Dr. Myoung An Dr. Jennifer Brower Dr. Jim Byrnes Dr ... · radar scheme to sonar ... Mine detection using Synthetic Aperture Sonar ... • Bullets 1-3 of “Next Steps” and parallel

21 November 2007 Prometheus Inc. Company Proprietary 1

Prometheus … a team Dr. Myoung An Dr. Jennifer Brower Dr. Jim ByrnesDr. Joseph J. KranzDr. Edmund SullivanDr. Richard Tolimieri


Why are we here ?

• Share a mathematically derived processingmethodology which utilizes existing signal content to identify the nature of materials of the objects of interest

• Provide an approach to transition this proven radar scheme to sonar

• Suggest applications using the method to resolve difficult operational sensor employment problems for torpedos and other platforms


“Providing Mathematics forScience and Innovation”

Servicing the US Government and International Technology Community: DARPA, Army, Navy, Air Force, NATOFounded in 1983Small business under NAICS 541330 Woman-ownedBased in Newport, RI12 Doctoral Level Mathematicians and Scientists


Relevant Prometheus Technology

Waveform Design and DiversityAdaptive radar

Feature-Based Pattern RecognitionMine detection using Synthetic Aperture Sonar

Acoustic ModelingPro-Verb torpedo reverberation model

Inverse ProblemsMaterials Identification Synthetic Aperture Radar


Waveform Design and Diversity

Design of waveform sets with optimal correlation propertiesAdaptive selection of transmitted waveforms using echo information

dB-plot of correlations of two length 792 signals

Response with Prometheus waveforms

Typical radar response


Feature Based Pattern Recognition

Undersea Mines

Originated as Prometheus IR&D program with Raytheon assistance.



Mine Detection ROC Curve



Design and implementation of spectral analysis toolbox for detection and classification of mine-like objects in high-resolution Synthetic Aperture Sonar data


SAS Mine-Like Object Detection ROC Curve

Pd

False Calls per Image


Meets or exceeds Weapons Analysis Facility (WAF) requirementsPulse length from 0.01 to 0.5 secondsCenter frequency of 10 kHz to 40 kHzBandwidth as high as 25% of center frequencySupports element-level time series data for 100+ elements

Pro-VerbTorpedo Reverberation Modeling


MISAS

Materials Identification Using Synthetic Aperture Sonar


• Based on MISAR, Materials Identification Synthetic Aperture RADAR, a proven method

• MISAR Phase I, II• USAF, Brooks City Base, Richard Albanese• Time-domain deconvolution algorithm development

– Phase III• National Reconnaissance Office (NRO)• Time-frequency space processing

MISAS foundations


Suggested MISAS Applications

• Classification of targets in mid and low frequency ranges

• Reduction of false alarms

• Mine detection, localization & identification

• Reverberation discrimination in harsh environments


OUTLINE

1. Background

2. Deconvolution

3. Algorithm

4. Discussion


BACKGROUND


Reflectivity Kernel Estimation

Material properties of target summarized in reflectivity kernel R(t)

radar/sonartargetpulse

echo

echo = convolution of pulse and R + noise

Goal: Recover material information from noisy echo through deconvolution


MISAS Process Diagram

EchoesDenoise andDeconvolve

withZak transform

A priori informationon pulse

BayesianStatistical test

A priori statisticalinformation

Comparison test

Library

Discriminationdecision

Identification decision


DECONVOLUTION


Deconvolution

Given the input or “probe” signal, find the Kernel, K, from the received or scatteredsignal. K characterizes the material

This is an inverse problem. The associated forward problem is: Given K and an inputsignal s, find the scattered or output signal

∫ +′′′= noisexdtsttKtf )(),()(

Output Kernel Input


Examples of Reflectivity Kernels

•Heavy metals•Composite materials

•Water•Biological tissue•Radar-absorbing urethane foam

Atmospheric interference


The ILL-Posed Problem

Deconvolution is an inverse problem, therefore is “ill-posed,’’ which means it can be

1. Sensitive to noise2. Non-unique3. Subject to observability problems


Observability Requirements

1. The information must be in the data

2. The signal must be sensitive to the desired data

3. The receiver must be sensitive to therelevant characteristics of the signal


Example of Poor Observability

Consider a towed array attempting toestimate both range and bearing

If the range is much larger than the aperture, it is “weakly” observable and thus essentially impossible to estimate


MISAS APPROACH

Gain observability with signal design

Denoise and deconvolve with the Zak Transform

Increase observability with SAS


ALGORITHM


Based on the Zak Transform

∑+∞

−∞=

−=

k

Nnki

n eksfπ2

)(Fourier Transform

∑+∞

−∞=

−+=k

kfimnm

nektsftZ π2)(),(Zak Transform

The Zak transform is a time-frequency representation. Forour purposes, it provides a time-frequency map which “deconstructs” the signal and provides noise reduction.


Nyquist Samples

Critical Samples ShiftedCritical Samples

1 M 2M 3M KM

Nyquist sampling vs “Critical sampling”KM=2 X Highest Freq. (Nyquist)K=2 X Bandwidth (Critical)


Data Sample Map

003

02

01

113

12

11

321

K

K

MK

MMM

xxxx

xxxx

xxxx

LL

LL

MM

L Shift Right M Samples

Shift Right 1 Sample

No Shift


Zak Time-Frequency Map

003

02

01

113

12

11

321

K

K

MK

MMM

ffff

ffff

ffff

LL

LL

MM

L

Tim

e

Frequency


Zak Time-Frequency mapFor 2 Chirps

t Note that

Tt <<∆T

1t2t

ttt ∆=− 12

f


Example For a Multi-Point Scatterer

We consider a multi-point scatterer and a linear frequency modulated (LFM) signal, or “chirp” as the probe.

