坐标系转换公式.doc

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1 ( Coordinate Conversions and Transformation including Formulas part 2 Formulas for Coordinate Operations other than Map Projections EPSG GPS GPS WGS84 WGS84 XYZ XYZ WGS84 GPS dxdydz

2 Molodenski Helmert7 EPSG - Bursa-Wolf - Molodenski-Badekas Clarke GRS 1980 Clarke 1966 Meades Ranch Molodenski Helmert EPSG NAD83 US Coast & Geodetic SurveyNADCON EPSG NAD27 NAD83 ED ED Statens Kartwerk 15 4 From To ϕ λ XYZ Z X Y 90

3 a b 1/f X = ( ν ϕ λ Y = ( ν ϕsin λ Z = 2 (( ) ν ϕ ν ϕ ν = a/(1 e sin ϕ) ϕ λ h e e = ( a b )/ a = 2f f N XYZ ϕ = tg [( Z + eν sin ϕ)/( X + Y ) 1 λ = tg ( Y / X ) h= X secλsecϕ ν λ 3.2 AA > 0 X = X A new old EPSG 1999 X = X + A t s Xs Xt A

4 EPSG Xt = Xs + A X = [( X * U ) + ( A* U )]*( m / U ) t s s A t Xt = Xs = A m m=1 m = 1 UsUt U A EPSG dxdydz X = X + dx t t t Y = Y + dy s Z = Z + dz s s 2.1 WGS84 GPS ϕ = 53 48'33.82''N s λ = 207'46.38''E s h = 73.0m s ED50 International 1924 WGS84 ED50 dx = m dy = mdZ = m WGS84 X Y s Z s s = m = m = m ED50 X t t t = = m Y = = m Z = = m

5 2 ED50 ϕ = 53 48'36.565''N t λ = 207'51.477''E t h = 28.02m t International 1924 Molodenski Molodenski ϕ = ϕ + dϕ t λ = λ + dλ t h = h + dh t s s s dϕ'' = ( dx.sin ϕ.cos λ dy.sin ϕ.sin λ+ dz.cos ϕ + [ adf. + fda. ].sin2 ϕ)/( ρ.sin1'') dλ'' = ( dx.sin λ+ dy.cos λ)/(.cos ν ϕ.sin1'') 2 dh = dx.cos ϕ.cos λ + dy.cos ϕ.sin λ + dz.sin ϕ + ( adf. + fda. ).sin ϕ da dxdydz ρ ϕ ρ = a(1 e )/(1 e sin ϕ) ν ϕ ν = a/(1 e sin ϕ) / /2 da da = a a df df = f f = 1/(1/ f) 1/(1/ f ) dϕ λ ϕ λ t s t s t s WGS84 GPS ϕ = 53 48'33.82''N s λ = 207'46.38''E s h = 73.0m s ED50 International 1924 WGS84 ED50 dx = m dy = m dz = m

6 WGS 1984 a = /f = International 1924 a = /f = da = = 251 df = = E-05 dϕ = 2.545'' dλ = 5.097'' dh= 44.98m ED50 International 1924 ϕ = 53 48'36.565'' N t λ = 207'51.477'' E t = 28.02m t Helmert 7 7 XT 1 R + R Z Y XS dx Y T M * RZ 1 RX * Y S dy = + + Z T RY RX 1 + Z S dz XsYsZs XtYtZt EPSG dxdydz RXRYRZ M M = (1 + ds*10-6 ) ds ppm

7 2.1 WGS72 WGS84 dx = m dy = m dz = +4.5 m RX = RY = RZ = ds = ppm WGS72 ϕ = 55 00'00''N S λ = 400'00''E S h = 0m S X Y Z S S S = m = m = m 7 X Y T Z T T = m = m = m WGS84 ϕ = 55 00'00.090''N T λ = 400'00.554''E T h =+ 3.22m T EPSG XT 1 + R R Z Y X S dx Y T M * RZ 1 RX * Y S dy = + + Z T RY RX 1 + Z S dz dxdydz

