GELE Adjustment Computations (Least Squares) — Least Squares — Observation EquationsSlides
Least Squares — Observation Equations slides, sized for screen and print. Flip through them for a five-minute pre-mock refresh, or print the deck for on-paper annotation. Either way, the slides cover Least Squares — Observation Equations at the depth Professional Regulation Commission (PRC) — Board of Geodetic Engineering tests for the GELE 2026.
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 Least Squares — Observation Equations is the 2nd 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).
Least Squares — Observation Equations - Slides
Slides
Introduction to Least Squares Adjustment
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S1
The Least-Squares Principle: Core Concept
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Observation Equations: Parametric Form
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Matrix Form of the Adjustment Problem
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S4
The Normal Equations and Solution
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Residuals and Quality Control
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Reference Variance and Variance-Covariance Matrix
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The Single-Unknown Case: Weighted Mean
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Worked Example 1: Three Leveling Routes (Philippine Context)
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Worked Example 1 (Continued): Computing Residuals and Reference Variance
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Two-Unknown Case: Design Matrix Setup
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Worked Example 2: Two-Unknown Coordinate Adjustment
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Redundancy and Degrees of Freedom
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Common Board-Exam Pitfalls and Tips
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Applications in Philippine Surveying (RA 8560, RA 4374, PD 1529, CA 141)
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Adjustment in Leveling Networks (Vertical Control)
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Adjustment in Horizontal Networks (Traverse, Trilateration, GNSS)
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Covariance Propagation and Uncertainty in Adjusted Results
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Iterative Refinement and Convergence in Nonlinear Adjustment
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Summary: Least-Squares Adjustment Workflow
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Key Formulas Reference Sheet
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Chapter Summary and Learning Outcomes
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Stored In
chapter_slides
Slide Count
22
Summary Only
true
Previous chapter
Theory of Errors, Weights and Most Probable Value
Next chapter
Condition Equations and Figure Adjustment
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