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Eng.Survey Chap 2
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CHAPTER 1
Prepared by: Siti Kamisah binti Mohd Yusof
The end of this chapter, student should be able to:1) Understand the theory of survey adjustment 2) Understand mathematical model 3) Understand accuracy versus precision 4) Understand the types of errors
Survey Adjustment is a method toadjust the observations to obtain themost accurate value on theseobservations, in addition tominimizing the error exist in theobservations.
1) Sizes of error can be assessed.2) All quantities in a survey or network
are consistent.3) Precisions of final quantities are
increased.
1) It is the most accurate of all adjustmentprocedures.
2) It can be applied with greater ease thanother methods.
3) It enables accurate post-adjustmentanalyses to be made.
4) It can be used to perform pre-surveyplanning.
5) It is the oldest currently used adjustmentmethod.
1) Precision estimates of measurements areneeded
2) The method is computation-intensive, andtherefore, a high speed computer is needed
3) A large redundancy (large degree offreedom) is necessary to get a meaningfuladjustment
4) A knowledge of statistics is necessary to doa good analysis of results
Probability is the ratio of the number of timesthat an event should occur to the total numberof possibilities. There are two function ofprobability:i. Function of cumulative distributionii. Function of Probability density
i. Function of cumulative distribution
F(t) = P (x t)
ii. Function of Probability density Is a function that describes the relative likelihood for this
random variable to take on a given value. Normal density
The value used to measurethe accuracy of a data set.
Population variance wasused to determine the dataset which consists of theentire population.
Variance,
Redundant of observationrequired for determining avalue.
From this value, it candetermining the best solutionset and will involve the part ofselection and removal.
Most Probable Value,
Difference value between observation value and the most probable value. v = x - x
Residual,
Square root of population ofvariance. The equation can beused to Variance and StandardError for a quantity of nobservations.
Standard Error,
Covariance is a measure of thedegree of correlation betweenany two components of amultivariate.
Covariance
is defined as the square-rootof the sample variance.
The square of the standarddeviation 2 is known asthe variance
Standard Deviation, S
A quantities theoretically correct or exact value.
The true value can be determined.
True Value,
The correlation Coefficient is a measureof how closely two quantities are related.
Correlation Coefficient
The midpoint of the sample setwhen arranged in ascending ordescending order.
Median
For a set of n observations, x1, x2,.., xn, this is the average ofthe observation.
Arithmetic Mean,
Within a sample of data, the mode is the most frequently occurring value.
Mode
A mathematical model is comprised of two parts:1. Functional Model:
Describes the deterministic (i.e. physical, geometric)relation between quantities.
Expresses the functional relationship between quantities (c,x,1) cConstants
- e.g. the speed of light xUnknown parameters
- the quantities we wish to solve for- e.g., Area of a triangle, co-ordinate (x, y, z) of a point
lObservables- Measurements- e.g., distances, angles, satellite pseudoranges
2. Stochastic Model : Stochastic = Weighting
* Weighting measure of its relative worth compared toother measurement.
- Used to control the sizes of corrections appliedto measurement.
Describes the non-deterministic (probabilistic) behaviour ofmodel quantities, particularly the observations.
Definition of Error: Difference between a measured quantity and its true value.
= -
= error = measured value = true value
There are THREE (3) types of error:1) Mistake Error / Blinder Error2) Systematic Error / Biases3) Random Error
MISTAKE ERROR
By an observers
carelessness.
By confusion
They are not classified as error.
Must be removed from any set of observation
Example:i. Mistakes in readingii. Mistakes in writing down
(i.e : 27.55 for 25.75)
SYSTEMATIC ERROR
These error can predicted
Error follow some physical law
Some systematic error are removed by following correct measurement procedure.
Example:i. Balancing backsight and
foresight.ii. Index error of the Vertical
Circle of Total Station instrument.
Correction can be computed.
RANDOM ERROR
Error after all Mistakes &
Systematic error have been
removed from the measured
value.
Generally small To be positive (+ve) and
negative (-ve). Example:
i. Bubble not centered at the instant a staff is read.
ii. Imperfect centering over appoint during distance measurement with Total Station Instrument.