The scattered signal then consists of multiple LFM signals mixed in space and time.


Closely-Spaced Target Separation

Incident FM Chirp

Noisy Echo From Point Scatterers


Zak Transform of Noisy Sum


Recovered Decomposition


MISAS APPROACH

Gain observability with signal design

Denoise and deconvolve with the Zak Transform

Increase observability with SAS


MISAS Process Diagram

A priori statistical

EchoesDenoise andDeconvolve

withZak transform

A priori informationon pulse

BayesianStatistical test

Discriminationdecision

information

Comparison test

Library

Identification decision


Improving Observability with Synthetic Aperture Sonar (SAS)


SAS: Multiple Measurements

Use SAS to increase effective pulse duration by combining multiple measurements. Extends algorithm to cases where pulse duration < material relaxation time.

Multiple measurements at different aspects Increases cross-range resolution and observability


SAS Geometry

Ideal along track path

Transmit/Receivelocations

x

y

z

Physical array Physical aperture

footprint

Synthetic aperture footprint(constant resolution)

Synthetic array


Technical Issues

• Sensitivity

• Availability of data

• Defining meaningful experiments


Suggested Applications

• Classification of targets in mid and low frequency ranges (coda)

• Reduction of false alarms

• Mine detection, localization & identification

• Reverberation discrimination in harsh environments


Courtesy of Naval Undersea Warfare Center – Division, Newport,

Code 8133 (15 November 2007)


Courtesy of Naval Undersea Warfare Center – Division, Newport, Code 8133 (15 November 2007)


Next Steps• Develop SONAR version of MISAR

– Radar to Sonar conversion details• Concept modeling & validation• Develop library of reflectivity kernels

– NUWC Acoustic Test Facility– Advanced Processing Build (APB)

• Identify candidate host system• Perform technical and operational tests


Available Funding Vehicles

• Phase III SBIR – USAF/NRO

• Materials Identification Synthetic Aperture Radar (MISAR) (new sensor application)

– NUWC Weapons Analysis Facility (WAF)

• ProVerb follow-on (reverberation mitigation)


Initial Effort (First three “Next Steps”)

• Algorithm Conversion• Algorithm Validation/Testing

– Acoustic Test Facility• Kernel library development – steel, composites,

structural plastics, flesh, rubber, rock, sand, etc.• Experiment design/test fixture design-construction• Sensitivities to waveform, impulse intensity, etc.

• Physics issues research• Waveform/Signal Processing optimization• Source/receiver/transducer requirements


Level of Effort/Period of Performance Estimation – Initial Effort

• Bullets 1-3 of “Next Steps” and parallel APB definition*~ 4 to 7 work-years

(Prometheus + NUWC, details of NUWC involvement TBD)~ 1 to 1.5 yearsDetailed research plan within 30 days

* Does not include development/coding of the APB, host system identification/integration and engineering required to conduct WAF ‘hardware-in-the-loop’ testing or at-sea testing of a prototype.


ReferencesGroup Filters and Image ProcessingMyoung An and Richard TolimieriPsypher Press, 2003, ISBN 0-9741799-0-6

Time-Frequency RepresentationsMyoung An and Richard TolimieriBirkhauser, Applied and Numerical Harmonic Analysis Series,

1998, ISBN 0-8176-3918-7

Ideal Sequence Design in Time-Frequency SpaceMyoung An, A.K. Brodzik and Richard TolimieriBirkhauser, Applied and Numerical Harmonic Analysis Series, 2007, ISBN 0-8176-4737-6


Thank You

Dr. Jim [email protected](781) 784-2355(401) 849-5389

mailto:[email protected]


Example of Convolution

SystemIN OUT

)( ttR ′−)( tt ′−δ

t′t′ tt

)(tfOUT)(tfIN

tt

)()()( ttRtftft

INOUT ′−′≅ ∑′


Zak Transform of Chirp

∑+∞

−∞=

−+=k

kiektftZ πυυ 2)(),(

2

)( tietf π= )2( 22

)( kkttiektf ++=+ π

∑ −+=k

ktkiti eetZ )][2( 22

),( υππυ

2/10),( −−=≠ ktwhenonlytZ υυ


tdttRtftft

INOUT ′′−′= ∫′

)()()(

)()()( 2211 ttattattR −+−=′− δδ

Recall

For the 2-point scatterer

Thus, the kernel has been extracted directlyfrom the time frequency map


In The Limit

tdttRtftft

INOUT ′′−′= ∫′

)()()(

Or, More Generally

∫ +′′′= noisexdxsxxKxf )(),()(

Output Kernel Input


Time-Frequency mapFor a Complex Scatterer

υ

t

R(t)

t


Affordable Acquisition Decision Aid (AADA)

Genetic algorithm based objective function to identify the ‘fittest’decisions in campaign based multi-objective investment decision-making problems

Dr. Myoung An Dr. Jennifer Brower Dr. Jim Byrnes Dr ... · radar scheme to sonar ... Mine detection using Synthetic Aperture Sonar ... • Bullets 1-3 of “Next Steps” and parallel

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