneofhand,
due
thecomplexity.
robustness
of theIQ mixing
chine
tool. ADue
block
diagram
of amixing
singleprocess
sensorthemodule and th
small is
size
andtolow
Furelement.
to the
homodyne
technology and the low cost arguments of the electronic hardsignal processing components is given in Fig. 3 showing th
ware.Adv.
OnRadio
the other
hand,
the 2014
available space in any machine
RF front-end, which
includes the 24 GHz voltage controlle
Sci., 12,
35–41,
www.adv-radio-sci.net/12/35/2014/
tool is limited. This only permits additional components of
oscillator (VCO), a 90° hybrid coupler, the transmitting (Tx
small size and low complexity. Furthermore, the large operand receiving (Rx) 4-patch antenna array and the IQ mixin
ating temperature range and the rapid fluctuation of temperelement. Due to the homodyne mixing process the output o
T. J.et
Wächter,
U. Siart, T. F. Doppler
Eibert andradar
S. Bonerz:
Doppler Radar for Machine Tools
T. J. Wächter
al.: Multi-sensor
for Multi-Sensor
machine tools
Analog Baseband Processing
RF Front-End
Tx/Rx
Patch-Ant
3
37
Algorithm for Distance Estimation
Digital Signal Processing
Stereo-Audio
Codec
LO
active
90°
Hybrid
LPF
RF
balanced
IQ-Mixer
fc = 20 kHz
24 GHz
A
including
digital LPF,
Downsampling (M ),
Windowing,
D
fs = 48 kHz
Radix-2-FFT,
Spectral Estimation,
Distance Estimation, etc.
VCO
Figure 3. Block
diagram of the radar system and signal processing components of a single module.
Fig. 3. Block diagram of the radar system and signal processing components of a single module.
Table 1.of
Overview
several system
parameters
of the
prototype.
Table 1. Overview
severalofsystem
parameters
of the
prototype.
system parameter
system parameter value value
supply voltage +5 V +5 V
supply voltage
power consumption
4×
power consumption
∼ 4 × ∼0.6
W0.6 W
center frequency
24.125 GHz
center frequency
24.1258.6
GHz
antenna gain
dBi
antenna gain
transmit power 8.6 dBi+15 dBm (EIRP)
half-power beamwidth
80° (Azimuth)
transmit power
+15 dBm
(EIRP)
34° (Elevation)
half-power beamwidth 80◦ (Azimuth)
IF bandwidth
3 Hz to 20 kHz
34◦ (Elevation)
IF gain
40 dB
IF bandwidth
3
Hz
to
20 dBm
kHz
receiver sensitivity
−80
IF gain
40 dB (B = 20 kHz, RIF = 1 kΩ)
Doppler shift
160 Hz/(m/s)
receiver sensitivity
−80 dBm
sampling frequency
48 kHz
(B = 20
kHz, R = 1k)
ADC resolution
16 bit −1 IF
Doppler shift
160 Hz/(m s )
sampling frequency
48 kHz
ADC resolution
16 bit
the single modules of the radar network. Interfering downconversion is then filtered out. The analog input stage consists of an active anti-aliasing low-pass filter (LPF) with a
3 dB cutoff frequency of 20 kHz, based on a low-noise operamplifier.
input impedancecomplex
is 1 kΩ. This
configoutput of theational
module
is theThe
downconverted
Doppler
uration a receiver sensitivity of −80 dBm. A standard stereosignal. A frequency
of 30
between
thequadrature
carrier freaudio codecgap
is used
for MHz
converting
the analog
sigquencies is introduced
by
tuning
the
VCOs
to
avoid
crosstalk
nal to a digital IQ data stream at a sampling frequency
of
Some system
of the Interfering
radar module
between thefsingle
modules
of the parameters
radar network.
s = 48 kHz.
and theisinput
are given
Table
1, compare
down-conversion
thenstage
filtered
out.inThe
analog
inputRFbeam
stage
Microwave GmbH (2011).
consists of an As
active
anti-aliasing
low-pass
filter
(LPF)
with
a
the radar system acts in severe environmental condi3 dB cutoff tions
frequency
of
20
kHz,
based
on
a
low-noise
operwith fluid, drizzle, heat etc., hermetically sealed modules areThe
necessary.
enclosuresisof1the
radar
front-end
ational amplifier.
input The
impedance
k.
This
config-in
Fig.a2receiver
are made from
polyethylene
and dBm.
are closed
and sealed
uration allows
sensitivity
of −80
A standard
the final application. Additionally, they increase the flexstereo-audioforcodec
is used for converting the analog quadraibility for positioning and tilting of the modules. Coverage
ture signal to a digital IQ data stream at a sampling frequency
of fs = 48 kHz. Some system parameters of the radar module and the input stage are given in Table 1, compare RFbeam
Microwave GmbH (2011).
As the radar system acts in severe environmental conditions with fluid, drizzle, heat etc., hermetically sealed modules are necessary. The enclosures of the radar front-end in
Fig. 2 are made from polyethylene and are closed and sealed
for the final application. Additionally, they increase the flexibility for positioning and tilting of the modules. Coverage
simulations based on deterministic ray-tracing showed that
www.adv-radio-sci.net/12/35/2014/
simulations
on deterministic
ray-tracing
that of the sur15◦ tiltingbased
of the
modules gives
best showed
coverage
15° tilting of the modules gives best coverage of the surrounding space around the tool (Azodi et al., 2013).
rounding space around the tool (Azodi et al., 2013).
Theinput
input
stage
is into
builta metal
into ashielding
metal shielding
The
stage
is built
enclosure. Itenclosure. It
supposed
to protect
the circuit
only
against electromagisissupposed
to protect
the circuit
not onlynot
against
electromagnetic
but also
the harshthe
environmental
neticinterference
interference
but against
also against
harsh environmental
conditions
in machine
tools. tools.
Experiments
showed that
inter- that interconditions
in machine
Experiments
showed
ference from power supplies and switching electrical actuaference
power supplies,
switching
electrical actuators
tors
as wellfrom
as mechanical
vibrations are
there to effectively
and mechanical
vibrations
are thereinterference
to effectively
increase
increase
the noise level.
The high-frequency
can
be
after data
by digitalinterference
filtering as de- can be supthesuppressed
noise level.
Theacquisition
high-frequency
scribed
in the
nextdata
section.
The low frequency
components
pressed
after
acquisition
by digital
filteringinas described
the sub-kilohertz range remains as superimposed interfering
in the next section. Low frequency components in the subsignals.
kilohertz range remains as superimposed interfering signals.
