Design and Analysis of an Automatic Target Recognition algorithm using optimized Euler ISAR Imagery

Christopher S. Baird Advisor: Robert Giles

Submillimeter-Wave Technology Laboratory (STL)

SeminarUniversity of Massachusetts Lowell

March, 2007

Outline

I. Introduction to Polarimetry and the Euler Parameters

II.Methodology

A. Euler Parameter Derivations

B. Implementation of the full ATR Algorithm

I. Results

IV. Conclusions

Electromagnetic Scattering Cross SectionI. Introduction to Polarimetry and the Euler Parameters

Unpolarized Cross Section Polarimetric Cross Sections

Radar Scattering Matrix, Field RepresentationI. Introduction to Polarimetry and the Euler Parameters

The Scattering coefficient preserves

the phase of the polarized EM wave:

General Scattering Equation:

Scattering Matrix Equation

in H-V basis:

Complex Sinclair

Scattering Matrix

Propagation Term

(Normalized Out)

Scattered Field Incident Field

Conventional Polarization Basis: H-VI. Introduction to Polarimetry and the Euler Parameters

Any polarized EM wave has an electric

field vector that can be broken up into

horizontal and vertical components

In practice, field components are

measured one at a time. Here the SVH

matrix element is measured.

Downrange ImagingI. Introduction to Polarimetry and the Euler Parameters

Crossrange ImagingI. Introduction to Polarimetry and the Euler Parameters

Doppler Effect allows crossrange imaging using

Inverse Synthetic Aperture Radar (ISAR)

Two-Dimensional ISAR ImagingI. Introduction to Polarimetry and the Euler Parameters

Euler DecompositionI. Introduction to Polarimetry and the Euler Parameters

PURPOSE: Decompose information in the scattering matrix into

parameters that better represent the object's fundamental scattering

properties, and not the configuration of the measurement apparatus

METHOD: Transform scattering matrix to the optimal polarization basis,

which basis depends only on the scattering object and not the detector

set-up. The optimal polarization basis is reached when all of the energy

is returned in the co-polar channels, i.e. when the scattering matrix S is

diagonalized.

Diagonalize S using unitary conjugate-similarity transformation:

Euler Parameter DefinitionsI. Introduction to Polarimetry and the Euler Parameters

Unitary Matrix

Diagonalized Sinclair Matrix

maximum reflectivity

orientation angle

symmetry angle

bounce angle

polarizability angle

Meaning of the Euler ParameterI. Introduction to Polarimetry and the Euler Parameters

I. Introduction to Polarimetry and the Euler Parameters

Euler Parameter SignificanceI. Introduction to Polarimetry and the Euler Parameters

• The Euler Parameters represent more fundamental scattering properties of an object than the traditional H-V polarization parameters.

• Transforming to Euler Parameters should thus improve Automatic Target Recognition (ATR) as well as give more intuitive scattering images.

Euler Parameter DerivationsII. Methodology

PURPOSE: Derive the Euler parameters as functions of the known Sinclair matrix

METHOD: Invert the Euler definition equations:

where

Instead of being attempted in this Sinclair matrix representation, the equations are

best inverted by first switching to the power matrix representation:

The Power RepresentationII. Methodology

The equations that transform from the Sinclair matrix to the Kennaugh matrix can be

found by expanding out both matrix equations and matching up coefficients

The Power RepresentationII. Methodology

Before switching to the power matrix, the Sinclair matrix is reduced to 5 meaningful

parameters by factoring out an overall phase factor N and using reciprocity to set

SHV=SVH. The 5 remaining Sinclair matrix parameters are relabelled a, b, c, d, f:

reduce & relabel

After matching up coefficients, the Kennaugh power matrix is found in terms of the

original known Sinclair matrix parameters:

The Power RepresentationII. Methodology

To ease notation, the parameters are again relabelled according to Huynen's

conventions:

The measured Sinclair scattering data is thus represented in succinct, power

matrix form and can be expanded when needed into the original parameters.

For example:

It should be noted that the Kennaugh matrix has 16 elements, but because it was

transformed from 5 meaningful parameters, there is much redundant information

Euler Parameter Derivation: psiII. Methodology

• Using the Kennaugh matrix K, the Euler parameters are derived one at at time.