8 RXRYRZ M M = (1 + ds*10-6 ) ds ppm dx = m dy = m dz = +4.5 m RX = RY = RZ = ds = ppm ISO Molodenski-Badekas XT 1 + R R Z Y XS XP X P dx Y T M * RZ 1 RX * YS Y P Y P dy = Z T RY RX 1 + ZS Z P Z P dz dxdydz RXRYRZ XPYPZP

9 M M = (1 + ds*10-6 ) ds ppm Molodenski-Badekas 6*10 1 6* *10 6 XY X S0 Y S0 X T0 Y T0

10 X Y S S X Y S0 S0 X Y T T X Y T0 T0 U = m ( X X ) S S S0 V = m ( Y Y ) S S S0 X S Y S X S0 Y S0 m S UV AnBn dxdy m T m dx = A + A U + A V + A U + A U V + A V T 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 dy= B + B U + B V + B U + B U V + B V T 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 dxdy EPSG Aumvn Bumvn m U n V A17 Au3v2

11 ( X X ) = ( X X ) + dx T T0 S S0 ( Y Y ) = ( Y Y ) + dy T T0 S S0 X = X X + X + dx T S S0 T0 Y = Y Y + Y + dy T S S0 T0 X T Y T X S Y S X S0 Y S0 X T0 Y T0 dxdy 6 EPSG 9648 TM75 ETRS89 X0X 0 = ϕ 0 = 5330'00.000'' N = S Y0Y 0 = λ 0 = 742'00.000'' W = 7.7 S S S X0X 0 = ϕ 0 = 5330'00.000'' N = T Y0Y 0 = λ 0 = 742'00.000'' W = 7.7 T T m S = 0.1 m T = 3600 T A0 = A1 = A24 = A27 = 0 B0 = B1 = B24 = B27 = 0 TM75 X Y ϕ λ TM75 TM75 S S0 TM75 S0 S S0 TM75 S0 = X = 55 00'00'' N = S = Y = 630'00'' W = S X = ϕ ϕ = = 1.5 Y = λ λ = 6.6 ( 7.7) = 1.2 U = m ( X X ) = m ( ϕ ϕ ) = 0.1*(1.5) = 0.15 S S S0 S TM75 S0 V = m ( Y Y ) = m ( λ λ ) = 0.1*(1.2) = 0.12 S S S0 S TM75 S0 3 3 dx = ( A0 + A1 U A24 U V )/ K TCD dx 3 3 = { ( 4.487*0.15) ( *0.15 *0.12 )}/3600=

12 3 3 dy = ( B0 + B1 U B24 U V )/ K TCD dy 3 3 = { ( 0.341*0.12) ( *0.12 *0.12 )}/3600= ϕ λ = X = X + dx = = 55 00' '' N ETRS89 T S = Y = Y + dy = = 630' '' W ETRS89 T S 1 2 EPSG n dxdy 1 X SO = X T0 = X 0 Y SO = Y T0 = Y 0 m S = m T = m dxdy dxdy dxdy ED50 ED ED50 ED N0E4 dx dy 10-6

13 10 6 EPSG 4 EPSG 9651 ED50 ED87 X Y = 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 = X = 52 30'30'' N = S = Y = 2 E =+ 2 S U = m ( X X ) = m ( ϕ ϕ ) = 1.0*( ) = S 0 ED50 0 V = m ( Y Y ) = m ( λ λ ) = 1.0*( ) = 2 S 0 ED dx = ( A0 + A1 U A14 V )/ K CD = [ E 06 + ( E 06* ) ( E 09*2.0 4)]/1.0 = E 06 4 dy = ( B0 + B1 U B14 V )/ K CD = [ E 05 + ( E 05* ) ( E 09*2.0 4)]/1.0 = E 06 ϕ λ = X = X + dx = E 06= 52 30' '' N ED87 T S = Y = Y + dy = 200' '' E ED87 T S

