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Adjustment of Trilateration

Adjustment of Trilateration. 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

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Adjustment of Trilateration

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  1. Adjustment of Trilateration

  2. 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

  3. 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

  4. Distance Observation What is the observation? What are the unknowns?

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

  6. Partial Derivatives

  7. Distance Observation Equation

  8. Example 13.2

  9. 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.

  10. Matrix Form

  11. Initial Approximations

  12. Approximations - Continued

  13. Approximations - Continued

  14. Set Up Matrices

  15. Set Up Normal Equations

  16. Solve and Update

  17. Second Iteration

  18. Form Matrices

  19. Update Further iterations are negligible.

  20. Post Adjustment Statistics

  21. Statistics - Continued

  22. Estimated Errors of Adjusted Observations

  23. Solution Summary

  24. More Complex Network The same process applies to more complex networks. You just need to be careful with selection of I and J

  25. Iteration Termination • Maximum number of iterations • Correction threshold • Convergence of estimate of standard deviation of unit weight

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