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Kerangka Dasar Geodetik Irwan Meilano 2008 Objective • Memberikan pengetahuan dasar tentang pembangunan kerangka dasar geodetik • Perencanaan, pengambilan data, pengolahan data, dan evaluasinya. • Merancang pembangunan suatu kerangka dasar geodetik dengan pendekatan terkini Topik Perkuliahan • Hitung perataan (review) • Sistem koordinat & sistem referensi (review) • Sistem tinggi dan penentuan posisi vertikal • Pemodelan bobot data ukuran • Hitung perataan jaring kerangka dasar • Desain jaring kerangka dasar • Presentasi. References • PR Wolf, CD Ghilani, Adjustment Computations, John Wiley & Sons, 1997 • Linear Algebra, Geodesy and GPS, Strang and Borre,1997 • S Kuang, Geodetic Network Analysis and Optimal Design, Ann Arbor Press, 1996 • P Vanicek, EJ Krakiwsy, Geodesy : The Concepts, North-Holland Pub.Co., 1982 Basic concepts 1. Statistical concepts • Distributions Normal-distribution 2. Linearizing 3. Least-squares • • The overdetermined problem The underdetermined problem Histogram. Describes distribution of repeated observations At the same place but different times Aturan dasar dalam survey 1. No Measurement is exact 2. Every measurement contains errors 3. The true value of a measurement is never known 4. The exact size of the error present are always unknown Pertanyaan Apa perbedaan Precision and Accuracy ? PRECISION • The number of decimal places assigned to the measured number • It is sometimes defined as reproducibility ACCURACY • Accuracy can be defined as how close a number is to what it should be. • Accuracy is determined by comparing a number to a known or accepted value. Contoh • How long is a piece of string? – Budi measures the string at 2.63 cm. – Using the same ruler, Badi measures the string at 1.982 cm. – Who is most precise? – Who is most accurate? Accuracy vs. Precision • The actual measurement is 2.65 cm. • Budi is fairly accurate and also very precise. • Badi is very precise, however, he is not very accurate. His lack of accuracy is due to using the ruler incorrectly. ACCURACY/PRECISION • You can tell the precision of a number simply by looking at it. The number of decimal places gives the precision. • Accuracy on the other hand, depends on comparing a number to a known value. Therefore, you cannot simply look at a number and tell if it is accurate Position errors and maps Map Scale large scale small scale 1:1,250 Ground Distance (m) corresponding to 0.5 mm map distance 0.625 1:2,500 1:5,000 1:10,000 1.25 2.5 5 1:24,000 1:50,000 12 25 1:100,000 50 1:250,000 1:1,000,000 125 500 1:10,000,000 5000 Mengapa kita peduli? • Scientific value Do the data support the conclusions you’re drawing from them? • Data distribution People may use freely-distributed data without knowing the consequences • Management purposes Risk management important in many environmental applications • Legal purposes Presentation of uncertainty important in litigation Beberapa konsep statistik: Average, Standard Deviation, RMSE 1 n x xi : unweighted mean n i 1 n x 2 ( x x ) i i 1 n(n 1) x n : standard deviation of unweighted mean n x 2 ( x x ) i i 1 n 1 standard deviation of single measuremen t n RMSE 2 ( x x ) i i 1 n root mean square error (" average error" ) Statistical Errors • Bias Systematic but unaccounted-for error in measurement affects accuracy of result measurements True value Precise, but inaccurate • Noise Random error in measurement affects precision (repeatability) of result Less precise, but more accurate Rencana Materi Perkuliahan