14 ED87 ED A0A14B0B14 X Y = 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 = X = 52 30' '' N = S = Y = 200' '' E = S U = 1.0*( ) = V = 1.0*( ) = dx = ( A0 + A1 U A14 V )/ K CD = [ E 06 + ( E 06* ) ( E 09* )]/1.0 = E 06 4 dy = ( B0 + B1 U B14 V )/ K CD = [ E 05 + ( E 05* ) ( E 09* )]/1 = E 06 ϕ λ = X = X + dx = E 06= 52 30'30.000'' N ED50 T S = Y = Y + dy = 200'00.000'' E ED50 T S

15 ABUV 3 m ( dx + idy ) = ( A + i A )( U + iv ) + ( A + i A )( U + iv ) T ( A + i A )( U + iv ) + ( A + i A )( U + iv ) U = m ( X X ) S S S0 V = m ( Y Y ) S S S0 m S m T 2 4 Amersfoort / RD ED50 / UTM U V 2 2 U V m dx 2 T + A1 A2 + A3 A4 + A5 A UV 6 + A7 A8 * 3 2 m U 3UV T dy = A2 A1 A4 A3 A6 A5 A8 A UV V U 6UV + V 3 3 4UV 4UV X = X X + X + dx T S S0 T0 Y = Y Y + Y + dy T S S0 T0 X T Y T X S Y S X S0 Y S0 X T0 Y T0 0 A0 B0

16 4 EPSG 9653 Amersfoort / RD New ED50 / UTM zone 31N X S Y S X T Y T m S 10-5 m T 1.0 A1 A A2 A A3 A A4 A A5 A A6 A A7 A A8 A X Amersfoort / RD = X S = m Y Amersfoort / RD = Y S = m U = m X X = = 5 S ( S S0) ( ) V = m Y Y = = 5 S ( S S0) ( ) dx = / 1.0 dy = / 1.0 X ED50 / UTM 31 = X T = X S X S0 + X T0 + dx = m Y ED50 / UTM 31 = Y T =Y S Y S0 + Y T0 + dy = = = m

17 EPSG 9617 Madrid 1870 Struve 1860 Madrid El Servicio Geografico del Ej rcito Madrid 1870 ED Madrid 1870 ED50 dϕ( ) = A + ( A * ϕ ) + ( A * λ ) + ( A * H ) 0 1 S 2 S 3 S dλ( ) = B + B + ( B * ϕ ) + ( B * λ ) + ( B * H ) S 2 S 3 S ϕ s λ s Madrid 1870 Hs 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 = S λ = 339'34.57'' EMadrid ( ) = ( Madrid) S H S = 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 EPSG EPSG 9624 CAD GIS rubber sheeting XT A0 A X 1 A2 S * Y = B + B B Y T S X = A + A X + A Y T 0 1 S 2 S Y = B + B X + B Y T 0 1 S 2 S X T Y T P X S Y S 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 EPSG X = X + Y sinθ + X cosθ TP T0 SP Y SP X Y = Y + Y cosθ X sinθ TP T0 SP Y SP X ds X ds Y k k 0

20 k k X TP Y TP X SP Y SP P X = X + X k ds cosθ + Y k ds sinθ T T0 S X X S Y Y Y = Y X k ds sinθ + Y k ds cosθ T T0 S X X S Y Y XT XT0 cosθx sinθy k ds X 0 XS = + * * Y Y sinθ cosθ 0 k ds Y T T0 X Y Y S X TO Y TO ds X ds Y k X Y A = X A 0 T 0 1 A B B B 2 0 T = k ds X = k ds = Y Y = k ds = k ds Y *cosθ *sinθ X Y *sinθ *cosθ X Y X 1 2 XS 1 1/ ds 0 cos sin 0 * X θ T T * Y θy X X = * YS k D 0 1/ ds Y sinθx cosθ X YT YT0 D = cos( θ θ ) X Y X = [( X X )cos θ ( Y Y )sin θ ]/[ k ds cos( θ θ )] S T T0 Y T T0 Y X X Y Y = [( X X )sin θ + ( Y Y )cos θ ]/[ k ds cos( θ θ )] S T T0 X T T0 X Y X Y

