Geomatics and Measurement in Civil Engineering

LECTURE 4 (CH16)
OBSERVATION EQUATIONS
 Least Squares adjustment by observation equation method:
 Written relating observed values to residual errors and unknown parameters
 1 observation equation for each observation
 Number of equations = number of unknowns
 If redundant observations made, least squares method can be applied
 Expression for each residual obtained from every observation equation
 Residuals then squared and added to get a function:
 Squared variance

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 Weighted squared variance:

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 From Example:
 Compute most probable value for equally weighted distance observations:




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 Find mean value (most probable value of observed length)
 Write following observation equations that define residual for any observed quantity at
difference between most probable value and any individual observations

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 From Example: