Surveying and Geomatics

3.

Theory of Errors and Measurement Adjustment

3.1.

Nature of Surveying Measurements

3.1.1.

Direct Measurements

3.1.2.

Indirect Measurements

3.1.3.

Conditional Measurements

3.1.4.

Most Probable Values

3.2.

Sources of Error

3.2.1.

3.2.1.1.

Atmospheric Refraction

3.2.1.2.

Temperature Effects

3.2.1.3.

Wind and Vibration

3.2.1.4.

Earth Curvature

3.2.2.

Instrumental Errors

3.2.2.1.

Calibration Errors

3.2.2.2.

Manufacturing Imperfections

3.2.2.3.

3.2.2.4.

3.2.3.

Personal Errors

3.2.3.1.

3.2.3.2.

Judgment Errors

3.2.3.3.

Systematic Mistakes

3.2.3.4.

Fatigue Effects

3.3.

Classification of Errors

3.3.1.

Mistakes or Blunders

3.3.1.1.

Detection Methods

3.3.1.2.

Elimination Procedures

3.3.1.3.

Prevention Strategies

3.3.2.

Systematic Errors

3.3.2.1.

Constant Errors

3.3.2.2.

Proportional Errors

3.3.2.3.

Detection and Correction

3.3.3.

3.3.3.1.

Statistical Nature

3.3.3.2.

Normal Distribution

3.3.3.3.

Standard Deviation

3.4.

Precision and Accuracy

3.4.1.

Definitions and Distinctions

3.4.2.

Measures of Precision

3.4.3.

Measures of Accuracy

3.4.4.

Relationship between Precision and Accuracy

3.4.5.

Methods for Improvement

3.5.

Error Propagation

3.5.1.

Linear Functions

3.5.2.

Nonlinear Functions

3.5.3.

Correlation Effects

3.5.4.

Variance-Covariance Matrices

3.6.

Statistical Analysis of Measurements

3.6.1.

Measures of Central Tendency

3.6.1.1.

3.6.1.2.

3.6.1.3.

3.6.2.

Measures of Dispersion

3.6.2.1.

3.6.2.2.

Standard Deviation

3.6.2.3.

3.6.3.

Confidence Intervals

3.6.4.

Hypothesis Testing

3.7.

Weighting of Observations

3.7.1.

Weight Assignment Principles

3.7.2.

Weight from Precision

3.7.3.

Weighted Mean Calculations

3.7.4.

Weight Propagation

3.8.

Least Squares Adjustment

3.8.1.

Principles of Least Squares

3.8.2.

Observation Equations

3.8.3.

Condition Equations

3.8.4.

Normal Equations

3.8.5.

Matrix Solutions

3.8.6.

Parametric Adjustment

3.8.7.

Applications to Survey Networks

3.8.7.1.

3.8.7.2.

Traverse Networks

3.8.7.3.

Triangulation Networks

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4. Distance Measurement and Linear Surveying