• Because each Euler parameter is some form of a rotation angle, the dependence of

K on each parameter can be rotated out and K is forced to be piecewise diagonal.

• First the dependence of K on the orientation

angle psi is removed by back-rotating:

• The rotation matrix is found by casting the Euler definition into the power

representation:

Euler Parameter Derivation: psiII. Methodology

The resulting Kennaugh matrix K' is independent of psi and the elements are

relabelled:

Analysis of the Euler definitions reveals that any Kennaugh matrix that is

independent of psi must have H'=0. Forcing this condition on K' yields the

solution to psi:

Euler Parameter DerivationsII. Methodology

The same general approach is used to the remaining Euler parameters:

Visual Analysis of Euler Parameters: SlicyII. Methodology

Visual Analysis of Euler Parameters: T-72II. Methodology

Implementation of the ATR AlgorithmII. Methodology

PURPOSE: • Test the effectiveness of the Euler parameters in Automatic Target Recognition (ATR)• Also, develop a full ATR algorithm that prototypes a complete field system and needs no information about the unknown target.

METHOD: • Create a full ATR algorithm that uses a reference library of pre-rendered ISAR images of every possible target to match to the unknown target. • Use the Euler parameter images and persistence-weighted APD method when matching images to test their effect on ATR performance. •Use a test suite of model tanks to test performance.

Implementation of the ATR AlgorithmII. Methodology

Testing the ATR algorithmII. Methodology

T-72 M1 T-72 BK

Two tanks from the test suite showing the similarity of the

tanks chosen in order to create a difficult ATR test

Testing the ATR algorithmII. Methodology

• A test suite of high-fidelity T-72 tanks and variations of the T-72 tank were

chosen. The tanks in the test suite all have the same shape and only differ in

the armour or in other detailed variations, thus posing a difficult target

recognition test.

• The tanks were obtained as high-quality scaled models through the ERADS

program. The tank geometry, material properties, and radar system were

scaled properly to ensure identical results as for full-scale measurements.

• The full suite of test targets was compared and formed into probability curves with persistence optimization and without to investigate its effect.

• An alternate, more succinct way that was used to plot the ATR performance results is the Receiver Operating Characteristic (ROC) curve.

Testing the ATR algorithmII. Methodology

• Each comparison at several azimuth angles yields one probability density

curve.• The amount of overlap between the curves for matching targets and the

curves for non-matching targets indicates the performance of the ATR

algorithm

The ROC Curve DefinitionII. Methodology

• To construct a ROC curve, a decision threshold is scanned across the group of

probability density curves.• At each possible threshold, the percent of all comparisons below the threshold

that are true-positive (TP) and false-positive (FP) identifications is computed.

The ROC Curve DefinitionII. Methodology

Performance of the ATR AlgorithmIII. Results

• As described in the Methodology section, a full ATR Algorithm was

developed that takes a single ISAR image of an unknown target and gives it

an identification without knowledge of the targets orientation or configuration.

• Thousands of test images from the model test suite were run through the full

ATR algorithm and the results gathered into ROC curves

ATR Results - UnoptimizedIII. Results

ATR Results – Unoptimized (zoomed)III. Results

Full-ATR Tests ConclusionsIII. Results

• The ATR algorithm tests show better target recognition for the magnitude

parameters than the angular parameters, with the Euler magnitude

parameter m giving the best results

ATR Score ConsolidationsIII. Results

• The angular parameters perform too poorly to be useful when treated separately.

• When consolidated, the Euler parameters can improve ATR performance because they specify independent properties of the same scattering object.

• The consolidated score is defined as the distance in 5-dimensional Euler space between the Euler scores si and some reference point si0.

• The reference point si0 is found by using a training data set separate from the

test data sets, and adjusting the reference point until ATR performance is optimized for the training data.

Full-ATR Score ConsolidationsIII. Results

Full ATR Final ResultsIII. Results

General ConclusionsIV. Conclusions

• A full ATR algorithm has been developed that has been shown to better recognize targets than the traditional methods.

• The best ATR configuration was found to involve the persistence-optimized Euler parameters images when the scores are consolidated to a score s.