AESA Airborne Radar Theory and Operations Technical Training Course Sampler

AESA Airborne Radar Theory and Operations

Instructor:
Bob Phillips

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Copyright 2013 R.A. Phillips

AESA Airborne Radar Theory and
Operations Course Sampler

Robert A Phillips
AnnapolisStar@gmail.com

Introduction Page 1


Objective Number 1
1) Learn how to interleave modes, intercept targets using
advanced LPI techniques, and develop requirements for an AESA
radar from the pilots point of view.

AESA Radar engaging and launching
missiles on three targets

Introduction: Page 2


Objective Number 2
2) Present the theory of an AESA Radar and learn how to design
the air-air and air-ground modes from the requirements up
Antenna Receive Pattern using a
diamond layout with true symmetric
Dolph Chebyschev sidelobe weighting
(from supplied Radar Theory eBook)

Clutter
Template
Pulse
Compress

FFT

Square
law
Detector

CFAR

M of N
Correlate

Block Diagram for Search mode



Objective Number 3
3) Provide the simulations, tools, and references for “putting the
theory into practice”
500 page interactive
electronic book on
class material including
antennas, Space Time
Adaptive Processing,
Kalman filters, and
automatic target
recognition, with
simulations & examples
Win 7 Professional Radar mode
design spread sheet with software

AESA Radar Theory eBook

"You cannot mandate productivity, you must provide the tools to
let people become their best.“ Steve Jobs



Some of the Questions to be Answered
1) How do you design and compute the performance
for the AESA search modes?
2) How do you design an AESA mode to track 50
targets ?
3) What is Space Time Adaptive Processing (STAP)
and how do you design for it?
4) How can you use an AESA antenna to detect slow
moving ground targets which are much smaller than
the background clutter.
5) How do you design an automatic target detection
and recognition mode?
This sampler presents the top level charts from the course on
how to answer these tough questions



Sampler

1) Design of an AESA
Medium PRF Search
Mode
AESA Radar in Medium PRF search




MED PRF Search Block Diagram
The Block Diagram for a MED PRF Search radar [Skolnick,fig 17.6]
Altitude
Speed

Clutter
Template
[12]

Sum Channel
Compress

FFT

Square
law
detect

CFAR

We will use an AESA antenna and receiver
with parameters like size, noise figure,
power and cooling appropriate for a fighter
type aircraft (from Stimson) to design the
modes and compute the performance


Smallest allowable
Target size m2
Skolnick Fig 17.12
Unfold
Detects

M of N
Range
Correlator
M of N
Doppler
Correlator

Target Reports
Range, Doppler,
Cross Section


Clutter Template from Supplied Simulation
Tail aspect

Head

• In this region the template tells us
we should use a backend STC or
guard channel
• In this region we are competing
with altitude line – Use special
processing to blank returns
• In this region the template tells us
we are competing with noise only
and we can use the noise PFA
threshold.
• In this region we are competing
with Main Beam Clutter. Due to
its magnitude we will use a notch
filter

The template [12] guides us in choosing a CFAR design



Baseline MED PRF Search Parameters
Parameter

Value

Comments

FFT Size

512

Controls S/N and scan rate

PRF

70KHz

For good tail aspect visibility

CHIP

0.5mics

For reduced clutter

PCR

4

Higher average power

M of N

3 of 7

Range correlation

TFA

30sec

Specification time between FA’s

Freq Agile

Look-Look

Good LPI design

Xmit Pulse

2mics

Duty

14%

Derived
Avg Power
parameters Pfa

471watts
5.8E-6

CFAR probability of false alarm

The course will show the student how to select the parameters and
enter them into the Mode Design spreadsheet



MED PRF Single Scan Performance
Single Scan PD - Low PRF .VS. Medium PRF

Cross Section 5m2

Chart from the
mode design
spreadsheet
using VBA
software from the
eBook on
Detection Theory
(supplied with
course)

The Mode Design Spreadsheet 1) Guides the student in the
designing a mode, 2) Captures the designs and 3) Compares
the performance for different configurations



Sampler

2) How to Track 50 Targets
with an AESA Radar

AESA Radar engaging and launching
missiles on six targets


Introduction Page 11


Vector Tracking Loop
Error
∼∆kANT

Steering vector
k(α,β)

For monopulse vector processing see [9] Haupt
and eBook on antennas

Compute
Monopulse
Error ∆kANT

kT(θ,φ)
target

k(α,β)
antenna steering

General radar tracking loop

Transform
To NAV
Coords
Transform
to ANT
Coords

Kalman
Filter in
NAV
Target
Relative
Position

Ownship position vector
in NAV reference

The Σ and ∆ channels are used to compute the error vector ∆k in
ANT coordinates



Three Channel (Az,El,Range) Kalman [1]
Gain Computation
For n in 1..3
= Pn H
Kn

T

( HP H
n

T

+ Rn )

