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ASU MAT 591: Opportunities In Industry!

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ASU MAT 591: Opportunities In Industry!

Advanced MTI

Algorithms

Howard Mendelson

Principal Investigator

21 August 2000

- SAR systems provide excellent intelligence concerning status of fixed installations (assuming no electronic countermeasures (ECM) are employed)
- Warfighter requires precise information describing MOVING formations of troops and weapons
- Formations may be slow moving and thus difficult to distinguish from background clutter
- Formations (as well as fixed targets) may be screened by ECM

- Our customers now specify high fidelity moving target indication (MTI) and fixed target indication (FTI) with interference rejection capabilities for their battlefield surveillance systems.
- These issues make it imperative for us to develop the techniques necessary to provide these capabilities

- DPCA
- Not data adaptive

- ADSAR
- Data adaptive but not jammer resistant

- SPACE TIME ADAPTIVE PROCESSING (STAP)
- No Fielded GMTI Systems
- Computationally Intensive
- Traditional SMI Approach Produces Large Numbers of False Alarms

- Develop Post Doppler Eigenspace Analysis Techniques
- Advantages
- Lower false alarm rate than traditional SMI approach
- Simultaneous SAR and MTI in the presence of ECM
- Common processing framework for clutter and jammer suppression
- Higher Signal-to-Background Ratio (SBR) after interference suppression
- Smaller training data set required for STAP algorithms
- Computational Efficiency

- Advantages

Sample Matrix Inversion (SMI)

Interference Suppression Algorithm

Input Data (N channels)

Invert Covariance

Matrix

Apply

Inverse

Form Covariance Estimates

Detection

Processing

Beamform

Eigendecomposition

Interference SuppressionAlgorithm

Input Data (N channels)

Perform

Eigendecomposition

Determine No. of

Interference Sources

Form Covariance Estimates

Project Data Orthogonally

to Interference Subspace

Detection

Processing

Beamform

Channel 1

N/2 Rng Cells

Guard

Cells

Cell of

Interest

Guard

Cells

N/2 Rng Cells

Channel 2

N/2 Rng Cells

Guard

Cells

Cell of

Interest

Guard

Cells

N/2 Rng Cells

X1

.

.

.

XN

Channel N

N/2 Rng Cells

Guard

Cells

Cell of

Interest

Guard

Cells

N/2 Rng Cells

No. of range cells used for Eigen

processing is typically

1.5 x No.of channels

(Higher for SMI)

Covariance estimate is computed

in sliding window at every pixel

No. of guard cells depends on range

resolution

His complex conjugate transpose

Sample Matrix Inversion (SMI)

subject to

$

R

Sample Covariance Matrix

C

Constraint Matrix

f

Coefficient Vector

w

Weight

Vector

Hermitian adjoint (conjugate transpose)

H

subject to

and

Matrix of eigenvectors of estimated covariance matrix

associated with interference

Q

r

C

Constraint Matrix

f

Coefficient Vector

w

Weight Vector

Minimum Norm Eigencancler (MNE)

24”

7”

adjustable

Channel 2

Receive

Channel 1

Transmit/Receive

Channel 0

Receive

flight

Controlled Moving Target

FFT

1 2 3 . . . P - 1 P

FFT

S

T

A

P

FFT

1 2 3 . . . P - 1 P

Elements (or beams)

FFT

FFT

1 2 3 . . . P - 1 P

FFT

Channel 1 Stagger 0

N/2 Rng Cells

Guard

Cells

Cell of

Interest

Guard

Cells

N/2 Rng Cells

Channel 2 Stagger 0

N/2 Rng Cells

Guard

Cells

Cell of

Interest

Guard

Cells

N/2 Rng Cells

X10n

.

.

.

XLNstg-1n

Channel L Stagger Nstg - 1

N/2 Rng Cells

Guard

Cells

Cell of

Interest

Guard

Cells

N/2 Rng Cells

No. of range cells used for Eigen

processing is typically

1.5 x No.of channels x No. of staggers

(Higher for SMI)

Covariance estimate is computed

in sliding window at every pixel

No. of guard cells depends on range

resolution

His complex conjugate transpose

Unprocessed Image

SMI Processing

Eigendecomposition Processing

Adaptive Matched

Filter (SMI)

H1

>

<

H2

aAMF

H1

>

<

H2

Generalized Likelihood

Ratio Test (SMI)

aGLRT

H1

>

<

H2

Eigendecompsition Likelihood

Ratio Test

aPC

Unprocessed Image

SMI - AMF Detection Reports

SMI - GLRT Detection Reports

LRT - Eigendecomposition Detection Reports

Unprocessed Image

SMI - AMF Detection Reports

SMI - GLRT Detection Reports

LRT - Eigendecomposition Detection Reports

- Uses Channel-to-Channel Phase Differences to Obtain Target Direction of Arrival (DOA)
- Originally Developed for Three Channel “Uniformly” Spaced Array Without PRI Stagger
- Assumed Clutter as only Interference Source
- Insufficient number of degrees of freedom available to deal with more than one interfering source

- Can be extended
- No. of channels greater than 3
- Multiple interfering sources
- Non-uniform spacing

Assumed Signal Model

r

r

y

(

e

,

s

)

(

e

,

s

)

$

$

=

@

1

1

1

Tgt

r

r

y

(

e

,

s

)

(

e

,

s

)

$

$

=

@

2

2

2

Tgt

=

e

First ei

genvector

orthoganal

to clutte

r directio

n

$

1

=

e

Second e

igenvector

orthogana

l to clutt

er directi

on

$

2

Same eigen

vectors co

mputed dur

ing interf

erence sup

pression

and detect

ion proces

sing

Phase of target vector can now be found

by solving for roots of quadratic

Solution which provides largest return

after beamforming is assumed correct

Relocated Targets

Original Target Detections

Assumed Signal Model

Complex images from each channel are assumed

to have been relocated to a common point

r

r

y

(

e

,

s

)

(

e

,

s

)

$

$

=

@

1

1

1

Tgt

r

r

y

(

e

,

s

)

(

e

,

s

)

$

$

=

@

2

2

2

Tgt

=

e

First ei

genvector

orthoganal

to clutte

r directio

n

$

1

=

e

Second e

igenvector

orthogana

l to clutt

er directi

on

$

2

Same eigen

vectors co

mputed dur

ing interf

erence sup

pression

and detect

ion proces

sing

Phase of target vector can now be found

by solving for roots of quadratic

Solution which provides largest return

after beamforming is assumed correct

Cramer Rao bound of interferometer measurement accuracy

used to estimate cross range error

Known Targets

SMI based STAP

Eigenanalysis based STAP

Original Detections

Relocated Targets

Unprocessed Target Detections

Relocated Target Detections

Covariance

Estimate

Multichannel

Complex

Image Data

Find Eigenvalues

and Eigenvectors

Find Noise

Subspace

Dimension

Form Interference

Suppression

Projections

Form Estimated

Steering Vector

Produce

Interference

Suppressed

Data Field

Form Image

Projections

Compute AOA

(Radial Speed)

Estimates

Produce Low

Resolution SAR

Image

Perform CFAR

Thresholding

Compute

Cancellation

Ratios of

Threshold

Crossings

Determine AOA

Consistency

of Estimates

of Possible

Detections

Detection reports

Location, Speed

and Heading Estimates

- Multiple post-Doppler STAP algorithms studied and evaluated for clutter suppression and target detection
- Eigenanalysis, SMI
- Single Doppler bin, adjacent Doppler bin, PRI stagger

- “Mono-pulse” location algorithm developed and tested on collected data
- Work ongoing to develop algorithm upgrades