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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Adjustment of Observations in Geodesy: Types of Errors in Geodetic Observations.

This free course on Adjustment of Observations and Least Squares is designed for students and professionals in Geodesy, Surveying, and Geomatics. Each lesson includes theoretical explanations, solved examples, and practical exercises.

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Lesson 02 – Types of Errors in Geodetic Observations

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Objectives

1. Understand the different types of errors present in geodetic measurements.
2. Distinguish between systematic, random, and gross errors.
3. Identify the origin and behavior of each type of error.
4. Recognize the importance of error classification in the adjustment process.

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1. Introduction

Every geodetic observation contains errors. Since the true value of a measured quantity is unknown, it is essential to understand the nature of these errors in order to control, model, or minimize their effects.

Errors in geodetic measurements are generally classified into three main categories:

• Systematic errors.
• Random errors.
• Gross errors.

This classification is fundamental for the proper application of the Least Squares Method.

2. Systematic Errors

Systematic errors follow a predictable pattern and affect measurements in a consistent way.

2.1 Characteristics

• Same sign and similar magnitude under the same conditions.
• Caused by identifiable physical or instrumental factors.
• Can be modeled and corrected.

2.2 Examples

• Instrument calibration errors.
• Temperature effects on distance measurements.
• Atmospheric refraction.
• Scale factor errors.
• Incorrect prism constant.

2.3 Treatment

Systematic errors should be:

• eliminated through calibration, or
• modeled mathematically in the functional model.

If not treated, they affect the accuracy of the results.

3. Random Errors

Random errors are small variations caused by unpredictable factors.

3.1 Characteristics

• Irregular in magnitude and sign.
• Follow a normal (Gaussian) distribution.
• Mean value approximately equal to zero.
• Cannot be eliminated individually.

3.2 Sources

• Instrument noise.
• Environmental variations.
• Operator limitations.
• Small atmospheric fluctuations.

3.3 Treatment

Random errors are reduced by:

• Repeated observations.
• Redundancy.
• Least Squares Adjustment.

They affect the precision of the measurements.

4. Gross Errors

Gross errors are large mistakes caused by human or operational failures.

4.1 Examples

• Reading the wrong value.
• Data entry mistakes.
• Instrument misleveling.
• Loss of GNSS signal.
• Measuring the wrong point.

4.2 Characteristics

• Much larger than random errors
• Do not follow statistical behavior
• Cannot be corrected mathematically

4.3 Treatment

Gross errors must be:

• detected, and
• removed before or during adjustment.

They are usually identified through:

• residual analysis
• statistical tests
• consistency checks.

5. Importance for Adjustment of Observations

The Least Squares Method assumes that:

• systematic errors have been removed or modeled
• gross errors are absent
• remaining errors are random and normally distributed

If gross or systematic errors remain, the adjustment results may be unreliable.

6. Solved Example

A distance was measured five times (m): 152.334; 152.331; 152.336; 152.333; 152.335.

The values show small variations around the mean and no extreme values.

6.1 Interpretation:

• Errors are small and irregular.
• Behavior is consistent with random errors.
• Data are suitable for adjustment.

7. Proposed Example

Angle observations (seconds): 30.124; 30.118; 30.121; 30.950

7.1 Interpretation:

The value 30.950 is significantly different from the others and should be considered a gross error and investigated before adjustment.

8. Conclusion

Geodetic observations are affected by systematic, random, and gross errors. Correct identification and treatment of these errors are essential to ensure reliable and accurate results in the adjustment process.

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