3 Implemented Digital Signal Processing Stage
As
radar modules digital
are basedsignal
upon aprocessing
homodyne archi3 the
Implemented
stage
tecture, the IQ mixer output appears in baseband centered
around DC. The analog bandwidth of the active LPF is from
the20radar
modules
areneeded
based
upon
a homodyne
archi3As
Hz to
kHz. This
covers the
range
of relative
vetecture,
the
IQ
mixer
output
appears
in
baseband
centered
locities especially for slowly moving targets.
After digital
the bandwidth
signal is buffered
andactive
the DCLPF is from
around
DC. conversion
The analog
of the
bias
is removed.
NextThis
a decimation
stageneeded
follows. range
It consists
3 Hz
to 20 kHz.
covers the
of relative veof a digital LPF and subsequent downsampling by factor of
locities
especially
for
slowly
moving
targets.
M . Figure 4 illustrates the preprocessing steps between ADC
conversion
buffered
andAfter
spectraldigital
frequency
estimation.the
Thesignal
digitalisLPF
is a 4th and the DC
order
type Next
I filter awith
0.25 dB ripple
and follows.
fc =
bias Chebyshev
is removed.
decimation
stage
It con160Hz
cutoff
frequency.
equates todownsampling
the Doppler
sists of
a digital
LPFThis
andcutoff
subsequent
by facshift due to the highest expected relative velocity of 1 m/s.
tor of M. Figure 4 illustrates the preprocessing steps beThe filter process reduces the noise contribution, hence the
tween ADC
spectral
frequency
estimation. The digital
sensitivity
level isand
decreased
down
to −101 dBm.
Eachisobservation
window
has lengthtype
N T Iseconds
and is0.25 dB ripLPF
a 4th order
Chebyshev
filter with
weighted
a window
decimation.
T =cutoff
1/fs equates to
ple andwith
fc =
160 Hzfunction
cutoffafter
frequency.
This
is the sampling period and N is the number of sampling
the Doppler shift due to the highest expected relative velocity
points. The−1
decimation process does not change the observa-
of 1 m s . The filter process reduces the noise contribution,
hence the sensitivity level is decreased down to −101 dBm.
Each observation window has length N T seconds and is
weighted with a window function after decimation. T = 1/fs
is the sampling period and N is the number of sampling
points. The decimation process does not change the observation period. The new sampling period is TM = MT = M/fs
and the number of sampling points is N/M. A Kaiser window with 80 dB sidelobe suppression has proven sufficient
selectivity and low spectral leakage. The Kaiser window
shape parameter value was chosen as α = 3.422.
Adv. Radio Sci., 12, 35–41, 2014
4
38
T. J. Wächter, U. Siart, T. F. Eibert and S. Bonerz: Multi-Sensor Doppler Radar for Machine Tools
ui (k)
T. J. ′Wächter
et al.:
Multi-sensor
Doppler
radar
for machine
T. J. Wächter, U. Siart, T. F. Eibert
and S. Bonerz:
Multi-Sensor
Doppler
Radar for
Machine
Tools
4
k = 0, 1, 2, ..
.., N -1
u(k)
ui (k)
from ADC
fs
buffer
+
fs = 48 kHz
k = 0, 1, 2, ..
.., N -1
NT
u(k)
from ADC
·j
fs = 48 kHz
k = 0, 1, 2, ..
.., N/M-1
+
T = 1/fbuffer
s
uq (k)
·j
uq (k)
NT
T = 1/fs
LPF
Chebyshev
LPF
n=4
fc = 160 Hz
k′ M
= 0,↓1, 2, ..
.., N/M-1
fs
Chebyshev
n=4
fc = 160 Hz
u′ (k′ ),
u′ (k′ ),
sample
M ↓rate
reduction
ν = −L/2, ..
.., L/2-1
′
′
uw (k )
fs
M
νctr
ν = −L/2,
..
Ŝ(ν)
.., L/2-1
fs
M
tools
u′w (k′ )
Ŝ(ν)short time
Kaiser
window
sample rate
reduction
Kaiser
window
Fourier
transform
short time
Fourier
transform
νctr
band-limited
spectral
centroid
band-limited
spectral
centroid
Fig. 4. Preprocessing of complex signal from one single path.
Figure 4. Preprocessing
of complex signal from one single path.
Fig. 4. Preprocessing of complex signal from one single path.
Adv. Radio Sci., 12, 35–41, 2014
−50
−60
50
50
−70
0
−80
0
−50
−90
−50
−100
−100
−100
0.5
1
1.5
Time t in s
2
2.5
−110
Power Spectral Density S in dBm/Hz
−50
100
100
−150
−40
−40
−60
−70
−80
−90
(dBm/Hz)
Power Spectral Density S in
dBm/Hz
150
150
Frequency
in Hz
Frequency
f(Hz)
inf (Hz)
f(Hz)
tion period. The new sampling period is TM = M T = M/fs
tion
period.
The
sampling
period
T. M
M Tof
= winM/fs
Frequency
resolution
is new
determined
byN/M
theis duration
oband the number
of sampling
points is
A=Kaiser
and the number of sampling points is N/M . A Kaiser winservation.
The
number
of
sampling
points
for
each
segment
dow with dow
80 dB
sidelobe suppression has proven sufficient
with 80 dB sidelobe suppression has proven sufficient
areselectivity
kept to N
∼ 2nlow
for
utilization
ofleakage.
theThe
efficient
Radix-2and
spectral
leakage.
Kaiser
window
selectivity
and
low spectral
The
Kaiser
window
FFT
algorithm.
To
extract
Doppler
shift
and
relative
shape
parameter
value
was
chosen
as
α
=
3.422.
shape parameter value was chosen as α = 3.422. velocFrequency
resolution
is determined
byfrom
the
duration
ofobobity, the
short time
Fourier
spectrum
is derived
eachof
data
Frequency
resolution
is determined
by the
duration
servation.
The number
of sampling
points
each
segment
servation.
Theestimator
number
of nsampling
points
for for
each
segment
segment
by the
2 for utilization of the efficient Radix-2are kept
toareNkept
∼ 2ton Nfor∼ utilization
of the efficient Radix-2L−1
and relative velocX FFT algorithm. To extract Doppler
shiftshift
FFT
algorithm.
