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.