21 EPSG 9622 X = Y = XT XT0 cosθ sinθ k dsx 0 XS = + * * Y Y sinθ cosθ 0 k ds Y T T0 Y S X = X + X k ds cosθ + Y k ds sinθ T T0 S X S Y Y = Y X k ds sinθ + Y k ds cosθ T T0 S X S Y X TO Y TO ds X ds Y k Y Y X Y

22 EPSG 9621 ds X = ds Y = ds 10 X = X + Y sinθ+ X cosθ TP T0 SP SP Y = Y + Y cosθ X sinθ TP T0 SP SP X TP Y TP X SP Y SP P X = X + X ds cosθ + Y ds sinθ T T0 S S Y = Y X ds sinθ + Y ds cosθ T T0 S S XT XT0 cosθ sinθ XS = + (1 + ds)* * Y Y sinθ cosθ Y T T0 S X TO Y TO ds

23 Y Y A1 = B2 A2 = B1 ds 1 1/1+dS1-dS + X TO Y TO Astra Minas Grid Campo Inchauspe / Argentina 2 Astra Minas Grid X Y Campo Inchauspe / Argentina 2 X Y

24 Astra Minas Grid XY Campo Inchauspe / Argentina 2 YX X S = Astra Minas X Y S = Astra Minas Y X T = Campo Inchauspe / Argentina 2 Y Y T = Campo Inchauspe / Argentina 2 X X T0 = m Y T0 = m = k = k= 1.0 Astra Minas X= m Y= m X S = Astra Minas X = Y S = Astra Minas Y = Y= X = X 0 + X ds cosθ + Y ds sinθ T T S S = *1.0*cos *1.0*sin = m - 2 X= Y = Y 0 X ds sinθ + Y ds cosθ T T S S = *1.0*sin *1.0*cos = m 2 3 I 25 I 12.5 WGS84 /UTM Zone 31N E = N = I J X T0 = m Y T0 = m ds X = 25 ds Y = 12.5 k = = +20

25 I= 300 J = 247 X = = X + X k ds cosθ + Y k ds sinθ = m T T0 S X S Y Y = = Y X k ds sinθ + Y k ds cosθ = m T T0 S X S Y X = [( X X )cos θ ) ( Y Y )sin θ )]/[ k ds cos( θ θ )] = 230 S T T0 Y T T0 Y X X Y Y = [( X X )sin θ ) + ( Y Y )cos θ )]/[ k ds cos( θ θ )] = 162 S T T0 X T T0 X X X Y EPSG

http://www.globalsecurity.org/military/library/policy/army/fm/6-2/appe2.

26 semimajor axis a semiminor axis b flattening (1/f) b = a (1 - f)

27 WGS84 a WGS84 f X WGS XYZ WGS84 Airy

28 Modified Airy

29 Australian National

30 Bessel 1841

31 Bessel 1841Namibia

32 Clarke 1866

35 Clarke 1880

38 Everest 1830

39 Everest 1948

40 Modified Everest 1948

41 Modified Everest 1956

42 EverestPakistan

43 Modified Fischer 1960

44 Geodetic ReferenceSystem 1980

45 Geodetic ReferenceSystem 1980 China

46 Helmert 1906

47 Hough 1960

48 Indonesian 1974

49 International 1924

54 Krassovsky 1940 Krassovsky International 2030

55 Soviet Geodetic System 1985

56 South American 1969

57 ２３ Geodetic ReferenceSystem 1972 椭球体基准面转换参数 WGS72 转换到 WGS84 转换公式如下该公式计算精度比简化莫洛金斯基公式高所以不需要通过三参数平移

坐标系转换公式.doc

坐标系转换公式.doc (Email: qddqinfen@cg.gov.cn) hp://www.poc.org Coordinae Converion and ranformaion including Formula par 2 Formula for Coordinae Operaion oher han Map Projecion EPG 1995 2004 hp://www.globalecuriy.org/miliary/library/policy/army/fm/6-2/appe2.hm#abe_22