To
extract
Doppler
relative
veloc0
0
0
the)short
Fourier/L
spectrum
derived
from each
data
uity,
exp time
−j 2πνk
, isand
(2)
Ŝ(ν) =
w (k
ity, the
short
time
Fourier
spectrum
is
derived
from
each
data
segment
by
the
estimator
k 0 =0
segment by the estimator
L−1
Xand u0 (k 0 ) is the preprocessed signal.
where k 0 is an
integer
Ŝ(ν)
=
u′w (k ′ )wexp (−j2πνk ′ /L) ,
(2)
L−1
The Fourier spectrum
is
′
′ k ′=0 calculated at
′ discrete points ν, where
Ŝ(ν) =
uw (k ) exp (−j2πνk /L) ,
(2)
ν = −L/2, ′. where
. . , L/2
1 and
L and
= N/M.
k′ −
is an
integer
u′w (k ′ ) is the preprocessed signal.
k =0
FrequencyThe
estimation
is based
on computation
the bandFourier spectrum
is calculated
at discreteof
points
ν, where
′
′
where
k ′ isν =
an
integer
)L
isbandwidth
the
preprocessed
signal.
−L/2,
. .centroid.
.,and
L/2u−w1(k
and
=
N/M
.
width
limited
spectral
The
for calculaspectrum
is calculated
at
points
ν,the
where
estimation
is based
on
computation
of
bandtionThe
is Fourier
limitedFrequency
to a window
which
is discrete
identical
to the
LPF
width
limited
spectral
centroid.
The
bandwidth for calculaν
=
−L/2,
.
.
.,
L/2
−
1
and
L
=
N/M
.
passband, excluding
a small guard
intervalisaround
DC.
Extion estimation
is limited toisabased
window
identical
to the
LPF
Frequency
onwhich
computation
of the
bandploiting
the passband,
sign of the
received
Doppler
shift
provided
excluding a small guard interval around DC.by
Exlimited
spectral
centroid.
The bandwidth
forprovided
calculathewidth
IQ mixer
architecture
integration
limits can
set toby
ploiting
the signthe
of the
received Doppler
shift be
is limited
a νwindow
which
iswhere
identical
tocan
thebe LPF
theindices
IQ to
mixer
architecture
the
integration
limits
set to
thetion
frequency
<ν<
νmax
all
indices
are
min
passband, the
excluding
aindices
smallνguard
interval
around
DC.
Exfrequency
<
ν
<
ν
where
all
indices
are
min
max
positive for positive Doppler shifts and negative for negative
positive
DopplerDoppler
shifts andshift
negative
for negative
ploiting the
sign for
of positive
the received
provided
by
Doppler shifts.
The shifts.
spectral
centroid
is thenis calculated
only
Doppler
Thethe
spectral
centroid
then can
calculated
the IQ mixer
architecture
integration
limits
be setonly
to
in the frequency
interest
by by
in theinterval
frequencyofinterval
of interest
the frequency indices νmin < ν < νmax where all indices are
2
ν
max
νP
maxfor positive
2 Doppler
positive
P
ν Ŝ(ν) shifts and negative for negative
ν Ŝ(ν)
ν=νmin
Doppler
shifts.
The
spectral
is then calculated only
.
(3)
ν=νminνctr = νmax 2centroid
P. interest by
νctrin=the νfrequency
(3)
interval
of
Ŝ(ν)
max
2
P
min
2
Ŝ(ν) ν=ν
ν
max
the summation
ν=νminLimiting
in Eq. (3) reduces noise to a minν Ŝ(ν)
ν=νimum
min
and prevents erroneous biased estimation. In case of
νctr = theνmax
.
(3)
Limiting
summation
in
Eq.
(3)
reduces noise to a min2
multi-target
scenarios
different methods must be utilized re
imum and prevents
erroneous
biased
estimation.
In
case
of
Ŝ(ν)
garding more than one spectral maximum. But this case is
ν=νmin
multi-target
scenarios
different
methods
must
be utilized
not
discussed
in this paper
since first
investigations
andreperformance
testsspectral
assume
that
there
is a single
dominant
Limiting
the
summation
in Eq.
(3)
reduces
noise
a target.
mingarding
more
than
one
maximum.
But
thistocase
is
From
the value
fˆd =
νestimation.
calculated.
ctr fs /(LM ) is
and prevents
erroneous
In
case
notimum
discussed
in
thisνctr
paper
sinceofbiased
first
investigations
and
per-of
An estimate for the relative velocity can be obtained with the
multi-target
scenarios
different
methods
must
be
utilized
reformance
tests
assume
that
there
is
a
single
dominant
target.
well-known equation v̂rel = fˆd λ/2, where λ = c0 /fc is the
ˆ
garding
than
one
spectral
maximum.
But
this
case
From
νctrmore
the
value
of
f
=
ν
f
/(LM)
is
calculated.
An
ctr s
wavelength of thed corresponding
carrier frequency fc . is
not discussed
this paper
since can
first be
investigations
and the
perestimate
for the inrelative
velocity
obtained with
ˆd λ/2,is where
formance tests
assume
a singleλdominant
target.
well-known
equation
v̂relthat
= fthere
= c0 /fc is
the
From νof
thecorresponding
value of fˆd =carrier
νctr fs /(LM
) is f
calculated.
ctrthe
wavelength
frequency
c.
An estimate
for the
relativespectrogram
velocity can be
obtained
withthe
the
5 shows
a typical
acquired
from
Figure
well-known
equation
= fˆd λ/2,
where with
λ = cone
is the
rel front
0 /fcsingle
observation
of the
spacev̂in
of a sensor
wavelength
of This
the corresponding
carrier
frequency
fc .
dominant
target.
example is based
on real
measurements
performed with the prototype shown in Fig. 2. In this case the
sensor platform is centrally arranged to the sphere and first
approaches to it and afterwards departs from it. The spectrogram in Fig. 5 shows a distinct main frequency component.
−100
−110
−150
1.5
2
0.5
1
2.5
Fig. 5. Doppler spectrogram for a closing and receding movement
Time t (s)
in (s)
of the sensor platform. A metallic sphere serves as reflecting object.
Figure 5. Doppler spectrogram for a closing and receding moveFig. of
5. Doppler
spectrogram
formetallic
a closing
and receding
ment
the sensor
platform. A
sphere
serves asmovement
reflecting
5 shows
a typical
spectrogram
from
the
of Figure
the sensor
platform.
A metallic
sphereacquired
serves as
reflecting
object.
object.
observation of the space in front of a sensor with one single
dominant target. This example is based on real measurements
performed with the prototype and equipment shown in Fig. 2.
Short
phases
of
acceleration
and
deceleration
beginIn this
case5the
sensor
centrally
arranged
toatthethe
Figure
shows
aplatform
typicalisspectrogram
acquired
from
the
ning
and
the
end
and
a
turning
point
can
be
identified.
sphere
and
first
approaches
to
it
and
afterwards
departs
from
observation of the space in front of a sensor with one single
it.A
The
spectrogram
infor
Fig.
