Adjustment of Observations in Geodesy: Precision, Accuracy, and Trueness.

In geodetic and surveying work, evaluating the quality of measurements is essential. Three concepts are fundamental for this evaluation: precision, accuracy, and trueness. Understanding the differences between them helps professionals interpret results correctly and identify the sources of measurement errors.

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Lesson 04 – Precision, Accuracy, and Trueness

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Objectives

1. Understand the concepts of precision, accuracy, and trueness.
2. Distinguish between random and systematic effects.
3. Interpret measurement quality using statistical indicators.
4. Relate these concepts to geodetic observations and adjustment.

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1. Precision

Precision describes the degree of agreement among repeated measurements of the same quantity.

Characteristics:

• Related to the dispersion of observations.
• Evaluated using statistical measures such as variance and standard deviation.
• High precision means small dispersion.

Example: If repeated distance measurements are very close to each other, the observations are precise, even if they are not close to the true value.

2. Trueness

Trueness refers to the closeness between the mean of the observations and the true value.

Characteristics:

• Affected mainly by systematic errors.
• Cannot be evaluated directly if the true value is unknown.
• Improved through calibration and error modeling.

3. Accuracy

Accuracy combines both precision and trueness.

A measurement is accurate when:

• It has small dispersion (high precision), and
• Its mean is close to the true value (high trueness).

In practice:

Situation	Interpretation
High precision, low trueness	Systematic error present
Low precision, high trueness	Large random errors
High precision and high trueness	High accuracy

4. Relationship with Error Types

• Random errors affect precision.
• Systematic errors affect trueness.
• Gross errors affect both and must be removed.

Understanding this relationship is essential before performing adjustment.

5. Importance in Geodesy

In geodetic applications:

• Precision is evaluated using standard deviation.
• Trueness is improved through instrument calibration and modeling.
• Accuracy is achieved after proper error control and adjustment.

The Least Squares Method improves precision by reducing the effect of random errors.

6. Solved Example

Two distance measurement sets (m):

• Set A: 100.002; 100.003; 100.001; 100.002.
• Set B: 99.980; 100.020; 100.005; 99.995.

Assume the true value is 100.000 m.

6.1 Analysis

Set A:

• Small dispersion → high precision
• Mean = 100.002 → small systematic bias

Set B:

• Large dispersion → low precision
• Mean ≈ 100.000 → good trueness

6.2 Interpretation:

• Set A: precise but less true
• Set B: true but not precise

7. Proposed Exercise

Two observation groups of an angle (degrees):

• Group 1: 45.002; 45.003; 45.001; 45.002.
• Group 2: 44.990; 45.015; 45.005; 44.995.

Assuming the true value is 45.000°, determine which group is:

a) More precise

b) More accurate

7.1 Answer

• Group 1: more precise
• Group 2: less precise and less accurate

Conclusion

Precision describes the consistency of measurements, trueness indicates closeness to the true value, and accuracy combines both. These concepts are fundamental for evaluating observation quality and for reliable geodetic adjustment.

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