MV4920

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MV-4920 Battlefield Data Processing Theory-II
Generic Processing Cycle Truth Table
Program Data Processing Automation Input and
Output Transforms Calculation Levels
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Generic Processing Cycle
Program Detector Status to Actuator Commands
output
input
WRITE
READ
Actuator
Detector
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Generic Processing Steps
1) Read - Reads Detector Content into Input
array for the calcualtion phase 2) Process -
Execute the program which connects a set of
Inputs to a set of Outputs 3) Write - Sends
Actuator Commands from calcualtion output
array into Actuator 4) Wait - reset go back to
step 1
Generic Data Structures
Detector Readings - Detector name, detector
content Actuator Commands- Actuator Name,
Actuator content Input - Memory Cell Name,
Memory Cell Content Output - Memory Cell Name,
Memory Cell Content
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READ
The Transform from detector name space to program
input name space is done by the Read function
enable
Detector Readings
READ
Input
disable
Read ( radix DetectorNames, radix
Input) Enable (DetectorNamesI) For
(I0,IltNumber of detector names,I) (InputI)
(DetectorNames I) Disable
(DetectorNamesI) return
Low level simple assignment example
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WRITE
The Transform from program output to actuator
commands is done by the WRITE function
enable
Actuator Commands
WRITE
Output
disable
Write( radix ActuatorNames, radix
Output) Enable (ActuatorNamesI) For
(I0,IltNumber of ActuatorNames,I) Output
(ActuatorNames I) Disable
(ActuatorNamesI) return
Low level simple assignment example
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Generic Truth Table Program
Radix InputTable MaxInput Possibilities Radix
OutputTable MaxOutputPossibilities TruthTablePro
gram(Radix Input,Radix Output)
while(ThisltMaxInput Possibilities) if
(Input InputTablethis) Output
OutputTableThis return This This 1
return
Input
Output
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Truth Table Program
INPUT OUTPUT
Detector names
Actuator names
1 2 3 . Dmax
1 2 3 . Amax
0 1 1 0 1 0 0 1 0 1 0
1 1 0 0 0 1 1 1
0 1 1 1 1 ...
0 0 0 0 1 0 0 0 0 1 0
0 1 1 0 0 0 0 1
0 1 0 1 0 ...
If this do that
All possible actuator commands
All possible detector content states
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Some Properties of the Truth Table Program
Any calculation doable with a Turing machine can
be written as a Truth Table Program. The program
execution steps are trivial. All the complexity
is in the Input and Output tables. The Input and
Output Tables can get very big. For example
suppose besides the immediate detector input the
program also considers the past history ie. The
memory of the machine. Then the Input would
contain the not just the detector readings but
also the the content of all the memory cells.
HOW BIG? Assume there are Dmax detectors
reporting one of Dc readings and Mmax memory
cells reporting a 0 or 1 each of then the total
number of Configurations is
DcDmax 2Mmax Each additional cell will
multiply the volume of possibilities by the
number of different contents that can be read
from the cell. If this number of input
possibilities requires a response to Amax
actuators with l levels the total truth table
array is Amax l DcDmax 2Mmax
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Simple Surface Seeker Example
Input 2 detector 2 levels
L R 0 1
L R
L N R
Output 1 actuator 3 positions wheel
L N R
Program Truth Table
Detector Name L R 0 0 0 1 1 0 1 1
Actuator name Wheel L R L N
Reason no target seek left target right go
right target left go left target center go
straight
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EXAMPLE HARDWARE IMPLEMENTATION OF A TRUTH TABLE
PROGRAM

L
R
N
R
L
EXAMPLE LOOKUP Table Implementation OUTPUT
TRUTHTABLEINPUT
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How many gates does it take to Implement?
For a system with INmax 2 state inputs and
outputs the Total Gates 2 (INmax 1) 2INmax
Suppose each set of these gates are a micro meter
in size.How big a problem could you fit into a
sphere of size R in meters. Total Gates 4/3 ?
1024R3
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How fast could a calculation be done ? Time to
for the speed of light to go from the center to
the surface and back. T 2R/c
T (2R/c ) 2/c (3 ? /410-24G)1/3 (2/c)
10-6 (3 ? 2 /4)1/3 ((IN1) 2IN )1/3 5 10-14
((IN1) 2IN )1/3 IN 30 bits T
3.4x10-10 R 10 cm IN 100 bits
T .004 sec R 1.2 x106
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TRICKS TO REDUCE IMPLEMENTATION COST
Truth Table Program solves any problem in real
time but complex problems cost a lot what can you
do?