5 shows a distinct
main frequency
critical
pointThis
unambiguous
detection
tracking of
dominant
target.
example
is based
on realand
measurements
component.
Short
phases
of
acceleration
and
deceleration
at observobjects
are with
spurious
frequencyand
components
that are
performed
the
prototype
equipment
shown
the beginning and the end and a turning point in the middle in Fig. 2.
able
in Fig.
artifacts
arise
from IQ arranged
imbalance.
In this
case5.theThese
sensor
platform
is centrally
to The
the
can
be identified.
origins
of
signaltodistortion
aretracking
fabrication
tolerA critical
point
for
unambiguous
detection
and
of
sphere
andthis
firstanalog
approaches
it and afterwards
departs
from
objects
frequency
that are observances
thespurious
Schottky
theatransmission
in the
it. Theofare
spectrogram
indiodes
Fig. components
5 and
shows
distinct
mainlines
frequency
able instage.
Fig. 5. Shifts
These artifacts
arise fromofIQthe
imbalance.
The
mixer
or distortions
diode
characteristic
component.
Short
phases
of acceleration
and deceleration
at
origins of this analog signal distortion are fabrication toleron
the
one handand
andthe
slightly
unequal
power
division
ormiddle
phase
the
beginning
end
and
a
turning
point
in
the
ances of the Schottky diodes and the transmission lines in the
deviation
from ideal dividers on the other hand are the consecan be identified.
quences.
Thispoint
causes
between
the output
signalsof
of
A critical
forvariations
unambiguous
detection
and tracking
the
two
mixing
units
which
results
in
degraded
signal
qualobjects are spurious frequency components that are observity.
Like
clutter,
spurious
peaksarise
potentially
the false
able
in Fig.
5. These
artifacts
from IQincrease
imbalance.
The
alarm
rate
considerably.
Especially,
if
solids
with
fluctuating
origins of this analog signal distortion are fabrication tolerradar
(RCS)
have
detected, e.g.
cuboids
ancescross
of thesection
Schottky
diodes
andto
thebetransmission
lines
in the
or cylinders, image components will influence the algorithm
performance of the decision unit when this special problem
remains unconsidered. This issue is investigated in detail in
future work.
www.adv-radio-sci.net/12/35/2014/
T. J. Wächter, U. Siart, T. F. Eibert and S. Bonerz: Multi-Sensor Doppler Radar for Machine Tools
T. J. Wächter et al.: Multi-sensor Doppler radar for machine tools
Table 2. Simulation results for the standard deviation: fs = 48 kHz,
Table
Simulation
fd =2.25.6
Hz, SNRresults
= 10 for
dB.the standard deviation: fs = 48 kHz,
fd = 25.6 Hz, SNR = 10 dB.
10 0
N = 1024
N = 2048
N = 4096
var{fˆd } (Hz2 )
10-1
10-2
5
39
NN
1024
1024
2048
2048
4096
4096
3σ/Hz
3σ/Hz 0.8161
0.8161 0.2999
0.2999 0.1190
0.1190
3σ3σ
/Hz 0.7662
crb
0.7662 0.2709
0.2709 0.0958
0.0958
crb /Hz
10-3
10-4
10-5
0
5
10
15
SNR (dB)
20
25
30
Figure 6. Frequency estimation simulation results for a single comFig.sinusoid
6. Frequency
estimation
simulation
resultsand
forthe
a single
complex
with unknown
amplitude
and phase
theoretical
plex
sinusoid
with
unknown
amplitude
and
phase
and
the
theoretibounds for estimation variances. fs = 48 kHz, fd = 25.6 Hz.
cal bounds for estimation variances. fs = 48 kHz, fd = 25.6 Hz.
4 Single target scenario
mixer stage. Shifts or distortions of the diode characteristic
onathe
one hand
slightlywith
unequal
division
or phase
In
single
targetand
scenario
one power
dominant
scatterer
at
T
deviation
dividers
on
the
other
hand
are
the
conseposition
r 0from
= (xideal
,
y
,
)
the
observed
discrete-time
Doppler
0 0
quences.
causesbyvariations
between
the output
shift
signalThis
detected
the ith sensor
is modeled
by signals of
the two mixing units whichresults in degraded signal quali Like clutter,
i
i
i
spurious
potentially
increase the false
uity.
(k) = Ai exp j(
) +w
(k),
(4)
d k + ϕpeaks
alarm rate considerably. Especially, if solids with fluctuating
where
normalized
frequency
and w
radar 
cross
section
(RCS)
have toDoppler
be detected,
e.g. cuboids
d=ω
d T is the
isorband-limited
measurement
and processing
noise.
cylinders, image
components
will influence
theMeasurealgorithm
ments
reveal that
w isdecision
Gaussian
white
noise
the problem
normal
performance
of the
unit
when
thiswith
special
distribution
remains unconsidered. This issue is investigated in detail in
future work.
p(w) ∼ N (0, C),
(5)
where
C is the
noiseScenario
covariance matrix.
4 Single
Target
In this application the parameters A, ωd and ϕ are all unknown.
In thetarget
following
the index
is omitted.
Thescatterer
Cramer-at
In a single
scenario
with ione
dominant
T
Rao-Bound
on the
minimum achievposition r0(CRB)
= (x0 ,isy0a)lower
the bound
observed
discrete-time
Doppler
able
depending
signalis properties.
shiftvariances
signal detected
by theoniththesensor
modeled byIn (Rife
and Boorstyn, 1974) results for
single com a discrete-time
i
i
ui (k)
= Ai exp
) +CRB
wi (k),
(4)
plex
sinusoid
can j(Ω
be found.
on the variance of the
d k + ϕThe
ˆ
Doppler frequency estimate fd = ω̂d /(2π) is given by
where Ωd = ωd T is the normalized Doppler frequency and w
n o
is band-limited
measurement
and processing noise. Measure12σN2
ˆ
=
var
f
, noise with the normal
(6)
d
ments reveal that2 w2 is2Gaussian
white
(2π ) A T N(N 2 − 1)
distribution
where σN2 is the variance of the noise. The variance of fˆd dep(w) ∼ N (0, C),
(5)
pends on the SNR = A2 /σN2 and the observation time N T
which
a trade-off
between accuracy and
where is
C determined
is the noise by
covariance
matrix.
agility
of
signal
processing
algorithm.
