Datum Problems - Map Projections: Cartographic Information Systems - page 525

vec dA T +Lvecd y (21.55)

subject to
(decomposition of a double Cayley product by a Kronecker-Zehfuss
product)
vec(ABC) = (C T ⊗ A)vec B . (21.56)

vec d x =QvecdA+Rvecd y (21.57)

subject to

Q:= − (A x ) T

⊗ N]I 7 , 2 +[( y ) T ⊗ N − 1 ]I 7 , 2 − [( x ) T

⊗ L] ,

R:=L . (21.58)

vec d x =Qvec ∂ A

∂p k d p k +Rvec ∂y ∂p k d p k

(21.59)

with respect to the parameters p k := { l,b,L,B,H } .

Dispersion transformation:

D( x )=M k D( p k ,p l )M l (21.60)

subject to
M k := Q ∂ A

∂p k +R ∂y

(21.61)

∂p k

with
{k, l}∈{ 1 , 2 , 3 , 4 , 5 }. (21.62)

Box 21.10 (Error propagation with respect to synthesis [ L, B ]( l,b, t x ,...,δe 2 )).

Parameters :
L i := [ L, B ] , i := [ l,b ] , p := [ t x ,t y ,t z ,α,β,γ,s,δα,δe 2 ] .

(21.63)

Error propagation:

= δ ij + ∂b 0

∂L i
∂l j ∂l j t p , ∂L i

ip

∂t p = b 0

ip ,

(21.64)