ADJUSTMENT OF MEASUREMENTS

ADJUSTMENT OF SURVEY MEASUREMENTS

Although measurement of a quantity is a single act, a typical survey measurement may involve several elementary operations, such as centering, pointing, setting and reading. In performing these operations and due to human limitations, imperfection in instrument, environment changes or carelessness on the part of the observer, certain amount of errors is bound to creep into the measurements. Hence, the measurement always contains errors. Since the measured quantities are used to calculate other quantities such as area, volume, elevation, slope, through relationships with the measured quantities, the errors in measured quantities get propagated into the calculated quantities.

The errors in the measured quantities should be eliminated or minimized before they are used for computing other quantities.

After removing the blunders and systematic errors, the errors which remain in the measurements are residual, random or accidental errors. These errors are minimized or adjusted, and the adjusted quantity is known as the most probable value of a measured quantity. It is the most probable value of a measured quantity which is used for computing other quantities.

The following definitions of some of the terms should be clearly understood in adjustment of the measurements:

          TRUE VALUE:  The value of a quantity which is free from all errors is called the true value of quantity. Because it is not possible to eliminate all the errors completely from a measured quantity, the true value cannot be determined.

          OBSERVATION:  The measured numerical value of a quantity is known as observation. No measurement is made until something is observed. Accordingly, the terms measurement and observation are often used synonymously.

          The observations may be classified as:

·       Direct observations

·       Indirect observations

Direct observation: If the value of a quantity is measured directly, for example, measurement of an angle, the observation is said to be direct observation.

Indirect observation: An observation is said to be indirect if the value of the quantity is deduced from the measurements of other quantities. For example, the value of the angle at the main triangulation station computed from the measured angles at the satellite station.

Observed value of a quantity: Observed value of a quantity is the value obtained from the observation after eliminating the mistake and systematic errors. The observed values contain random or residual errors.

     The observed value of a quantity may be classified as:

·       Independent quantity.

·       Conditioned quantity.

Independent quantity:  If the value of an observed quantity is independent of the value of other quantities, it is said to be an independent quantity. For example, the reduced level of a point.

Conditioned quantity: If the value of an observed quantity is dependent upon the value of other quantities it is called a conditioned quantity. For example, the three angles A, B and C in a plane triangle are conditioned quantities since they are related by the condition equation A + B + C = 180⁰.

Most probable value:  The most probable value of a quantity is the value which has more chances of being true than any other value.

True error: The difference between the true value and the observed value is known as true error. Thus

True error = Observed value – True value.

Most probable error:  It may be defined as the quantity which is subtracted from or added to the most probable value of a quantity. It fixes the bounded limits within which, the true value of the observed quantity may lie.

Residual error: The difference between the observed quantities and its most probable value is called residual error, residual error or variation. Thus,

Residual error or residual = Observed value – Most probable value.

Observation equation: The relation between the observed quantities is known as an observation equation. For example, α + β = 87⁰ 40’ 38”.

Condition equation: A condition equation is the equation expressing the relation existing between the several dependent quantities. For example, at a station if four angles ϴ₁, ϴ₂, ϴ₃ and ϴ₄ have been observed then ϴ₁ + ϴ₂ + ϴ₃ + ϴ₄ = 360⁰.

In a braced quadrilateral the sum of all the eight observed angles is 360⁰. Thus,

ϴ₁ + ϴ₂ + ϴ₃ + ϴ₄ + ϴ₅ + ϴ₆ + ϴ₇ + ϴ₈ = 360⁰

Normal equation: A normal equation is the one which is formed by multiplying each equation by the coefficient of the unknown whose normal equation is to be found and by adding the equations thus formed. The number of normal equation is the same as the number of unknowns. The most probable values of the unknowns are found out by using by the normal equations.