坐标系转换公式.doc

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畸麴
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1 ( hp:// Coordinae Converion and ranformaion including Formula par 2 Formula for Coordinae Operaion oher han Map Projecion EPG hp:// GP GP WG84 WG84 Z Z WG84 GP dddz

2 Molodenki Helmer7 EPG - Bura-Wolf - Molodenki-Badeka Clarke GR 1980 Clarke 1966 Meade Ranch Molodenki Helmer EPG NAD83 U Coa & Geodeic urveynadcon EPG NAD27 NAD83 ED ED aen Karwerk 15 4 From o ϕ λ Z Z 90

3 a b 1/f = ( ν ϕ λ = ( ν ϕin λ Z = 2 (( ) ν ϕ ν ϕ ν = a/(1 e in ϕ) ϕ λ h e e = ( a b )/ a = 2f f N Z ϕ = g [( Z + eν in ϕ)/( + ) 1 λ = g ( / ) h= ecλecϕ ν λ 3.2 AA > 0 = A new old EPG 1999 = + A A EPG

4 = + A = [( * U ) + ( A* U )]*( m / U ) A = = A m m=1 m = 1 UU U A EPG dddz = + d = + d Z = Z + dz 2.1 WG84 GP ϕ = 53 48'33.82''N λ = 207'46.38''E h = 73.0m ED50 Inernaional 1924 WG84 ED50 d = m d = mdZ = m WG84 Z = m = m = m ED50 = = m = = m Z = = m 2 ED50

5 ϕ = 53 48'36.565''N λ = 207'51.477''E h = 28.02m Inernaional 1924 Molodenki Molodenki ϕ = ϕ + dϕ λ = λ + dλ h = h + dh dϕ'' = ( d.in ϕ.co λ d.in ϕ.in λ+ dz.co ϕ + [ adf. + fda. ].in2 ϕ)/( ρ.in1'') dλ'' = ( d.in λ+ d.co λ)/(.co ν ϕ.in1'') 2 dh = d.co ϕ.co λ + d.co ϕ.in λ + dz.in ϕ + ( adf. + fda. ).in ϕ da dddz ρ ϕ ρ = a(1 e )/(1 e in ϕ) ν ϕ ν = a/(1 e in ϕ) / /2 da da = a a df df = f f = 1/(1/ f) 1/(1/ f ) dϕ λ ϕ λ WG84 GP ϕ = 53 48'33.82''N λ = 207'46.38''E h = 73.0m ED50 Inernaional 1924 WG84 ED50 d = m d = m dz = m

6 WG 1984 a = /f = Inernaional 1924 a = /f = da = = 251 df = = E-05 dϕ = 2.545'' dλ = 5.097'' dh= 44.98m ED50 Inernaional 1924 ϕ = 53 48'36.565'' N λ = 207'51.477'' E = 28.02m Helmer R + R Z d M * RZ 1 R * d = + + Z R R 1 + Z dz Z Z EPG dddz RRRZ M M = (1 + d*10-6 ) d ppm

7 2.1 WG72 WG84 d = m d = m dz = +4.5 m R = R = RZ = d = ppm WG72 ϕ = 55 00'00''N λ = 400'00''E h = 0m Z = m = m = m 7 Z = m = m = m WG84 ϕ = 55 00'00.090''N λ = 400'00.554''E h =+ 3.22m EPG 1 + R R Z d M * RZ 1 R * d = + + Z R R 1 + Z dz dddz RRRZ

8 M M = (1 + d*10-6 ) d ppm d = m d = m dz = +4.5 m R = R = RZ = d = ppm IO Molodenki-Badeka 1 + R R Z P P d M * RZ 1 R * P P d = Z R R 1 + Z Z P Z P dz dddz RRRZ PPZP M

9 M = (1 + d*10-6 ) d ppm Molodenki-Badeka 6*10 1 6* *

10 U = m ( ) 0 V = m ( ) m UV AnBn dd m m d = A + A U + A V + A U + A U V + A V A U + A U V+ A U V + A V A U + A U V+ A U V + A U V + A V A U + A U V + A U V + A U V + A U V + A V A U + A U V + A U V + A U V + A U V + A U V + A V A V m d= B + B U + B V + B U + B U V + B V B U + B U V+ B U V + B V B U + B U V+ B U V + B U V + B V B U + B U V + B U V + B U V + B U V + B V B U + B U V + B U V + B U V + B U V + B U V + B V B V dd EPG Aumvn Bumvn m U n V A17 Au3v2

