Common Core State Standards Activity Packet ANSWERS & EXAMPLES

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Oklahoma State Department of Education Page 1 Office of Standards and Curriculum Common Core State Standards Common Core State Standards Activity Packet ANSWERS & EXAMPLES
  • relationships of congruency of triangles
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Publié le : mercredi 28 mars 2012
Lecture(s) : 20
Source : cs.unc.edu
Nombre de pages : 48
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STC Lecture Series
An Introduction to the Kalman Filter
Greg Welch and Gary Bishop
University of North Carolina at Chapel Hill
Department of Computer Science
http://www.cs.unc.edu/~welch/kalmanLinks.html
UNC Chapel Hill Computer Science Slide 1Where We’re Going
• Introduction & Intuition
• The Discrete Kalman Filter
• A Simple Example
• Variations of the Filter
• Relevant Applications & References
UNC Chapel Hill Computer Science Slide 2The Kalman filter
• Seminal paper by R.E. Kalman, 1960
• Set of mathematical equations
• Optimal estimator
– minimum mean square error
• Versatile
predict correct
predict
– Estimation
– Filtering
– Prediction
– Fusion
UNC Chapel Hill Computer Science Slide 3Why a Kalman Filter?
• Efficient “least-squares” implementation
• Past, present and future estimation
• Estimation of missing states
• Measure of estimation quality (variance)
• Robust
– forgiving in many ways
– stable given common conditions
UNC Chapel Hill Computer Science Slide 4Some Intuition
UNC Chapel Hill Computer Science Slide 5s
s
s
First Estimate
Conditional Density Function
2
z ,
z
1
1
x = z
ˆ
2
1 1
N(z , )
1 z
1
2 2
ˆ
s =
-2 0 2 4 6 8 10 12
14
z
1
1
UNC Chapel Hill Computer Science Slide 6s
s
Second Estimate
Conditional Density Function
2
z ,
z
2
2
2
N(z , )
2 z
2
x = ...?
ˆ
2
2
ˆ
s = ...?
-2 0 2 4 6 8 10 12
14
2
UNC Chapel Hill Computer Science Slide 7s
s
s
s
s
s
s
-
s
s
Combine Estimates
2 2 2 2 2 2
= + z+ + z
x
ˆ
() ()
[][]
z z z 1 z z z 2
2 2 1 2 1 1 2
= x + K z x
ˆ ˆ
[]
1 2 2 1
where
2 2 2
+
K =
()
z z z
2
1 1 2
UNC Chapel Hill Computer Science Slide 8s
s
s
Combine Variances
2 2 2
1 = 1 +1
()()
2
z z
1 2
UNC Chapel Hill Computer Science Slide 9s
s
Combined Estimate Density
Conditional Density Function
2
N(x,
)
ˆ
ˆ
x = x
ˆ ˆ
2
2 2
ˆ
s =
2
-2 0 2 4 6 8 10 12
14
UNC Chapel Hill Computer Science Slide 10

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