Reduce bits use value changes some
patterns cannot happen collect patterns with
the same solution Add time ( program steps)
calculate each possibility when it happens
Hybrid - pre-calculate partial solutions
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Data Processing Automation
WHAT IS AUTOMATION? The transfer of what a
human does to a machine. Automation Steps 1)
Learn the human operation sequences. 2)Build a
machine that automatically executes machine
operations 3) Map the human to sequences of
machine operations 4) if mapping not complete
add machine operations and go to 2. We already
have a machine that does any calculation we can
imagine. So what is left to do? Learn how
the human writes the truth table program.
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How is the program written? Input and output
possibilities are defined by all possible content
configurations in the space of input and output
cell names. The programmer visualizes the meaning
of an input content configuration
possibility. The programmer decides for each
possible input what is the appropriate output and
writes this decision into a truth table. The
programmer goes to the next possible content
configuration until all possible input
configurations are exhausted.
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Context and Reason for Program Supplied by
Programmer
Programmers World Concept
Program Detector Status to Actuator Commands
input
output
READ
WRITE
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Programmer Writers Process
Programmers World Concept
Output Meaning
Input meaning
decision
Interpret detector readings in terms of input
Interpret Meaning of output in terms
of Actuator commands
Program
input
output
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Transforming The Program to a Higher Level
Programmers World Concept
input
output
HIGHER LEVEL Program
Transform
Transform
input
READ
WRITE
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Steps to Solve the Intercept Problem at a Higher
Level
Example Specific
General functions
Select Hunter and Target Object Space. Solution
Minimized distance.
1) Find a space in which the Problem Solution
decision can be made 2) Make the decisions in
this space 3) Transform from measurements to
Decision Space and add detectors as necessary. 4)
Transform from Decision to Command Space and add
Actuators as necessary.
Write the Program (Input Hunter and Target Object
Space ,Output Hunter and Target Object Space )
Write the Transform (Readings Detector Space
, Input Hunter and Target Object Space )
Write the Program (Output Hunter and Target
Object Space ,Commands Actuator Space )
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Step 1) Find the Decision Space
Solution is to close the distance
Hunter Position Xh,Yh,Zh,Th
Target Position Xt,Yt,Zt,Tt
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Step 2) Write the Interceptor Truth Table
Program(3x3x3 Example)
Name dimensions
All Possibilities
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How is the Intercept program written?
Visualize Next Possible Input Configuration
Predict new position based on constant
velocity Xh3 2Xh2 - Xh1, Yh3 2Yh2 - Yh1,
Zh3 2Zh2 - Zh1 Xt3 2Xt2 - Xt1, Yt3
2Yt2 - Yt1, Zt3 2Zt2 - Zt1 Calculate
Hunters best velocity Change R
(Xh3-Xt3)2 (Yh3-Yt3)2 (Zh3-Zt3)2 ?X
(Xh3-Xt3) /R ?Y (Yh3-Yt3) /R
?Z (Zh3-Zt3) /R Calculate desired
position Xhout Xh3 ?X , Yhout Yh3
?Y , Zhout Zh3 ?Z
Calculate the best Move
Write Output decision
?
Next Next1
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Step 3 ) Detector Reading to Object Space
Transform
Transform( Detector readings HunterPosition,Targe
tPosition)
Transform program in Truth Table format
Corresponding Hunter Position, Target
Position Xt,Yt,Zt,Xh,Yh,Zh
Instant HunterPosition,TargetPosition
All possible Detector readings D,Az,El,f,Xh,Yh,Zh
Instant Detector readings
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How is the Detector Reading to Object Space
Transform Programmed?
2) Find Detector Reading Context
o
f
D
5)Single Instant Transform XtOcos(el)cos(az) Yt
Ocos(el)sin(az) ZtOsin(el) O mf
1) paramterize Object Space
F
Az El
4) Add Additional Detectors for Target Positioning
GPS receiver
Xh Yh Zh Th
3) add Additional Detectors for Hunter
positioning
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How is Object Space to Actuator Command Transform
Programmed?
Spectrum of Actuator Command
1) If the vales Yr,Pr,Th were applied 2) The
change in position in Vehicle coordinates in ?T F
Th drag ?F ?Th drag ?U F
(1-cos(Pr)/2) ?R F (1-cos(Yr)/2) 3) Transform
from Vehicle to Object Space Coordinates ?X
Vehicle ?F ?Y to ?U ?Z space ?R 4)
The change ?X, ?Y, ?Z Would result in the
position.
PitchRate
YawRate
Thrust
Reverse calculation to get Actuator Commands
U
R
F
Desired ?X, ?Y, ?Z from Program
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THEORY II SUMMARY
T a k e s P r o c e s s i n g
H i g h e r L e v e l s
Automation Trend
D a t a F l o w to
LEVELS OF ABSTRACTION
Time