IGARSS 2011, July 24 -29, Vancouver, Canada Demonstration of Target Vibration Estimation in Synthetic Aperture Radar Imagery Qi Wang 1,2, Matthew Pepin

IGARSS 2011, July 24 -29, Vancouver, Canada

Demonstration of Target Vibration Estimation in Synthetic Aperture Radar Imagery

Qi Wang1,2, Matthew Pepin1,2, Ryan J. Beach2, Ralf Dunkel3, Tom Atwood2,4, Armin W. Doerry4, Balu Santhanam2, Walter

Gerstle5, and Majeed M. Hayat1,2

1Center for High Technology Materials, University of New Mexico, Albuquerque, NM, 87131 USA

2Depart. of Electrical and Computer Science, University of New Mexico, Albuquerque, NM, 87131 USA

3General Atomics Aeronautics Systems, Inc., San Diego, CA 92064 USA4Sandia National Laboratories, Albuquerque, NM 87185 USA

5Depart. of Civil Engineering, University of New Mexico, Albuquerque, NM, 87131 USA


Content

• Motivation• Signal model• Algorithm development– The discrete fractional Fourier transform

• Experimental results• Performance analysis• Conclusions


Motivation Vibration signatures associated with objects such as active

structures (e.g. bridges and buildings) and vehicles can bear vital information about the type and integrity of these objects

The ability of remote sensing target vibrations is important: Avoids the cost of acquiring and installing accelerometers

on remote structures Enables sensing vibrations of structures that not easily

accessible Synthetic aperture radar has the potential due to its active

illumination feature


Data collection positions

Azimuth direction

Range direction

Platform height

The image is generated by the Lynx system built by General Atomics Aeronautical Systems. Inc

Synthetic Aperture Radar

A single static target

A single vibrating target


Freq

uenc

y (H

z)

t (sec)Doppler frequency caused by the plane’s motion

Doppler frequency caused by both the plane’s motion and target vibration

y (azimuth)

X0/2|| ),2cos()( cc tttftp

RF pulse:

Micro-Doppler effect


Signal model• The SAR phase history is de-ramped and reformatted; autofocus is

performed if necessary. The signal from a vibrating scatterer after range compression is:

.0

0 ,][44

exp][ Idc

prf

c Nnnrc

fn

fR

Vy

c

fjns

• The Taylor series expansion is applied to rd[n] in a short time window starting at m, the signal in the time window is approximately :

.2

0

,][2

][4

][4

exp][ wprf

dcd

prf

cd

c Nmnmncf

mafnmv

R

Vy

cf

fmr

c

fjns

• σ : reflectivity of the vibrating scatterer• fc: carrier frequency• c: speed of the microwave• V: speed of the antenna• y: azimuth position of the vibrating scatterer• fprf: the pulse repetition frequency• rd[n]: time-varying range of the vibrating scatterer• φ: other (constant) phase terms•NI : total number of pulses


The discrete fractional Fourier transform Uses a new parameter α to exploit the linear time-frequency relation of the signal (equals to DFT for α = π/2) Concentrates a linear chirp into a few coefficients we obtain an impulse-like transform analogous to what the discrete Fourier transform produces for a sinusoid.

The DFRFT of a complex-valued signal containing two component: a pure 150 Hz sinusoid and a chirp with a center frequency of 200 Hz and chirp rate of 400 Hz/s.

Intersection for α = π/2


The DFRFT (cont’d)

The DFRFT of a signal x[n] is the DFT of an intermediate signal for each index k (k = 0,1, …,N-1), that is

where r = 0,1,…,N-1 is the newly introduced angular index and α=2πr/N. The intermediate signal is calculated by

.VVW TG

2

G

,2

exp][ˆ][1

0

prNjpxrX

N

pk

,][][ˆ )(1

0

)( np

N

p

kp vnxvpx

][ˆ px

][ˆ px

where vp is the pth column vector of VG.

Let W denote the transformation matrix of the centered-DFT, the fractional power of W is defined as

J. G. Vargas-Rubio and B. Santhanam, “On the multiangle centered discrete fractional Fourier transform,” IEEE signal Processing Letters, vol. 12, pp. 273-276, 2005


Incorporating the chirp z-transformLeft: regular DFRFT; right: CZT-incorporated DFRFT with a zoom-in factor of 2

• The CZT can be easily incorporated into the DFRFT to provide a fine resolution in estimating the angular position of the peak.• The relation between the peak location and the chirp rate is

2tan

2 pr N

c


Vibration estimation procedure

1. Demodulate and re-format the SAR phase history, perform autofocus;

2. Apply range compression to the SAR phase history, identify the signal from the vibrating scatterer;

3. For all m = 0 to m = N – Nw + 1 do

Apply the DFRFT to the signal of interest in each time window and calculate the vibration acceleration via

4. End for5. Reconstruct the history of the vibration acceleration and

calculate its DFT spectrum

2tan

2)( )(

2 mp

cw

prf

fN

cfma


Experiment

•Aluminum triangular trihedral with lateral length of 15 inches• The vibration is caused by the rotation of an unbalanced mass.• Vibration magnitude: 1.5 mm; vibration frequency: 5 Hz

Vibrating target

static targets

SAR image of the test ground near Julian, CA. It was generated by the Lynx system on 2010.


Experiment: the DFRFT spectra

Frequency (Hz)

Angl

e (r

ad)

The changing of position of the peak in the DFRFT plain indicates a time-varying vibration acceleration of the target.


Estimation resultsEstimated vibration acceleration (x: time (s); y: acceleration ( m/s2)

Estimated DFT spectrum of the vibration (x: frequency (Hz); y: magnitude (AU)

Actual vibration frequency: 5 Hz


Performance analysis

• The vibration frequency resolution is limited by the SAR observation time of the target

• For the Lynx system, it ranges from 0.3 Hz to 1.0 Hz depending on the data collection geometry and the radar cross section of the target.

• The maximum measurable vibration frequency is upper-bounded by fprf /2 theoretically

• In practice, vibration frequencies up to 25 Hz can be easily estimated when fprf = 1000 Hz;


Conclusions

• A DFRFT-based method is proposed for SAR vibration estimation

• In the experiment, the proposed method successfully estimated a 1.5 mm, 5-Hz vibration from a corner reflector

• Performance analysis of the proposed method is carried out in terms of vibration frequency resolution and maximum measurable vibration frequency


Acknowledgement

This work was supported by the United States Department of Energy (Award No. DE-FG52-08NA28782), the National Science Foundation (Award No. IIS-0813747), National Consortium for MASINT Research, and Sandia National Laboratories. The authors also thank GA-ASI for making the Lynx system available to this project.

Documents

IGARSS 2011, July 24 -29, Vancouver, Canada Demonstration of Target Vibration Estimation in Synthetic Aperture Radar Imagery Qi Wang 1,2, Matthew Pepin