Simulation
In this application the parameters A,
ωd and ϕresults
are allfor
unaknown.
noisy complex
sinusoid
with
varying
SNR
and
various
In the following the index i is omitted. The Cramernumbers
of sampling
are illustrated
in Fig. achiev6, toRao-Bound
(CRB) is apoints
lowerNbound
on the minimum
gether
with
the
theoretical
lower
bounds
given
by
Eq.
(6).
able variances depending on the signal properties. In (Rife
ForBoorstyn,
low SNR1974)
the frequency
is distorted
and
and
results forestimation
a discrete-time
single comthe
variance
rapidly
increases.
In
Tab.
2
the
values
for
three
plex sinusoid can be found. The CRB on the variance of the
standard
of thefˆestimated
mean
frequency
Doppler deviations
frequency 3σ
estimate
is given
by are
d = ω̂d /(2π)
given. This range includes 99.7 % of all estimates.
n o
2
12σN
Thefˆobtained
Doppler
frequency ,shift depends on the
var
(6)
d =
2
2
2
(2π) A TviaNthe
(N 2inner
− 1)product of the distance
sensor-target geometry
www.adv-radio-sci.net/12/35/2014/
2−s) and the velocity vector v = (vx , vy , vz )T . The
vector
where(rσ0N
is the variance of the noise. The variance of fˆd de2
2
equation
theSNR
general
case withtime
sensor
pends onforthe
=T Athree-dimensional
/σN
and the observation
NT
atwhich
position
is a trade-off between accuracy and
x , sy , sz ) by
is (s
determined
agility of signal
processing algorithm. Simulation results for
2 (r − s)T v
noisy 0complex, sinusoid with varying SNR and various
fda =
(7)
λ krof
sk
0 −sampling
numbers
points N are illustrated in Fig. 6, togetherk·k
with
the theoretical
lowerEuclidean
bounds given
in Eq.
(6).
where
represents
the standard
vector
norm.
For low SNR the frequency estimation is distorted and
4.1
Data model
the variance
rapidly increases. In Tab. 2 the values for three
standard deviations 3σ of the estimated mean frequency are
Ingiven.
this application
a special99.7
kind
observation
This range includes
% of
of all
estimates.scenario
arises.
Several
sensors
are
closely
spaced
a maneuverThe obtained Doppler frequency shiftondepends
on the
able
platform
monitoring
the
space
in
front
with
onedistance
domsensor-target geometry via the inner product of the
scenario
with
sensorT
inant
scatterer.
Figure
vector
(r 0 − s)
and 7theillustrates
velocity the
vector
v = (v
x , vy , vz ) .
platform
and
object
inside
the
closed
machine.
The
platform
The equation for the general three-dimensional case with
typically
with
on straight-lined traT
sensor atmoves
position
(sxconstant
, sy , sz )velocity
is
jectories.
Compilation
ofTEq.
v (7) for a radar network with several
2 (r 0 − s)
,
f
=
d
distributed
sensors
results
in a system of nonlinear equations(7)
λ kr − sk
0
where k·k represents the standard Euclidean vector norm.
f d = A(ξ ) + w.
(8)
4.1 Data Model
with the observation matrix A(ξ ) which contains the
and the
vectorscenario
ξ=
the
model
of Eq. a(7)special
In this
application
kind parameter
of observation
T
(x,
y,
z,
v
,
v
,
v
)
for
the
general
three-dimensional
case.
x
y
z
arises. Several sensors are closely spaced on a maneuverable
The
number
unknowns
is reduced
to with
four one
as the
twoplatform
andofmonitor
the space
in front
dominant
∗ the
dimensional
case
is
considered.
To
find
the
optimal
ξ
scatterer. This scenario is illustrated in Fig. 7 with the sensor
constrained
minimization
problem
Bjoerk,
1996),
platform and
an object inside
the(e.g.,
closed
machine.
The platform typically
minimize
F (ξ ) moves with constant velocity on straight-lined
ξ
trajectories.
for. . .a, p
radar network with several
suchCompilation
that g(ξ ) ≤of
b` ,Eq.`(7)
= 1,
(9)
distributed sensors results in a system of nonlinear equations
has
to be
solved, where F (ξ ) is the cost function and g(ξ )
of the
form
contains linear and nonlinear constraints for maximum disf d =between
A(ξ) + sensor
w.
tances
and object and maximum velocities in(8)
all directions. To solve this nonlinear minimization problem
with
the aobservation
matrix rA(ξ)
which contains the
and
to find
solution for position
0 and velocity of the platthe v,model
of Eq.or(7)
and the parameter
vector ξA=
form
Newton-type
Gauss-Newton
method is applied.
(x, y, z, vx ,problem
vy , vz )Tisfor
the general
three-dimensional
case.
fundamental
to find
the global
minimum. For cost
The number
of unknowns
is reduced
four asthethe
twofunctions
and their
Jacobian with
several to
minima,
accudimensional
casestrongly
is considered.
findinitial
the optimal
ξ ∗ the
racy
of the results
depend To
on the
guess. More
constrained
minimization
problem
(e.g.,
Bjoerk,
1996),
advanced
methods
are necessary
which
find
the global
minimum, e.g. grid search methods. These account for higher
minimize F
(ξ)
computing
capacity
at the beginning of a new trajectory.
ξ
Then, the previously found solutions can be used recursively.
such that g(ξ) ≤ bℓ , ℓ = 1, . . . , p
(9)
The problem is investigated in detail in future works.
Adv. Radio Sci., 12, 35–41, 2014
6 6
T. J.
J. Wächter,
Wächter, U.
Eibert
andand
S. Bonerz:
Multi-Sensor
Doppler
RadarRadar
for Machine
Tools Tools
T.
U.Siart,
Siart,T.T.F.F.
Eibert
S. Bonerz:
Multi-Sensor
Doppler
for Machine
40
T. J. Wächter et al.: Multi-sensor Doppler radar for machine tools
0.5
0.5
object
space
object
x
x
y
machine
enclosure
machine
enclosure
y
sensor
platform
sensor
platform
estimated vx (s1)
estimated vx
estimated vx (s2)
vx
estimated estimated
vx (s3)
vx
estimated estimated
vx (s4)
estimated
vx
machine data
vx
0.4
(s1)
(s2)
(s3)
(s4)
machine data vx
0.3
Estimated velocity vx (m/s)
observed
observed
space
Estimated velocity vx (m/s)
0.4
0.3
0.2
0.2
0.1
0
−0.1
0.1
0
−0.2 −0.1
−0.3 −0.2
−0.4 −0.3
−0.5 −0.4
0
−0.5
0.4
0.8
0.8
1.6
2
2.4
1.2
2
1.6
Time
t
(s)
Figure 8. Estimated velocity from Doppler shift measurements for
0
0.4
1.2
Time t (s)
2.4
Fig.
