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

2. Outline Introduction Spectral Analysis of Micro-Doppler Frequency  Inertial Model  Spectral Structure Estimation Methodology Results Conclusion 2 IGARSS 2011

3. Introduction Background Micro-Doppler (mD) effect -- the frequency modulation phenomenon in radar echoes caused by objects’ micro-motions 3 IGARSS 2011 mD effect micro- motions attitude dynamics limb/respiratory movement engine vibration/ wheel rotation … micro-motion parameters classification EXPLORE

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 4 IGARSS 2011

5. 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 5 IGARSS 2011 moments of inertia initial rotation state attitude angles (at any time t) Rot(t) signal model mD echoes linear time variant

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 6 IGARSS 2011 rotation parameters precession of a gyroscope from http://en.wikipedia.org/wiki/Precession

7. 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 7 IGARSS 2011

8. 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 8 IGARSS 2011 linear sum of four sinusoidal components

9. Spectral structure of mD time-frequency sequence  Spectral Analysis of MD Frequency 9 IGARSS 2011  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

10. KEY: the mD time-frequency features Process to estimate the rotation parameters  Estimation Methodology 10 IGARSS 2011 radar mD echoes spectrogram time-frequency sequence spectral estimationrotation parameters Time-frequency analysis (Short Time Fourier Transform) Formation of mD time-frequency sequence Spectral estimation STFT mapping RELAX

11. Time-frequency analysis (STFT) Formation of mD time-frequency sequence  Morphological processing  Location mapping of “target” points Estimation Methodology 11 IGARSS 2011 time frequency two-dimensional (2D) matrix data time amplitude one-dimensional (1D) sampled data t t f g(ti)g(ti) h(tm,fn)h(tm,fn) time frequency t f r(tk)r(tk) 1D sequence data

12. Spectral estimation  The RELAX algorithm is an asymptotic maximum likelihood approach based on the Fourier transform Estimation Methodology 12 IGARSS 2011 frequency amplitude

13. Simulation conditions Simulation Results 13 IGARSS 2011 carrier frequency5 GHz PRF2 kHz radar-to-target direction(0.578, 0.578, 0.578) moments of inertia(108, 108, 23) kg·m 2 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

14. Spin rate estimates in Monte-Carlo simulations Simulation Results 14 IGARSS 2011 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%

15. Precession rate estimates in Monte-Carlo simulations Simulation Results 15 IGARSS 2011 when SNR>13dB, accuracy>91%

16. 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 16 IGARSS 2011

17. 17 IGARSS 2011