Trans_HelmertTransformasi Koordinat(metode Helmert)

TitikSistem Koordinat LamaSistem Koordinat BaruKeteranganx(m)y(m)X(m) Y(m) BPN -053987.4372777.941359753.092318649.751titik sekutuBPN -145732.6942727.528361498.327318598.121titik sekutuBPN -066142.998506.759361908.266316377.138titik sekutuBPN -034337.923794.338360103.518316666.233titik sekutuP1x(m)y(m)??

Koordinat P1 ?

1. Persamaan :X = px - qy + aParameter Transformasip, q, a, bY = qx + py + b2. Diperlukan minimal 2 Titik Sekutu3. Tahapan Hitungannya :Persamaan tsb:

XTDT 002 =pxTDT 002 - qyTDT 002 + aXTDT 103P =pxTDT 103P - qyTDT 103P+ aXTDT TB2 =pxTDT TB2 - qyTDT TB2 + aXTDT TB1 =pxTDT TB1 - qyTDT TB1 + aYTDT 002=qxTDT 002 +pyTDT 002 +bYTDT 103P =qxTDT 103P +pyTDT 103P +bYTDT TB2 =qxTDT TB2+pyTDT TB2 +bYTDT TB1 =qxTDT TB1 +pyTDT TB1 +b

Dibuat Matrik :Matrik A = xTDT 002-yTDT 00210Matrik F = XTDT 002xTDT 103P-yTDT 103P10XTDT 103PxTDT TB2 -yTDT TB2 10XTDT TB2 xTDT TB1-yTDT TB110XTDT TB1yTDT 002xTDT 00201YTDT 002yTDT 103PxTDT 103P01YTDT 103PyTDT TB2 xTDT TB2 01YTDT TB2 yTDT TB1xTDT TB101YTDT TB1

Matrik P = pqabMatrik P = [AT.A]-1.AT.F

Matrik A = 3987.437-2777.941105732.694-2727.528106142.998-506.759104337.923-794.338102777.9413987.437012727.5285732.69401506.7596142.99801794.3384337.92301

Matrik F = 359753.092361498.327361908.266360103.518318649.751318598.121316377.138316666.233

Matrik AT = 3987.4375732.6946142.9984337.9232777.9412727.528506.759794.338-2777.941-2727.528-506.759-794.3383987.4375732.6946142.9984337.9231111000000001111

Matrik ATA = 121361577.4411280.000000003720201.0526806.5660.0000000037121361577.441128-6806.56620201.05220201.052-6806.566406806.56620201.05204

Matrik [AT.A]-1 =0.0000001289-0-0.0006509231-0.0002193228-00.00000012890.0002193228-0.0006509231-0.00065092310.00021932283.9105416849-0-0.0002193228-0.000650923103.9105416849

Matrik ATF = 9458197655.42483959385353.039741443263.2031270291.243

Matrik P = [AT.A]-1.AT.FMatrik P = p =0.9999985939q =-0.0003801012a =355764.898055186b =315873.091253625

Jadi :

TitikKoordinat Lama (DGN 95)Koordinat Baru ( ITRF 2008)XYXY14444.9721005.342360210.246316876.742Rumus Var Post (s02)s02 =VTV / (n-u)

KeteranganVmatrik residuV = (ATA)-1.(ATF)

r=(n-u)derajat kebebasannbanyaknya persamaann =8uminimum persamaanu =4r = 4

V =(ATA)-1.(ATF)0.9999985939-0.0003801012355764.898055186315873.091253625

VT =0.9999985939-0.0003801012355764.898055186315873.091253625

VTV =226344472467.338

s02 =VTV / (n-u) =56586118116.8345ParameterNilaip0.9999993667q-2.15E-06a-0.5859375b1.796875

Trans_AffineTransformasi Koordinat(metode Affine)TitikSistem Koordinat LamaSistem Koordinat BaruKeteranganx(m)y(m)X(m) Y(m) BPN -053987.4372777.941359753.092318649.751titik sekutuBPN -145732.6942727.528361498.327318598.121titik sekutuBPN -066142.998506.759361908.266316377.138titik sekutuBPN -034337.923794.338360103.518316666.233titik sekutuP1x(m)y(m)??

1. Persamaan :X = ax + by + C1Parameter Transformasia, b, c, d, C1, C2Y = cx + dy + C22. Diperlukan minimal 3 Titik Sekutu3. Tahapan Hitungannya :Persamaan tsb:XBPN05 =axBPN05 + byBPN05 + C1XBPN14 =axBPN14 + byBPN14 + C1XBPN06 =axBPN06 + byBPN06 + C1XBPN03 =axBPN03 + byBPN03 + C1YBPN05 =cxBPN05 + dyBPN05 + C2YBPN14 =cxBPN14 + dyBPN14 + C2YBPN06 =cxBPN06 + dyBPN06 + C2YBPN03 =cxBPN03 + dyBPN03 + C2