Extrapolate
Where n is one of the
3 orthogonal channels
Rng, Az , El

XΦX
=
For n in 1..3
= ΦPn Q +
Pn P
n

n

−1

State Update
For n in 1..3
Nav
=
X X + K n En

P Update
For n in 1..3
Pn=

(1 − K n H ) Pn

The lectures will define each matrix in the design



Typical Track Performance

RMS Velocity Error

Angle Error

Tracking a Steady 3G S Turn at 20nm. RMS velocity errors
typically approach 200+ft/sec and are entirely adequate to guide
missiles to intercept




AESA Time Line

15 Target track interleaved with
search while displaying a SAR image.
Room for lots more!!



Sampler

3) Space Time Adaptive Cancellers




Space Time Adaptive Filters (Stimson, Haupt)
• The STAP canceller can remove multiple sidelobe jammer(s)
without prior knowledge of the jammer(s) location or antenna gains.
• STAP uses an Interferometric (space based) canceller.
• For each expected jammer we need one receiver and Auxilliary
antenna with a gain larger than the sidelobes of the main antenna.

Gain of AUX
Target

Adaptive Cancellers
Stimson [3,Ch 40],
Skolnick[4,Ch 9]

Standoff
sidelobe
jammer

STAP computes jammer phase
angles and antenna gains and
applies a spaced based adaptive
notch filter. By combining this
with an FFT to separate moving
targets we have a two
dimensional Space – Time
adaptive filter



The Adaptive Canceller [7] Elbert
V

V

V

Main

AUX2

AUXn

Store samples from each
channel in the rows of the
H matrix
H=[m a2 a3…an]
X1

X2

∑

See also Stimson [3,Pg509]

The optimal weights X
are the 1st column of
the inverse of the
covariance matrix
(HTH)-1
Xn

Note the order of
the matrix inverse
is equal to the
number of
channels i.e. two
channels means
we have to invert
a 2x2 matrix

Sum the weighted outputs of the multiple
antennas to cancel the jammer.

The space filter is a direct application of linear estimation theory [7]



Example of STAP With Multiple Jammers
Example of STAP with 4 Jammers. 4 Aux horns
Target
10deg
20deg
30deg

See eBook on
Antennas for
detailed
simulation of
multiple
jammers

40deg
Weighted
Sum

The optimal weights are:
x =1st Column of CovarianceMatrix −1

The cancelled jammer output equation is:
Output=Main+x1 Aux1 +x 2 Aux2 +x 3 Aux3 +x 4 Aux4

One 5th order Matrix Inversion and 25 dot products of length 10



FFT Before and After Cancellation
The target cannot be seen in
the FFT with 4 Sidelobe
jammers. Notice the magnitude
of the noise at 100 Q or more!
Uncancelled Jammer + Target

After cancellation the target
is easily seen in the FFT
and the noise is down to 5
quanta
Cancelled Jammer + Target

Example from eBook on Antennas




Sampler

4) Slow Ground moving target
indicator Main Beam
Clutter Canceller




Slow Moving Target Detection
Combining the
Interferometer technique
(used in STAP) with
multiple antenna beams
we can implement a high
performance mode to
cancel main beam clutter
and detect small slow
moving targets in a
situation which
otherwise would be
completely hopeless
SAR display with outputs from the slow
moving target detector

One of the most impressive applications of an AESA canceller..



Spatial vs Frequency Filtering
Tail aspect

Head

Frequency Filtering: With an FFT
we can separate targets with
different Doppler frequencies.
This fast moving target is separated
by frequency from main beam
clutter and is easily detected with
an FFT

FFT range/Doppler map

Spatial Filtering
This slow moving target,
overwhelmed in an FFT by main
beam clutter at the same frequency,
can only be detected by spatial
filtering with an interferometer

The course will describe this essential diagram in detail



Slow Moving Targets and Clutter
Stationary
target at
angle θt

Large MBC
Clutter at
angle θc

In a space diagram the target and
clutter are separable

θt

θc Angle Space Map

Slow
moving
target at
angle θt

Whereas in a normal FFT frequency
diagram the target and clutter overlay
each other and the smaller target
cannot be detected
Doppler Frequency Space Map

A Spatial Notch with multiple antennas can remove the clutter



Slow Mover - Canceller [Stimson Pg321]
k T (θ , φ )

k MBC (α , β )