11 ( ) = ( ) + d 0 0 ( ) = ( ) + d 0 0 = + + d 0 0 = + + d dd 6 EPG 9648 M75 ER = ϕ 0 = 5330'00.000'' N = = λ 0 = 742'00.000'' W = = ϕ 0 = 5330'00.000'' N = = λ 0 = 742'00.000'' W = 7.7 m = 0.1 m = 3600 A0 = A1 = A24 = A27 = 0 B0 = B1 = B24 = B27 = 0 M75 ϕ λ M75 M75 0 M M75 0 = = 55 00'00'' N = = = 630'00'' W = = ϕ ϕ = = 1.5 = λ λ = 6.6 ( 7.7) = 1.2 U = m ( ) = m ( ϕ ϕ ) = 0.1*(1.5) = M75 0 V = m ( ) = m ( λ λ ) = 0.1*(1.2) = M d = ( A0 + A1 U A24 U V )/ K CD d 3 3 = { ( 4.487*0.15) ( *0.15 *0.12 )}/3600=

12 3 3 d = ( B0 + B1 U B24 U V )/ K CD d 3 3 = { ( 0.341*0.12) ( *0.12 *0.12 )}/3600= ϕ λ = = + d = = 55 00' '' N ER89 = = + d = = 630' '' W ER EPG n dd 1 O = 0 = 0 O = 0 = 0 m = m = m dd dd dd ED50 ED ED50 ED N0E4 d d 10-6

13 10 6 EPG 4 EPG 9651 ED50 ED87 = ϕ = 55 00'00.000'' N = = λ = 000'00.000'' E = m = 1.0 A0 = E-06 A1 = E-06 A14 = E-09 B0 = E-05 B1 = E-05 B14 = E-09 ED50 ϕ λ ED50 ED50 = = 52 30'30'' N = = = 2 E =+ 2 U = m ( ) = m ( ϕ ϕ ) = 1.0*( ) = ED50 0 V = m ( ) = m ( λ λ ) = 1.0*( ) = 2 0 ED d = ( A0 + A1 U A14 V )/ K CD = [ E 06 + ( E 06* ) ( E 09*2.0 4)]/1.0 = E 06 4 d = ( B0 + B1 U B14 V )/ K CD = [ E 05 + ( E 05* ) ( E 09*2.0 4)]/1.0 = E 06 ϕ λ = = + d = E 06= 52 30' '' N ED87 = = + d = 200' '' E ED87

14 ED87 ED A0A14B0B14 = ϕ = 55 00'00.000'' N = = λ = 000'00.000'' E = m = 1.0 A0 = E-06 A1 = E-06 A14 = E-09 B0 = E-05 B1 = E-05 B14 = E-09 ED50 ϕ λ ED87 ED87 = = 52 30' '' N = = = 200' '' E = U = 1.0*( ) = V = 1.0*( ) = d = ( A0 + A1 U A14 V )/ K CD = [ E 06 + ( E 06* ) ( E 09* )]/1.0 = E 06 4 d = ( B0 + B1 U B14 V )/ K CD = [ E 05 + ( E 05* ) ( E 09* )]/1 = E 06 ϕ λ = = + d = E 06= 52 30'30.000'' N ED50 = = + d = 200'00.000'' E ED50

15 ABUV 3 m ( d + id ) = ( A + i A )( U + iv ) + ( A + i A )( U + iv ) ( A + i A )( U + iv ) + ( A + i A )( U + iv ) U = m ( ) 0 V = m ( ) 0 m m 2 4 Amerfoor / RD ED50 / UM U V 2 2 U V m d 2 + A1 A2 + A3 A4 + A5 A UV 6 + A7 A8 * 3 2 m U 3UV d = A2 A1 A4 A3 A6 A5 A8 A UV V U 6UV + V 3 3 4UV 4UV = + + d 0 0 = + + d A0 B0

