1. Radar Micro-Doppler Analysis and Rotation Parameter Estimation for Rigid Targets with Complicated Micro-Motions
Peng Lei, Jun Wang, Jinping Sun
Beijing University of Aeronautics and Astronautics
IGARSS 2011, Vancouver, Canada
July 26, 2011

2. Outline Introduction Spectral Analysis of Micro-Doppler Frequency
Inertial Model
Spectral Structure
Estimation Methodology
Results
Conclusion
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3. Introduction … Background
Micro-Doppler (mD) effect -- the frequency modulation phenomenon in radar echoes caused by objects’ micro-motions
mD effect
micro-motions
attitude
dynamics
limb/respiratory
movement
engine vibration/
wheel rotation …
micro-motion
parameters
classification
EXPLORE
Here, the “radar” generally refers to the microwave and laser sensors.
Although the mD effect is similar to the well-known Doppler phenomenon in theory, the special dynamics, micro-motion, should be our focus in some related research.
IGARSS 2011

4. 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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5. Spectral Analysis of MD Frequency
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:
moments of inertia
initial rotation state
kinematic equations
attitude angles
(at any time t)
Rot(t)
signal model
mD echoes
linear time variant
constant
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6. 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
rotation parameters
precession of a gyroscope
from
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7. Spectral Analysis of MD Frequency
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
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8. Spectral Analysis of MD Frequency
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
linear sum of four
sinusoidal components
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9. Spectral Analysis of MD Frequency
Spectral structure of mD time-frequency sequence
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
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10. Estimation Methodology
KEY: the mD time-frequency features
Process to estimate the rotation parameters
Time-frequency analysis (Short Time Fourier Transform)
Formation of mD time-frequency sequence
Spectral estimation
radar mD echoes
spectrogram
time-frequency sequence
spectral estimation
rotation parameters
STFT
RELAX
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mapping

11. Estimation Methodology
Time-frequency analysis (STFT)
Formation of mD time-frequency sequence
Morphological processing
Location mapping of “target” points f
g(ti)
time
frequency
two-dimensional (2D) matrix data
time
amplitude
one-dimensional (1D) sampled data t
h(tm,fn) t
time
frequency t f
r(tk)
1D sequence data
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12. Estimation Methodology
Spectral estimation
The RELAX algorithm is an asymptotic maximum likelihood approach based on the Fourier transform
It could be represented by this nonlinear least-square fitting problem, as this equation.
frequency
amplitude
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13. radar-to-target direction initial rotational velocities
Simulation Results
Simulation conditions
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
micro-motion trajectory in 3D space
theoretical mD frequency
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14. Simulation Results Spin rate estimates in Monte-Carlo simulations
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%
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15. Simulation Results
Precession rate estimates in Monte-Carlo simulations
when SNR>13dB,
accuracy>91%
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16. Conclusion
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
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17. Thank you
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