Dibuat Matrik :Matrik A = xBPN05yBPN050010Matrik F = XBPN05xBPN14yBPN140010XBPN14xBPN06yBPN060010XBPN06xBPN03yBPN030010XBPN0300xBPN05yBPN0501YBPN0500xBPN14yBPN1401YBPN1400xBPN06yBPN0601YBPN0600xBPN03yBPN0301YBPN03Matrik P =abcdMatrik P =[AT.A]-1.AT.FC1C2Matrik A = 3987.4372777.94100105732.6942727.52800106142.998506.75900104337.923794.3380010003987.4372777.94101005732.6942727.52801006142.998506.75901004337.923794.33801Matrik F = 359753.092361498.327361908.266360103.518318649.751318598.121316377.138316666.233Matrik AT = 3987.4375732.6946142.9984337.92300002777.9412727.528506.759794.338000000003987.4375732.6946142.9984337.92300002777.9412727.528506.759794.3381111000000001111Matrik ATA = 105317434.70853833271744.7311050020201.052033271744.73110516044142.73259006806.566000105317434.70853833271744.731105020201.0520033271744.73110516044142.7325906806.56620201.0526806.56600400020201.0526806.56604Matrik [AT.A]-1 =0.00000033070.000000081800-0.001809171900.00000008180.000000244300-0.0008287060000.00000033070.00000008180-0.0018091719000.00000008180.00000024430-0.000828706-0.0018091719-0.0008287060010.7969541933000-0.0018091719-0.000828706010.7969541933Matrik ATF = 7292155167.442722454813852.240216414199205.279942166042487.982071443263.2031270291.243Matrik P = [AT.A]-1.AT.FMatrik P = a =0.9999097411b =0.0000884651c =-0.0007803354d =0.9998931786C1 =355765.843045501C2 =315875.291920919Jadi :TitikKoordinat Lama (DGN 95)Koordinat Baru ( ITRF 2008)XYXY14444.9721005.342360210.503316877.058Rumus Var Post (s02)s02 =VTV / (n-u)

KeteranganVmatrik residuV = (ATA)-1.(ATF)

r=(n-u)derajat kebebasannbanyaknya persamaann =8uminimum persamaanu =6r = 2V =(ATA)-1.(ATF)0.99990974110.0000884651-0.00078033540.9998931786355765.843045501315875.291920919VT =0.99990974110.0000884651-0.00078033540.9998931786355765.843045501315875.291920919VTV =226346535126.001s02 =VTV / (n-u) =113173267563.00ParameterNilaia1.0000000112b0.0000000075c-0.0000040308d0.9999969304C10.59375C23.90625

Trans_LaufTransformasi Koordinat(metode Lauf)TitikSistem Koordinat LamaSistem Koordinat BaruKeteranganx(m)y(m)X(m) Y(m) BPN -053987.4372777.941359753.092318649.751titik sekutuBPN -145732.6942727.528361498.327318598.121titik sekutuBPN -066142.998506.759361908.266316377.138titik sekutuBPN -034337.923794.338360103.518316666.233titik sekutuP1x(m)y(m)??

1. Persamaan :X = a1(y2 x2) + 2a2 xy + b1y + b2x + C1 Parameter Transformasia1, a2, b1, b2, C1, C2Y = a2(y2 x2) 2a1xy + b2y b1x + C22. Diperlukan minimal 3 titik sekutu3. Tahapan Hitungannya :Persamaan tsb:

XBPN05 =a1(yBPN052 xBPN052) + 2a2 xBPN05yBPN05 + b1yBPN05 + b2xBPN05 + C1XBPN14 =a1(yBPN142 xBPN142) + 2a2 xBPN14yBPN14 + b1yBPN14 + b2xBPN14 + C1XBPN06 =a1(yBPN062 xBPN062) + 2a2 xBPN06yBPN06 + b1yBPN06 + b2xBPN06 + C1XBPN03 =a1(yBPN032 xBPN032) + 2a2 xBPN03yBPN03 + b1yBPN03 + b2xBPN03 + C1YBPN05 =a2(yBPN052 xBPN052) 2a1xBPN05yBPN05 + b2yBPN05 b1xBPN05 + C2YBPN14 =a2(yBPN142 xBPN142) 2a1xBPN14yBPN14 + b2yBPN14 b1xBPN14 + C2YBPN06 =a2(yBPN062 xBPN062) 2a1xBPN06yBPN06 + b2yBPN06 b1xBPN06 + C2YBPN03 =a2(yBPN032 xBPN032) 2a1xBPN03yBPN03 + b2yBPN03 b1xBPN03 + C2

Dibuat Matrik :Matrik A = (yBPN052 xBPN052)2xBPN05yBPN05yBPN05xBPN0510Matrik F = XBPN05(yBPN142 xBPN142)2xBPN14yBPN14yBPN14xBPN1410XBPN14(yBPN062 xBPN062)2xBPN06yBPN06yBPN06xBPN0610XBPN06(yBPN032 xBPN032)2xBPN03yBPN03yBPN03xBPN0310XBPN03-2xBPN05yBPN05(yBPN052 xBPN052)-xBPN05yBPN0501YBPN05-2xBPN14yBPN14(yBPN142 xBPN142)-xBPN14yBPN1401YBPN14-2xBPN06yBPN06(yBPN062 xBPN062)-xBPN06yBPN0601YBPN06-2xBPN03yBPN03(yBPN032 xBPN032)-xBPN03yBPN0301YBPN03

