Kerangka Dasar Geodetik

Irwan Meilano2008

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

1. Statistical concepts Distributions• Normal-distribution

2. Linearizing3. Least-squares• The overdetermined problem• The underdetermined problem

Basic concepts

Histogram.Describes distribution of repeated observationsAt the same place but different times

Aturan dasar dalam survey

1. No Measurement is exact2. Every measurement contains errors3. The true value of a measurement is never known4. 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 mapsMap Scale Ground Distance (m)

corresponding to 0.5 mm map distance

1:1,250 0.6251:2,500 1.251:5,000 2.51:10,000 51:24,000 121:50,000 251:100,000 501:250,000 1251:1,000,000 5001:10,000,000 5000

large scale

small scale

Mengapa kita peduli?

• Scientific valueDo the data support the conclusions you’re drawing from them?

• Data distributionPeople may use freely-distributed data without knowing the consequences

• Management purposesRisk management important in many environmental applications

• Legal purposesPresentation of uncertainty important in litigation

Beberapa konsep statistik: Average, Standard Deviation, RMSE

)error" average("error squaremean root )(

RMSE

tmeasuremen single ofdeviation standard1

)(

mean unweighted ofdeviation standard:n

)1(

)(

mean unweighted:1

1

2

1

2

1

2

1

n

xx

n

xx

nn

xx

xn

x

n

ii

n

ii

x

x

n

ii

x

n

ii

Statistical Errors

• BiasSystematic but unaccounted-for error in measurementaffects accuracy of result

• NoiseRandom error in measurementaffects precision (repeatability) of result

True valuemeasurements

Precise, but inaccurate

Less precise, but more accurate

Rencana Materi Perkuliahan