Transcript Kerangka Dasar Geodetik

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