Peng Lei, Peng Lei, Jun Wang, Jinping SunJun Wang, Jinping SunBeijing University of Aeronautics and
Astronautics
IGARSS 2011, Vancouver, CanadaJuly 26, 2011
Radar Micro-Doppler Analysis and Rotation Parameter Estimation for Rigid Targets with
Complicated Micro-Motions
Outline
Introduction Spectral Analysis of Micro-Doppler Frequency
Inertial Model Spectral Structure
Estimation Methodology Results Conclusion
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Introduction
Background
Micro-Doppler (mD) effect -- the frequency modulation phenomenon in radar echoes caused by objects’ micro-motions
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mD effectmicro-
motions
attitudedynamics
limb/respiratorymovement
engine vibration/wheel rotation
…
micro-motionparameters
classification
EXPLORE
Introduction
Objective of our work
Free symmetric rigid bodies with single scattering center
Micro-dynamic characteristics
─ select rotation parameters to represent them
Effect on the mD
─ non-sinusoidal variation of the mD frequency
MD-based parameter estimation of their attitude dynamics
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constant
Inertial model
Objects’ attributes Micro-motion states MD echoes
For the axisymmetric body ( ), the three attitude angles are given by:
─ spin angle:
─ precession angle:
─ nutation angle:
kinematic equations
Spectral Analysis of MD Frequency
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x yI I
moments of inertia
initial rotation stateattitude angles
(at any time t)
Rot(t)
signal modelmD echoes
0( , ) arccos( )z zI E 0I w
linear time variant
0( , , ) (1 )z x zt I I t 0I w
( , , ) xt E t I 0I w
Spectral Analysis of MD Frequency
Inertial model
Characteristics of the micro-motion
─ spin rate:
─ precession rate:
where are moments of inertia, are initial rotational
velocities, and is the total angular momentum.
─ this is well-known as the precession motion
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0(1 / )z x zI I / xE I
rotation parameters
( , , )x y zI I I 0 0 0( , , )x y z 2 2 2 2 2 2
0 0 0x x y y z zE I I I
precession of a gyroscopefrom http://en.wikipedia.org/wiki/Precession
Spectral structure of mD time-frequency sequence Micro-motions have an great effect on the time variation of
instantaneous mD frequency
The mD frequency of radar echoes is expressed as
Spectral Analysis of MD Frequency
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02( ) cos ,cos ,cos
( , , , ), ,
mD
T
ff t
CdRot t
x y zdt
Spectral structure of mD time-frequency sequence Considering the inertial model and constant terms, the mD
frequency from the scatterer on a free rigid body can be
rewritten as
─ HERE, behaves as a frequency function of the time t
Spectral Analysis of MD Frequency
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( ) sin
sin
sin
sin
mDf t H t
H t
H t
H t
linear sum of foursinusoidal components
( )mDf t
( ) sin
sin
sin
sin
mDf t H t
H t
H t
H t
Spectral structure of mD time-frequency sequence
Spectral Analysis of MD Frequency
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Amplitudes and constant phases
in are invariant , which
are with respect to , , x, y, z,
et al.
Frequencies of the four sinusoi-
dal components correspond to
the rotation parameters, and
( )mDf t
C 0f
KEY: the mD time-frequency features
Process to estimate the rotation parameters
Estimation Methodology
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radar mD echoes spectrogram time-frequency sequence
spectral estimation rotation parameters
Time-frequency analysis (Short Time Fourier Transform)
Formation of mD time-frequency sequence
Spectral estimation
STFTmapping
RELAX
Time-frequency analysis (STFT)
Formation of mD time-frequency sequence Morphological processing Location mapping of “target” points
Estimation Methodology
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time
fre
qu
en
cy
two-dimensional (2D) matrix data
time
am
plit
ud
e
one-dimensional (1D) sampled data
t t
f
g(ti)
h(tm,fn)
timefr
eq
ue
ncy
t
f
r(tk)
1D sequence data
Spectral estimation The RELAX algorithm is an asymptotic maximum likelihood
approach based on the Fourier transform
Estimation Methodology
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2
( , )1
, arg min exp( 2 )L
p l ll
r a j f n
f a
f a
frequency
am
plit
ud
e
( ) ( )
Simulation conditions
Simulation Results
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carrier frequency 5 GHz
PRF 2 kHz
radar-to-target direction (0.578, 0.578, 0.578)
moments of inertia (108, 108, 23) kg·m2
initial rotational velocities (1, 1, 26) rad/s
scatterer position (0.4, 0.3, -0.5) m
-0.6-0.3
00.3
0.6
-0.6-0.3
00.3
0.6-0.7
-0.5
-0.3
X / m Y / m
Z /
m
0 1 2 3 4-500
-250
0
250
500
Time / s
MD
fre
qu
en
cy /
Hz
micro-motion trajectory in 3D space
theoretical mD frequency
Spin rate estimates in Monte-Carlo simulations
Simulation Results
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5 10 15 20 25 303.2
3.4
3.6
3.8
4
SNR / dB
Sp
in R
ate
/ H
z
theory ideal estimation
16 18 20 22 24 26 28 303.255
3.256
3.257
1. theoretical values – calculation results
2. ideal values – simulation results under noise-free condition
3. estimation values – Monte-Carlo results at given SNR level
when SNR>13dB,accuracy>98%
5 10 15 20 25 300.9
1.1
1.3
1.5
1.7
SNR / dB
Pre
cess
ion
Ra
te /
Hz
theory ideal estimation
Precession rate estimates in Monte-Carlo simulations
Simulation Results
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when SNR>13dB,accuracy>91%
15 18 21 24 27 300.909
0.91
0.911
Free symmetric rigid objects generally take the precession motion, which has two important rotation parameters, i.e., spin rate and precession rate
Their mD frequency data sequence (1D) is composed of four sinusoidal components with respect to the spin and precession rates
The proposed method could achieve the estimation of rotation parameters under noise environment
Current exploration is extending to the multi-scatterer objects, which is more complex and needs more work
Conclusion
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