8. Estimated
from platform.
Doppler shift measurements for an
an
axial
movementvelocity
of the sensor
Fig. 7. Illustration of a typical scenario of the application: One domaxial movement of the sensor platform.
Figure
7. Illustration
a typical
scenario
of the application:
inant
scatterer
at fixedofposition
and
the maneuverable
sensor One
platFig. 8. Estimated velocity from Doppler shift measurements for an
dominant
fixedArrows
position
and
the
maneuverable
sensor
Fig.
7. Illustration
of at
a typical
scenario
ofout
thethe
application:
One
domform
with scatterer
radar modules.
point
typical rectilinear
axial movement of the sensor platform.
platform
withatradar
modules.
Arrows
point
out the typicalsensor
rectilin-platReferred to the coordinate system in Fig. 1 the velocimotions
during
manual
operation.
inant
scatterer
fixed
position
and the
maneuverable
ear with
motion
during
manual operation.
form
radar
modules.
Arrows point out the typical rectilinear tiy components vy and vz of the platform are both equal to
by overlapped data segments. Measurement and reference
zero
the y andand
z coordinates
8
data and
for position
speed of theremain
sensorconstant.
platformFigure
with the
shows
the
obtained
velocity
from
the
internal
machine’s
consame
rate of 4data
ms are
used for performance
testsand
withreference
byupdate
overlapped
segments.
Measurement
trol
unit
(solid graph)
and the
estimated
velocity
vx (dashed
the data
prototype.
Reference
data
available
from
the
machinewith the
for
position
and
speed
of
the
sensor
platform
and
dotted
from theexact
dataposition
of each of
the
four sensors.
toolsame
controlgraphs)
unit provides
and
velocity
data.
rate of
4 ms are
used
for sensor
performance
TheResults
smallupdate
time
shifts
between
the
various
streamstests with
of the following scenario are presented: Comparathe prototype.
Reference procedure.
data available
fromvalue
the machine
come
data
acquisition
The exact
ble to from
Figs. the
1 and
2, the
sensor platform is equipped
with four
tool
control
unit
provides
exact
position
and
velocity
issensors.
known The
and movement
can be compensated.
At platform
the beginning
a reced- data.
of the sensor
is bidirectioning
isofidentified
sign)Awith
continuously
Results
the
following
scenario
are
presented:
Comparaallymovement
(i.e.
back and
forth)
on(negative
an axial
path.
metal
sphere with
increasing
velocity
up 2,
to the
a deceleration
phase isaround
0.35 with four
ble
to
Figs.
1
and
sensor
platform
equipped
a diameter d = 15 cm serves as scattering object. Its position
to 0.45
s. Then,
turning point
is reached
and the movesensors.
Thethemovement
of the
sensor
platform
is bidirectionis fixed
and aligned
to the center
of the
platform.
As the
cirmentally
with
positive
acceleration
and
velocity
follows
(pos(i.e.of
back
and forth)
on an
axial
path.
metal sphere with
cumference
the sphere
is much
larger
than
theA
wavelength,
itive sign). The movement pattern is repeated three times.
diameter
= 15 is
cminserves
as scattering
the aRCS
of the dsphere
the optical
region andobject.
equal Its
the position
Against the background
of a dynamic scenario with evercross-section
areaaligned
d2 π/4 of
the
sphere.
is
fixed
and
to
the
center
of
the
platform.
As the circhanging velocity, the estimates are in very good agreement
Referred
to the
coordinate
system
inlarger
Fig. 1than
thethe
velocicumference
of
the
sphere
is
much
wavelength,
with the true velocity in Fig. 8. In this scenario velocities of
tiy components
vthe
vz ofisthe
are both equal
y and
RCS
sphere
in platform
themoptical
andtoequal the
0.47the
m s−1
andofaccelerations
up to
6.5
s−2 areregion
reached.
zerocross-section
and the y- andarea
z-coordinates
remain
constant.
Figure
8
2
d be
π/4
of the sphere.
Minor discrepancy can
identified
at the turning points
shows the obtained velocity from the internal machine’s conto the
coordinate
systembecomes
in Fig.small.
1 the velociwhere Referred
the velocities
and change
in position
trol unit (solid graph) and the estimated velocity vx (dashed
Thistiy
is due
to the limited
frequency
resolution.
Frequencies
components
vy the
and
vz of
the platform
are both equal to
and dotted graphs) from
data
of each of the four
−1 sensors.
lower
thanand
11.7
Hzy-(corresponding
to ∼ 73.1
mm sconstant.
in this
zero
the
and
z-coordinates
remain
The small time shifts between the various sensor streamsFigure 8
system)
arethe
actually
mapped
to zero
due the
to lack
of accuracy
shows
obtained
velocity
from
internal
machine’s
concome from the data acquisition procedure. The exact value
of the
estimate.
Improvements
are
achieved
by
using
adaptrol unit
and theAtestimated
velocity
vx (dashed
is known
and(solid
can begraph)
compensated.
the beginning
a recedtive parallel analyzing of longer sequences and subsequent
dottedisgraphs)
from
the data
of with
eachcontinuously
of the four sensors.
ing and
movement
identified
(negative
sign)
adjustment of the position.
increasing
velocity
to a deceleration
phase
aroundsensor
0.35 s streams
The small
timeupshifts
between the
various
to 0.45
s.
Then,
the
turning
point
is
reached
and
the
movefrom
data acquisition
procedure. The exact value
4.3 come
Results
for diagonal
motion
ment
positive
acceleration
and velocity
(positive a recedis with
known
and can
be compensated.
Atfollows
the beginning
sign).
The
movement
pattern
is
repeated
three
times.
Against
movement
is aidentified
(negative
sign) iswith
continuously
As aing
further
scenario
two-dimensional
motion
investithe
background
of
a
dynamic
scenario
with
ever-changing
gated.
Figure 9 shows
the up
results
a diagonal approaching
increasing
velocity
to afor
deceleration
phase around 0.35 s
velocity,where
the estimates
innonzero.
very good
agreement
with the
motion
vyare
are
Using
the coordinate
x and the
to 0.45 s. vThen,
turning
point
is reached
and the movetrue
velocity
in
Fig.
8.