16 4 EPG 9653 Amerfoor / RD New ED50 / UM zone 31N m 10-5 m 1.0 A1 A A2 A A3 A A4 A A5 A A6 A A7 A A8 A Amerfoor / RD = = m Amerfoor / RD = = m U = m = = 5 ( 0) ( ) V = m = = 5 ( 0) ( ) d = / 1.0 d = / 1.0 ED50 / UM 31 = = d = m ED50 / UM 31 = = d = = = m

17 EPG 9617 Madrid 1870 ruve 1860 Madrid El ervicio Geografico del Ej rcio Madrid 1870 ED Madrid 1870 ED50 dϕ( ) = A + ( A * ϕ ) + ( A * λ ) + ( A * H ) dλ( ) = B + B + ( B * ϕ ) + ( B * λ ) + ( B * H ) ϕ λ Madrid 1870 H B 00 Madrid Greenwich B 00 ϕ = ϕ + dϕ ED50 M1870( M) λ = λ + dλ ED50 M1870( M) Madrid 1870 ϕ = 42 38'52.77'' N = λ = 339'34.57'' EMadrid ( ) = ( Madrid) H = 0 m A0 = B00 = A1 = B0 = A2 = B1 = A3 = B2 = dϕ =+ 4.05'' ϕ ED 50 ED50 B3 = = 42 38'52.77'' N " = 42 38'56.82'' N d λ = '' = 341'10.54'' λ = 339'34.57'' E 341'10.54'' = 001'35.97''( Greenwich)

18 EPG EPG 9624 CAD GI rubber heeing A0 A 1 A2 * = B + B B = A + A + A = B + B + B P P 4.1 D= A B A B A ' = ( A B B A )/ D B ' = ( B A A B )/ D A ' =+ B / D 1 2 A ' = A / D 2 2 B ' = B / D 1 1 B ' =+ A / D 2 1

19 EPG = + inθ + coθ P 0 P P = + coθ inθ P 0 P P d d k k 0

20 k k P P P P P = + k d coθ + k d inθ 0 = k d inθ + k d coθ 0 0 coθ inθ k d 0 = + * * inθ coθ 0 k d 0 O O d d k A = A A B B B = k d = k d = = k d = k d *coθ *inθ *inθ *coθ / d 0 co in 0 * θ * θ = * k D 0 1/ d inθ coθ 0 D = co( θ θ ) = [( )co θ ( )in θ ]/[ k d co( θ θ )] 0 0 = [( )in θ + ( )co θ ]/[ k d co( θ θ )] 0 0

21 EPG 9622 = = 0 coθ inθ k d 0 = + * * inθ coθ 0 k d 0 = + k d coθ + k d inθ 0 = k d inθ + k d coθ 0 O O d d k

22 EPG 9621 d = d = d 10 = + inθ+ coθ P 0 P P = + coθ inθ P 0 P P P P P P P = + d coθ + d inθ 0 = d inθ + d coθ 0 0 coθ inθ = + (1 + d)* * inθ coθ 0 O O d

23 A1 = B2 A2 = B1 d 1 1/1+d1-d + O O Ara Mina Grid Campo Inchaupe / Argenina 2 Ara Mina Grid Campo Inchaupe / Argenina 2

24 Ara Mina Grid Campo Inchaupe / Argenina 2 = Ara Mina = Ara Mina = Campo Inchaupe / Argenina 2 = Campo Inchaupe / Argenina 2 0 = m 0 = m = k = k= 1.0 Ara Mina = m = m = Ara Mina = = Ara Mina = = = 0 + d coθ + d inθ = *1.0*co *1.0*in = m - 2 = = 0 d inθ + d coθ = *1.0*in *1.0*co = m 2 3 I 25 I 12.5 WG84 /UM Zone 31N E = N = I J = m 0 = m d = 25 d = 12.5 k = = +20

25 I= 300 J = 247 = = + k d coθ + k d inθ = m 0 = = k d inθ + k d coθ = m 0 = [( )co θ ) ( )in θ )]/[ k d co( θ θ )] = = [( )in θ ) + ( )co θ )]/[ k d co( θ θ )] = EPG

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