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.
Lesson 02 – Types of Errors in Geodetic Observations
Objectives
- Understand the different types of errors present in geodetic measurements.
- Distinguish between systematic, random, and gross errors.
- Identify the origin and behavior of each type of error.
- Recognize the importance of error classification in the adjustment process.
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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