Matrik P = a1a2b1b2Matrik P =[AT.A]-1.AT.FC1C2Matrik A = -8182697.62948822153729.4544342777.9413987.43710-25424371.50685231272166.8008642727.5285732.69410-37479619.7439236226039.046964506.7596142.99810-18186603.0956856891554.159948794.3384337.92310-22153729.454434-8182697.629488-3987.4372777.94101-31272166.800864-25424371.506852-5732.6942727.52801-6226039.046964-37479619.743923-6142.998506.75901-6891554.159948-18186603.095685-4337.923794.33801

Matrik F =359753.092361498.327361908.266360103.518318649.751318598.121316377.138316666.233

Matrik AT = -8182697.629488-25424371.506852-37479619.743923-18186603.095685-22153729.454434-31272166.800864-6226039.046964-6891554.15994822153729.45443431272166.8008646226039.0469646891554.159948-8182697.629488-25424371.506852-37479619.743923-18186603.0956852777.9412727.528506.759794.338-3987.437-5732.694-6142.998-4337.9233987.4375732.6946142.9984337.9232777.9412727.528506.759794.3381111000000001111

Matrik AT.A = 40038228614382300.046875210235759255.989-642974234861.169-89273291.975948-66543489.4622104003822861438230642974234861.169210235759255.98966543489.46221-89273291.975948210235759255.989642974234861.169121361577.441128-0.00000000376806.566-20201.052-642974234861.169210235759255.989-0.0000000037121361577.44112820201.0526806.566-89273291.97594866543489.462216806.56620201.05240-66543489.46221-89273291.975948-20201.0526806.56604

Matrik [AT.A]-1 = 00-0.00000000020.0000000007-0.0000015988-0.0000012103-00-0.0000000007-0.00000000020.0000012103-0.0000015988-0.0000000002-0.00000000070.000007995-0-0.00714952960.02097621930.0000000007-0.0000000002-00.000007995-0.0209762193-0.0071495296-0.00000159880.0000012103-0.0071495296-0.020976219362.53473106490-0.0000012103-0.00000159880.0209762193-0.0071495296062.5347310649

Matrik AT.F = -53422495351782.8-4314712929359.76-3959385353.039749458197655.42481443263.2031270291.243Matrik P = [AT.A]-1.AT.FMatrik P = a1 =-0.0000000407a2 =0.0000000116b1 =0.0003986064b2 =0.9995453584C1 =355766.052867267C2 =315873.538378194Jadi :y^2-x^2TitikKoordinat Lama (DGN 95)Koordinat Baru ( ITRF 2008)XYXY-18747063.5438214444.9721005.342360210.272316876.797Rumus Var Post (s02)s02 =VTV / (n-u)

KeteranganVmatrik residuV = (ATA)-1.(ATF)

r=(n-u)derajat kebebasannbanyaknya persamaann =8uminimum persamaanu =6r = 2V =(ATA)-1.(ATF)-0.00000004070.00000001160.00039860640.9995453584355766.052867267315873.538378194VT =-0.00000004070.00000001160.00039860640.9995453584355766.052867267315873.538378194VTV =226345576621.314s02 =VTV / (n-u) =113172788310.66ParameterNilaia10.0000009537a2-0.000005722b10.25b22C1524288C20

Analisis metodePERBANDINGAN KETELITIAN ANTARA 3 METODE TRANSFORMASI Perbandingan KetelitianUntuk mengetahui metode mana yang lebih teliti ,nilai varian posteriori masing-masing metode diperbandingkan,metode yang mempunyai nilai varian posteriori kecil menunjukkanbahwa metode tersebut lebih teliti dari pada metode yang mempunyainilai varian posteriori besar.A. Metode Helmert dan AffineNoMetodePengukuran LebihVarian PosterioriKesimpulanTransformasi1Helmert456586118116.83Metode Helmert lebih teliti dibandingkan metode Affine, karena nilai varian posteriorinya lebih kecil.2Affine2113173267563.00

B. Metode Helmert dan LaufNoMetodePengukuran LebihVarian PosterioriKesimpulanTransformasi1Helmert456586118116.83Metode Helmert lebih teliti dibandingkan metode Lauf, karena nilai varian posteriorinya lebih kecil.2Lauf2113172788310.66

C. Metode Affine dan LaufNoMetodePengukuran LebihVarian PosterioriKesimpulanTransformasi1Affine2113173267563.00Metode Lauf lebih teliti dibandingkan metode Affine karena nilai varian posteriorinya lebih kecil.2Lauf2113172788310.66

D. Metode Helmert ,Affine dan LaufNoMetodePengukuran LebihVarian PosterioriKesimpulanTransformasi1Helmert456586118116.8345Dari ketiga metode tersebut, metode helmert paling teliti daripada metode affine dan lauf karena nilai varian posteriorinya paling kecil.2Affine2113173267563.003Lauf2113172788310.66