GELE Adjustment Computations (Least Squares) — Error Propagation, Variance-Covariance and Error EllipsesSlides
Slide deck for GELE Adjustment Computations (Least Squares) — Error Propagation, Variance-Covariance and Error Ellipses. These slides are built for quick visual review, highlighting the key concepts, formulas, and question patterns from this chapter of the GELE 2026 syllabus.
Exam context
Professional Regulation Commission (PRC) — Board of Geodetic Engineering runs the Geodetic Engineer Licensure Examination on September 2026. Its Adjustment Computations (Least Squares) section sits under a "Core" weighting, and Error Propagation, Variance-Covariance and Error Ellipses is the 5th chapter in the 5-chapter GELE Adjustment Computations (Least Squares) rotation. The GELE passing mark is 70% weighted average, no sub-test below 50%, and the most recent 2026 paper drew about a meaningful share of questions from Adjustment Computations (Least Squares).
Error Propagation, Variance-Covariance and Error Ellipses - Slides
Slides
Introduction: Why Error Propagation Matters
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The Law of Propagation of Variances—Single Variable
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Multiple Independent Variables—The General Form
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Special Case: Sum or Difference of Quantities
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Special Case: Scaling and Multiplication
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Special Case: Mean of n Equal Observations
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Matrix Form: Error Propagation with the Jacobian
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Variance-Covariance Matrix: Definition and Structure
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Variance-Covariance Matrix in Least-Squares Adjustment
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Error Ellipse: What It Represents
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Computing Error Ellipse Parameters: Eigenvalues and Eigenvectors
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Worked Example 1: Sum of Two Distances
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Worked Example 2: Area from Measured Rectangle
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Worked Example 3: Error of a Mean from Repeated Measurements
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Worked Example 4: Error Ellipse from Covariance Matrix
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Error Ellipse Interpretation: Geometry and Design
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Common Pitfalls and Exam Mistakes
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Philippine Standards and Regulatory Context
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Summary: Key Formulas and Rules
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Key Takeaways and Learning Outcomes
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