In
this
scenario
velocities
of
0.47
m/s
system
of with
Fig. 1,
the starting
position
of the
object follows
(sphere,
ment
positive
acceleration
and
velocity
(positive
2
and
accelerations
up
to
6.5
m/s
are
reached.
T
d =sign).
15 cm)The
is atmovement
(0.5 m, 0.5 m,
0) and
the constant
velocity
pattern
is
repeated
three
times.
Against
Minor
discrepancy
be identified
the turning
of the
sensor
platform can
is (−0.707
m s−1 ,at−0.707
m s−1 points
, 0)T .
thethe
background
of achange
dynamic
scenario
with ever-changing
where
velocities
and
in position
The
position
of the object
is represented
bybecomes
circles.small.
The
mation.
The
signal
streams
are stored
andachieved
available results
are
in
very
good
agreement
ence on
thereceived
value of N
T . Variable
update
rates are
Thisvelocity,
isfor
duesynthetic
tothe
the estimates
limited
frequency
resolution.
Frequencies
data (+) and for real measurement
data with the
motions during manual operation.
hasIntothebenext
solved,
where
F (ξ) is the
cost
and g(ξ)
section
measurement
data
of afunction
one-dimensional
contains
linear
and
nonlinear
constraints
for
maximum
dislinear motion are analyzed to show the accuracy of the fretances
between
sensor
and
object
and
maximum
velocities
in
The second
a twohasquency
to be estimation.
solved, where
F (ξ) isexample
the costinvestigates
function and
g(ξ)
all
directions.scenario. A nonlinear solver is used to obtain
dimensional
contains linear and nonlinear constraints for maximum disTo solve
this nonlinear
minimization
problem and
to find
position
estimates
from
synthetic
data.
tances
between
sensor
and
object and
andmeasurement
maximum velocities
in
a solution for position r0 and velocity of the platform v,
allNewton-type
directions. or Gauss-Newton method is applied. A funda4.2 Measurement
results for linear motion
To
solve
this nonlinear
minimization
problem
andfuncto find
mental
problem
is to find the
global minimum.
For cost
a solution
for
position
r
and
velocity
of
the
platform
This
section
provides
the
results
of
the
algorithm
applied
to v,
tions and their Jacobian 0with several minima, the accuracy
aofset
of
measurements.
The
measurements
are
done
with
the
Newton-type
or
Gauss-Newton
method
is
applied.
A
fundathe results strongly depend on the initial guess. More adin-house
developed
depicted
in
Fig.the
2. global
They
clarify
mental
problem
is are
to prototype
find
the global
minimum.
For cost
funcvanced
methods
necessary
which
find
miniquality
and
accuracy
of
the
algorithm
for
frequency
estimamum,
gridJacobian
search methods.
Theseminima,
account the
for accuracy
higher
tions
ande.g.
their
with several
tion.
The received
signal
streams
available
foradcapacity
atdepend
the
beginning
of aand
new
trajectory.
of computing
the results
strongly
onare
thestored
initial
guess.
More
off-line
post
processing.
To
obtain
sufficient
frequency
resoThen, methods
the previously
found solutions
canfind
be used
vanced
are necessary
which
the recursively.
global minilution
the processed
block size
isdetail
set toinNfuture
= 4096
data points.
The
problem
is
investigated
in
works.
mum, e.g. grid search methods. These account
for higher
This
results
a resolution
of 1/(NT
)≈
Hz during the
In the
nextinsection
measurement
data
of11.7
a one-dimensional
computing
capacity
at
the
beginning
of
a
new
trajectory.
post processing.
decimation
process
has no influence
on
linear
motion areThe
analyzed
to show
the accuracy
of the freThen,
the
previously
found
solutions
can
be
used
recursively.
the
value
of
N
T
.
Variable
update
rates
are
achieved
by
overquency estimation. The second example investigates a twoThe
problem
investigated
in detailsolver
in future
works.
lapped
data is
segments.
Measurement
and
reference
for
dimensional
scenario.
A
nonlinear
is used
todata
obtain
In
the
next
section
measurement
data
of
a
one-dimensional
position
and
speed
of
the
sensor
platform
with
the
same
upposition estimates from synthetic and measurement data.
date motion
rate of 4are
ms are
used fortoperformance
tests with of
thethe
pro-frelinear
analyzed
show the accuracy
totype.
Reference
data
available
from
the
machine
tool
conquency
estimation. The
second
investigates a two4.2 Measurement
Results
for example
Linear Motion
trol unit provides
exactAposition
and velocity
data.
dimensional
scenario.
nonlinear
solver is
used to obtain
Results
of
the
following
scenario
are
presented:
This section
provides
results of
themeasurement
algorithm Comparaapplied
position
estimates
fromthe
synthetic
and
data.to
1 and 2, the sensor
platform is equipped
Figs.
able
settoof
measurements.
The measurements
are donewith
withfour
the
sensors. The
movement
of the sensor
platform
is2.bidirectionin-house
developed
prototype
depicted
in
Fig.
They
clar4.2allyMeasurement
Results
for Linear
Motion
(i.e. back
forth)
on
path. Afor
metal
sphere with
ify quality
andand
accuracy
ofan
theaxial
algorithm
frequency
estiamation.
diameter
d
=
15
cm
serves
as
scattering
object.
Its available
position
The received signal streams are stored and
This
section
ofthe
theplatform.
algorithm applied
is fixed
andprovides
aligned
tothe
theresults
center
of
the cir- to
for
off-line
post
processing.
To obtain
sufficientAs
frequency
a set
of
measurements.
The
measurements
are
done
cumference
of
the
sphere
is
much
larger
than
the
wavelength,
resolution the processed block size is set to N = 4096with
datathe
the
RCS
of
the
sphere
is
in
the
optical
region
and
equal
the
in-house
developed
prototype
depicted
in
Fig.
2.
They
clarpoints. This results in
a resolution of 1/(N T ) ≈ 11.7 Hz dur2 π/4 of the sphere.
cross-section
area
d
ifying
quality
andprocessing.
accuracy The
of the
algorithm
for frequency
estithe post
decimation
process
has no influ-
for off-line post processing. To obtain sufficient frequency
resolution the processed block size is set to N = 4096 data
Adv. This
Radioresults
Sci., 12,
2014 of 1/(N T ) ≈ 11.7 Hz durpoints.
in a35–41,
resolution
ing the post processing. The decimation process has no influence on the value of N T . Variable update rates are achieved
true velocity in Fig. 8. In this scenario velocities of 0.47 m/s
and accelerations up to 6.5 m/s2 are reached.
www.adv-radio-sci.net/12/35/2014/
Minor discrepancy
can be identified at the turning points
where the velocities and change in position becomes small.
