CA PLS Exam Preparation

Comprehensive preparation for the California Professional Land Surveyor (PLS) exam. Based on the January 2025 Test Plan with 6 modules and 57 topics. Content adapted from CalTrans LS/LSIT Video Exam Preparation Course materials.

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Lesson 6

Survey Adjustments (Least Squares, Error Analysis)

Survey Adjustments (Least Squares, Error Analysis)

Overview

Survey adjustments distribute measurement errors systematically and provide measures of precision. Understanding adjustment methods and error analysis is fundamental to professional practice.

Learning Objectives

  • Understand least squares adjustment principles
  • Apply traverse adjustment methods
  • Analyze residuals and statistics
  • Interpret adjustment results

Key Concepts

Least Squares Principles

Fundamental concepts:

  • Minimizing sum of squared residuals
  • Redundant observations
  • Weight matrix application
  • A priori vs. a posteriori variance

Traverse Adjustments

Common adjustment methods:

  • Compass Rule: Proportional to distance
  • Transit Rule: Proportional to latitudes/departures
  • Crandall Method: Distance adjustment only
  • Least Squares: Rigorous statistical adjustment

Error Analysis

Statistical evaluation:

  • Standard deviation of unit weight
  • Positional uncertainty ellipses
  • Relative error ellipses
  • Chi-square testing
  • Residual analysis

Adjustment Results Interpretation

Understanding output:

  • Adjusted coordinates
  • Residuals and their meaning
  • Statistical quality indicators
  • Outlier detection
  • Network reliability

Key Terms

  • Residual: Difference between observed and adjusted values
  • Redundancy: Number of observations minus unknowns
  • Error Ellipse: Graphical representation of positional uncertainty

Practice Questions

  1. What is the fundamental principle of least squares adjustment?
  2. How should large residuals be interpreted in an adjustment?

Based on CalTrans LS/LSIT Video Exam Preparation Course materials.