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Appendix I / Utilities / Covariance
_ _
COV_P_TO_C
B B
( P , , Ψ , σ , σ , σ , [ σ ] )
a , b
22.13-12
ΘA A R Θ Ψ
C
Equation 22.13-57
2 2 B 2 2 2 B 2 B 2 2 2 B 2 B
( 1 ) : = ( σ ⋅ c Ψ + P ⋅ σ ⋅ s Ψ ) ⋅ c Θ + P ⋅ σ ⋅ c Ψ ⋅ s Θ
σC R A a,
b Ψ A
A a,
b Θ
A
Equation 22.13-58
2 2 2 2 B 2 2 2 B B B
( 4 ) : = ( ( σ − P ⋅ σ ) ⋅ c Θ + P ⋅ σ ⋅ s Θ ) ⋅ cΨ
⋅ sΨ
σC R a,
b Ψ A a,
b Θ
A
A
A
Equation 22.13-59
2 2 2
B B B
( 7 ) : = ( P ⋅ σ − σ ) ⋅ cos Θ ⋅ sin Θ ⋅ cos Ψ
σC a,
b Θ
R
A
A
A
Equation 22.13-60
2 2 B 2 2 2 B 2 B 2 2 2 B 2 B
( 5 ) : = ( σ ⋅ s Ψ + P ⋅ σ ⋅ c Ψ ) ⋅ c Θ + P ⋅ σ ⋅ s Θ ⋅ s Ψ
σC R A a,
b Ψ A A a,
b Θ
2 2 2
B B B
( 8 ) : = ( P ⋅ σ − σ ) ⋅ cos Θ ⋅ sin Θ ⋅ sin Ψ
σC a,
b Θ
R
2 2 B 2 2 2 B
( 9 ) : = σ ⋅ sin Θ + P ⋅ σ ⋅ cos Θ
σC R A a,
b Θ
22.13.13 Covariance Matrix Main Diagonal Extraction
A
A
A
Equation 22.13-61
A
A
Equation 22.13-62
A
Equation 22.13-63
M_EXTDIAG takes a covariance matrix [C] of dimension (n) and returns the
state uncertainties from its main diagonal in vector (U).
i
∈
[ 1 ( 1 ) n ]
⎧ C
⎪
: ⎨
⎪
⎩
M_EXTDIAG
22.13.14 Covariance Matrix Eigenvalue Metric
( [ C ] , U , n )
Equation 22.13-64
−8
( i , i ) > 10 ⇒ U ( i ) : = C(
i , i )
C
( ) ( ) ⎪ −8
i , i ≤ 10 ⇒ U i : = 0
⎫
⎪
⎬
⎭
Equation 22.13-65
EIGEN_METRIC uses EIGEN to obtain eigenvalues and eigenvectors of a
covariance matric [C], returning the following state metric.
A