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

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

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

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 IGARSS 2011

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 IGARSS 2011

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 http://en.wikipedia.org/wiki/Precession IGARSS 2011

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 IGARSS 2011

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 IGARSS 2011

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 IGARSS 2011

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 IGARSS 2011 mapping

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 IGARSS 2011

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 IGARSS 2011

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 IGARSS 2011

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% IGARSS 2011

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

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 IGARSS 2011

Thank you IGARSS 2011