Approximating Sensor Footprints

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Spring 2006 Simulation Interoperability
Workshop SIW-06S-026 Approximating Sensor
FootprintsWith HLA DDM Rectangles Lines,
Quadrilaterals, and Multi-sectors Mikel D.
Petty, Ph.D. Center for Modeling, Simulation,
and Analysis University of Alabama in Huntsville
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Presentation outline ? Introduction - Data
Distribution Management - Sensor footprint
shapes - Extra area in DDM rectangles ? Area
analyses - Line - Quadrilateral - Multi-sector
? Summary, relevance, and future work
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Introduction
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Data Distribution Management
d1
Overlap
Subscription
Update
Subscription
DDM space
d2
Federate
Federate
Federate
Federation
RTI
RTI
RTI
Data flow
Network
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Geographic DDM scheme ? DDM space corresponds to
battle space ? Subscription regions for sensor
footprints ? Update regions for movement bounds
y
x
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Sensor footprint shapes
05S-SIW-061
05F-SIW-018
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Extra area in DDM rectangles ? DDM uses
axis-parallel rectangles ? Sensor
footprints - Usually not axis-parallel
rectangles - Approximated by DDM
rectangles - Approximation encloses extra
area ? Extra area can result in unwanted
data ? How much extra area?
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Area analysis Line
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Line ? Line has no area? Area of enclosing DDM
rectangle also depends on orientation
S at orientation ? ?/16 area(R) 0.19
S at orientation ? ?/4 area(R) ? 0.50
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Line and DDM rectangle area ? Area of enclosing
DDM rectangle if function of line length r,
orientation ?
y
Area function
Area function, simplified
R
r
r sin ?
S
?
x
r cos ?
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Average value of DDM rectangle area ? Find
average value of DDM rectangle area over all
line orientations (0 ? ? ? ?/2)
Antiderivative of area function
Average value of area function
Average value formula
Interval endpoint antiderivative values
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Line area ratios ? Average area ratios, DDM
rectangle to line - Line has no area, area ratio
rectangle/line undefined ? Laser designator not
actually line - Treated as triangle with b
h/4000 23 - Area of triangle ½bh
Length r of S
Average ratio area(R)/area(S)
1000
2,546.48
2000
2,546.48
4000
2,546.48
8000
2,547.48
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Area analysis Quadrilateral
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Quadrilateral ? Quadrilateral area depends on
shape ? Area of enclosing DDM rectangle also
depends on orientation
S at orientation ? 0 area(R) 66
S at orientation ? ?/4 area(R) 75
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Quadrilateral and DDM rectangle area ? Area of
enclosing DDM rectangle is function of
quadrilateral shape, orientation ?
Area function
y
B (xB, yB)
R
?1
?3
dB
?2
?4
C (xC, yC)
where
x
dC
dA
A (xA, yA)
ymax(?) ymin(?)
S
dD
D (xD, yD)
xmax(?) xmin(?)
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Quadrilateral area ratio calculation ? Sample
quadrilaterals - Area of quadrilateral function
of shape parameters ?1, ?2, ?3, ?4, dA, dB, dC,
dD - Sampling across parameter values
problematic - Sample quadrilaterals drawn from
literature ? Area of DDM rectangles found
numerically - Antiderivative of area function
problematic (piecewise) - Area of enclosing DDM
rectangle calculated at 8 evenly spaced values
of ? ? 0, p/2 - Mean area over ? values
calculated ? Area ratio mean DDM rectangle
area over quadrilateral area
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Sample quadrilaterals
y
y
y
x
R
S
x
x
S
S
R
R
Quadrilateral sample 1
Quadrilateral sample 2 24
Quadrilateral sample 3 25
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Quadrilateral area ratios ? Mean DDM rectangle
mean to quadrilateral area
Orientation ?
Quadrilateral 1
Quadrilateral 2
Quadrilateral 3
0
66.00
180.00
500.00
1p/16
70.61
120.41
433.13
2p/16
73.03
151.92
404.35
3p/16
78.47
194.26
410.72
p/4
75.00
250.00
437.50
5p/16
63.16
263.02
495.96
6p/16
44.75
259.71
515.17
7p/16
54.54
230.55
528.81
p/2
66.00
180.00
500.00
mean area(R)
65.69
206.24
465.70
area(S)
30.00
90.00
250.00
ratio
2.19
2.29
1.86
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Area analysis Multi-sector
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Multi-sector ? Multi-sector area depends on
shape ? Area of enclosing DDM rectangle also
depends on orientation
y
y
R
S
R
x
x
S
S at orientation ? 0 area(R) 1488
S at orientation ? ?/4 area(R) 2099
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Multi-sector and DDM rectangle area ? Area of
enclosing DDM rectangle is function of
multi-sector shape, orientation ?
Area function
where
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Multi-sector area ratio calculation ? Sample
multi-sectors - Area of multisector function of
shape parameters ?i, ?i, qi, si, 1 ? i ?
k - Sampling across parameter values
problematic - Sample multi-sectors drawn from
literature ? Area of DDM rectangles found
numerically - Antiderivative of area function
problematic ( lobes) - Area of enclosing DDM
rectangle calculated at 8 evenly spaced values
of ? ? 0, p/2 - Mean area over ? values
calculated ? Area ratio mean DDM rectangle
area over multi-sector area
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Sample multi-sectors
Multi-sector sample 2 27
Multi-sector sample 3 28
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Multi-sector area ratios ? Mean DDM rectangle
mean to multi-sector area
Orientation ?
Multi-sector 1
Multi-sector 2
Multi-sector 3
0
1,967.51
1,487.58
2,402.04
1p/16
2,481.56
1,682.58
2,733.66
2p/16
3,007.73
1,870.91
3,117.71
3p/16
3,489.83
2,005.26
3,499.66
p/4
3,680.73
2,099.45
3,622.18
5p/16
3,489.83
2,005.26
3,469.57
6p/16
3,007.73
1,870.91
3,175.25
7p/16
2,481.56
1,682.56
2,642.91
p/2
1,967.51
1,487.58
2,402.04
mean area(R)
2,950.81
1,838.06
3,082.87
area(S)
1,132.19
772.34
1,385.53
ratio
2.61
2.38
2.23
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Summary, relevance, and future work
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Summary, relevance, and future work ? Summary -
DDM rectangles larger than sensor
footprints - Ratio of areas can depend on
footprint orientation - Typical average area
ratios 2-4 - Larger ratios possible for thin
footprints ? Relevance ratios may be useful
to - Fed designers estimating data flow
volume - Fed designers evaluating simpler DDM
schemes - HLA designers considering
non-rectangular DDM
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? Future work - Other 2D sensor footprint
shapes? - 3D sensor footprint shapes - Treat
shape parameters other than orientation as
variables to be averaged on - Multiple DDM
rectangles per footprint
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End of presentation