Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Appendix I / Utilities / Covariance
_ _
B 2
2
2 2 2 2
( δ ξ ) : = 3.
41 ⋅ λ ⋅ λ : = 3.
41 ⋅ σ ⋅ σ − σ
E A
1 2
Θ Ψ ΘΨ
RAYLEIGH - CUMULATIVE PROBABLITY
RAYLEIGH - CUMULATIVE PROBABLITY
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.5 1 1.5 2 2.5 3 3.5 4
ANGULAR ERROR ( STANDARD DEVIATIONS )
1
0.999
0.998
0.997
0.996
0.995
0.994
0.993
0.992
0.991
0.99
3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4
ANGULAR ERROR ( STANDARD DEVIATIONS )
22.13-11
Equation 22.13-55
Figure 22-16
Rayleigh Cumulative Probability vs Standard Deviation
When determining the differential angular error for small angles,
( ) ( ) ( ) 2
C 2
B 2
C
δ ξ ≅ E δξ
+ E δ
E ξ
22.13.12 Polar to Cartesian Covariance Conversion
B
A
A
Equation 22.13-56
COV_P_TO_C takes the range from point (a) to point (b), and the YP Euler
angles defining the orientation of frame (B) with respect to frame (A), and
their uncertainties, returning a [3x3] covariance matrix with respect to (A).