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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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Taylor’s Series The observation equation is non-linear so Taylor’s 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
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