468 21 Datum problems
Continuation of Box.
vec dˆ x = Q vec dA + R vec dy
(21.57)
subject to
Q :=
ˆ − (Aˆ x)
T ⊗ N
˜
I 7,2 +
ˆ
(y)
T ⊗ N
−1 ˜
I 7,2 −
ˆ
(ˆ x)
T ⊗ L
˜
,
R := L .
(21.58)
vec dˆ x = Q vec
„
∂A
∂p k
dp k
«
+ R vec
„
∂y
∂p k
dp k
«
(21.59)
with respect to the parameters p k := {l, b, L, B, H}.
Dispersion transformation:
D(ˆ x) = M k D(p k , p l )M
T
l
(21.60)
subject to
M k := Q
∂A
∂p k
+ R
∂y
∂p k
(21.61)
with
{k, l} ∈ {1, 2, 3, 4, 5} .
(21.62)
Box 21.10 (Error propagation with respect to synthesis [L, B](l, b, ˆ
t x , . . . , δˆ e
2 ) ).
Parameters:
L i := [L, B] , l i := [l, b] , t p := [t x , t y , t z , α, β, γ, s, δa, δe
2 ] .
(21.63)
Error propagation:
∂L i
∂l j
= δ ij +
∂b
0
ip
∂l j
t p ,
∂L i
∂t p
= b
0
ip ,
(21.64)
D(L i , L j ) =
`
δ im + b
0
ip,m t p
´
D(l m , l n )
`
δ jn + b
0
jq,n t q
´
+ b
0
ip D(t p , t q )b
0
jq .
(21.65)
(Summation convention over repeated indices, {i, j, m, n} ∈ {1, 2} and {p, q} ∈ {1, . . . , 9}.)