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

2IGARSS 2011

Introduction

Background

Micro-Doppler (mD) effect -- the frequency modulation phenomenon in radar echoes caused by objects’ micro-motions

3IGARSS 2011

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

4IGARSS 2011

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

5IGARSS 2011

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

6IGARSS 2011

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

7IGARSS 2011

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

8IGARSS 2011

( ) 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

9IGARSS 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

( )mDf t

C 0f

KEY: the mD time-frequency features

Process to estimate the rotation parameters

Estimation Methodology

10IGARSS 2011

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

11IGARSS 2011

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

12IGARSS 2011

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

13IGARSS 2011

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

14IGARSS 2011

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

15IGARSS 2011

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

16IGARSS 2011

17IGARSS 2011