Adjustment of Trilateration

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Adjustment of Trilateration
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Introduction

• For a brief period of time, trilateration was a
  highly effective method of establishing
  horizontal control coordinates.
• This was after EDM technology matured but before
  GPS
• Measuring distances-only avoided the more
  labor-intensive task of angle measurement.
• This was a role-reversal, since previously, angle
  measurement was the easier operation

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Intro - Continued

• These trilateration surveys generally covered a
  large area
• Correction for earth curvature needed to be
  applied
• For some cases, state plane coordinate systems
  were used as a coordinate base
• Often coordinates are large, so offsets may be
  subtracted prior to adjustment and then added
  after the adjustment

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Distance Observation
What is the observation? What are the unknowns?
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Taylors Series
The observation equation is non-linear so
Taylors Series is applied.
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Partial Derivatives
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Distance Observation Equation
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Example 13.2
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Substitution for I and J in Equation
I J A U B U C U Note In this
example, the unknown station U is always in the J
station position of the prototype line.
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Matrix Form
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Initial Approximations
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Approximations - Continued
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Approximations - Continued
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Set Up Matrices
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Set Up Normal Equations
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Solve and Update
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Second Iteration
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Form Matrices
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Update
Further iterations are negligible.
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Post Adjustment Statistics
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Statistics - Continued
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Estimated Errors of Adjusted Observations
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Solution Summary
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More Complex Network
The same process applies to more complex
networks. You just need to be careful with
selection of I and J
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Iteration Termination

• Maximum number of iterations
• Correction threshold
• Convergence of estimate of standard deviation of
  unit weight