The target at the
same frequency as
clutter
-d/2

The phase for clutter at angle α ,β :
d/2
Right

Left

Get α,β for
each FFT
Cell
Get Gain
for each
FFT Cell

MBC comes from a known
angle α,β

Rg x
Filter
matrix

Rg x
Filter
matrix

Cancel
Clutter

GLeft
πd
ϕc =R • k =
sin(α ) cos( β ), G rel =
GRight
λ
Using the canceller equation:
G
Output = Main - Aux M exp(− j 2ϕ )
GA
The cancelled clutter for each filter is:
Cancelled n = Leftn − Rightn exp(− j 2ϕc )

Recompute
FFT

CFAR

Slow moving
ground
targets

A little complicated but very powerful



S

Sampler

ATR Finds 3 S-300
Surface – Air Missile
Launchers with
Pd>0.95 in 2 sec
S

5) Automatic Target Recognition
Target Detection
S

Bushehr nuclear power plant from Google Maps



Automatic Target Detection Outline [13]
SAR Targets +
Clutter

Data from MSTARS public website, algorithms from
Lincoln labs and Mathcad image processing library

CFAR
Detector
Get
Enhanced
Tgt Chips

Binarize
Image

Detected targets
sans clutter

Clumped
Detects

Open/Close
Shapes

Edit Clutter
False Tgts

Compute
Moments
Statistics

Library
Clutter Shadow
Removal

Target
Recognition
Target List

Detector uses general target signatures to find “military like” targets



Theory of Moments from [11] HU






Characterization of an image by statistical moments
like variance, and kurtosis, and invariant moments like
the eigenvalues is a common approach in ATR.
The Uniqueness theorem states that you can
completely reconstruct an image with knowledge of
the moments of the image.
If you use amplitude, translation, scale and rotation
invariant moments you increase the power of this
approach
E

All three E’s in this example are uniquely
identified by the same simple moments
which are independent of where they are
on the paper, their amplitude, scale or
rotation

We can also characterize tanks, trucks and guns by moments



Example Automatic Target Recognition[13]
Enhanced M113 Chip
from ATD with feature
vector consisting of
moments, stats and
Pose=-30deg
pose

1) Use the pose to index the library
2) Compute Score for each target in
the library using feature vectors
3) The highest score is the ID

Library Chips
with same pose
as detected
target

BTR60

M113 BMP2

Correlation

0.81

1

Eigenvalues

0.62

1

Area

0.89

1

Combined

0.45

1

Good Match

Feature Vec

BTR70

T72

M109

M2

HMMW

M1

0.92

0.88

0.87

0.86

.91

.93

.85

0.71

0.61

0.73

0.54

.72

.70

.41

1

1

0.81

0.69

.91

.91

.67

0.66

0.54

0.51

0.32

.59

.59

.23

Comparison of feature vectors for each target in library



References
1) Decoupled Kalman filters for phased array radar tracking: Automatic Control,
IEEE transactions on: Date of Publication: Mar 1983 Author(s):Daum F. Raytheon
Company, Wayland, MA, USA
2) Blinchikoff and Zverev, “Filtering in the Time and Frequency Domain” 1975
3) Rabiner and Gold, Theory and Application of Digital Signal Processing 1975
4) Stimson, “Introduction to Airborne radar” 1998
5) Skolnick “Introduction to Radar” 1995
6) William Skillman “Radar Calculations” Artech House ,1983
7) “Estimation and Control of Systems” Elbert 1984 – Contains all aspects of linear
estimation from least squares to the Kalman filter
9) Antenna Arrays - Randy Haupt IEEE Press
10) SDMS MSTARS Public Data Website https://www.sdms.afrl.af.mil/ Contains 1ft
SAR images of military targets
11) M.-K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans.
Information Theory, vol. 8, no. 2, pp. 179–187, 1962.
12) Radar CFAR Thresholding in Clutter and MultipleTarget Situations Hermann
Rohling AEG-Telefunken, IEEE Transactions On Aerospace and Electronic
Systems VOL. AES-19, NO. 4 JULY 1983 Discusses clutter maps for describing
clutter regions of differing clutter type. Excellent analysis of CA, GO CFAR and
ordered statistic CFAR



References


13) MIT Lincoln Lab Journal Archives
http://www.ll.mit.edu/publications/journal/journalarchives.html

Vol 10, Number 2 - 1997

Vol 8, Number 1 - 1995

Vol 6, Number 1 - 1993

Provides overview of the Automatic Target Recognition
and Detection including Super resolution SAR , CFAR’s
and effects of polarization and resolution on recognition



AESA Airborne Radar Theory and Operations Technical Training Course Sampler

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