This is due to the limited frequency resolution. Frequencies
T. J. Wächter, U. Siart, T. F. Eibert and S. Bonerz: Multi-Sensor Doppler Radar for Machine Tools
T. J. Wächter et al.: Multi-sensor Doppler radar for machine tools
0.6
true position
synthetic data
measurement data
sensor position
0.5
x (m)
0.4
0.3
0.2
0.1
0
0.5
0.25
0
y (m)
−0.25
−0.5
Figure 9. Target localization close to the sensor platform. The initial
Fig. 9. Target localization close to the sensor platform. The initial
guess of the parameter vector for the iterative nonlinear solver is
guess of the parameter vector for the iterative nonlinear solver is
(0.91 m, 0.53 m, 0, −0.66 m s−1 , −0.33 m s−1 ,T0)T .
(0.91 m, 0.53 m, 0, −0.66 m/s, −0.33 m/s, 0) .
() are very similar and close to the real position of the oblower than 11.7 Hz (corresponding to ∼ 73.1 mm/s in this
ject.
system) are actually mapped to zero due to lack of accuracy
The algorithm is based on the approach of Chan and Jarof the estimate. Improvements are achieved by using adapdine (1990) which uses a special cost function involving the
tive parallel analyzing of longer sequences and subsequent
time derivative of the Doppler shift f˙d (rate of change). For
adjustment of the position.
further details the reader is referred to the original paper.
example
the absolute
errors between real and esti4.3In this
Results
for Diagonal
Motion
mated position are lower than 4 cm, what is already sufficient
for
tools. Further
investigations
As collision
a furtherwarning
scenarioinamachine
two-dimensional
motion
is investiare
in
progress
to
improve
reliability
and
flexibility
of the algated. Figure 9 shows the results for a diagonal approaching
gorithm
to
make
it
applicable
for
arbitrary
linear
motions.
motion where vx and vy are nonzero. Using the coordinate
system of Fig. 1, the starting position of the object (sphere,
d = 15 cm) is at (0.5 m, 0.5 m, 0)T and the constant velocity
5of the
Conclusions
sensor platform is (−0.707m/s, −0.707m/s, 0)T . The
position of the object is represented by circles. The results
This paper presented an implementation of a prototype sysfor synthetic data (+) and for real measurement data (⋄) are
tem that aims at a new application of 24 GHz CW radar techvery similar and close to the real position of the object.
nology in machine tools of collision detection and avoidThe algorithm is based on the approach of Chan and Jarance. Important aspects for the mechanical design, the RF
dine (1990) which uses a special cost function involving the
hardware, the components for the baseband
processing and
time derivative of the Doppler shift f˙d (rate of change). For
the elements of the developed algorithm for velocity estimafurther details the reader is referred to the original paper.
tion have been described. This first approach treats singleIn this example the absolute errors between real and estitarget scenarios in a two-dimensional space. For validation
mated position are lower than 4 cm, what is already sufficient
the case of linear motion has been investigated. Results from
for collision warning in machine tools. Further investigations
conducted measurements reveal very good agreement of veare in progress to improve reliability and flexibility of the allocity estimates with the reference data provided by the magorithm to make it applicable for arbitrary linear motions.
chine’s control unit. The application of a nonlinear solver
for position estimation in a two-dimensional motion scenario
showed
acceptably low position estimation errors. This pro5 Conclusions
totype system serves as the basis for further investigations
and
towards
a multi-sensorofradar
systemsysfor
Thisdevelopments
paper presented
an implementation
a prototype
fast
collision
detection
in
machine
tools.
Due
to
the
rather
tem that aims at a new application of 24 GHz CW radar techweak
sensitivity
of the
usedofmodules
the coarse
nology
in machine
tools
collisionand
detection
andDoppler
avoidresolution
due
to
short
observation
windows
the
of
ance. Important aspects for the mechanical design,effect
the RF
multiple
targets
and
multiple
reflections
has
not
been
conhardware, the components for the baseband processing and
sidered.
It is of
expected
that thisalgorithm
simple approach
is suitable
the elements
the developed
for velocity
estimafor
the
majority
of
collision
scenarios.
However,
specificasingletion have been described. This first approach treats
tion
the actualinfalse
alarm and missed
detection
rates retargetofscenarios
a two-dimensional
space.
For validation
quires further studies. Further topics for future work are ex-
www.adv-radio-sci.net/12/35/2014/
7
41
the case of linear motion has been investigated. Results from
tension
to three
dimensions,
thevery
question
of the minimum
conducted
measurements
reveal
good agreement
of venecessary
number
of sensors
for uniqueness
of the
locity estimates
with
the reference
data provided
bysolution,
the maand
theircontrol
optimum
positioning
around the
Although
the
chine’s
unit.
The application
of atool.
nonlinear
solver
observation
is veryinshort
in this application
the effect
of
for position time
estimation
a two-dimensional
motion
scenario
cross
section
fluctuations
also needs
further errors.
investigations.
showed
acceptably
low position
estimation
This prototype system serves as the basis for further investigations
and developments towards a multi-sensor radar system for
Acknowledgements. The authors would like to thank M. Berger and
fast collision detection in machine tools. Due to the rather
D. Korff from the Institute of Production Management, Technology
weak sensitivity of the used modules and the coarse Doppler
and Machine Tools (PTW) of the Technische Universität Darmstadt
resolution
to shortduring
observation
windows
the effect of
for
their helpdue
and support
the execution
of the measurements.
multiple
targets
and
multiple
reflections
has
not
conThis work is funded by the Bavarian Ministry of been
Economic
sidered.
It
is
expected
that
this
simple
approach
is
suitable
Affairs and Media, Energy and Technology within the economic
for the majority
of collision
scenarios. However,
specificadevelopment
scheme
“Mikrosystemtechnik
Bayern” under
grant
tion of the actual false alarm and missed detection rates reBAY158/002.
quires further studies. Further topics for future work are exEdited
van Rienen
tensionby:toU.three
dimensions, the question of the minimum
Reviewed
two anonymous
referees
necessaryby:
number
of sensors
for uniqueness of the solution,
and their optimum positioning around the tool. Although the
observation time is very short in this application the effect of
References
cross section fluctuations also needs further investigations.
Abele, E., Brecher, C., Gsell, S. C., Hassis, A., and Korff, D.:
Steps towards a protection system for machine tool main spindles against crash-caused
damages,
Springer
Prod. Eng.,
6.6,
Acknowledgements.
The authors
would
like toJ. thank
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631–642,
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