5. Traverse and Least-Squares Adjustment
Traverse and Least-Squares Adjustment
This domain tests traverse design, misclosure detection, adjustment methods and least-squares concepts. Expect angular and linear misclosure, Bowditch and transit rules, observation equations, weights, redundancy and error ellipses.
Core rules
- Angular misclosure = observed sum - theoretical sum; compare with an allowable based on instrument and number of angles.
- Linear misclosure is the vector sum of coordinate increments; relative misclosure is misclosure divided by perimeter.
- Bowditch distributes misclosure in proportion to leg length; transit distributes by dE and dN separately.
- Least squares minimises weighted squared residuals; weights reflect observation variance.
- Redundancy enables detection of errors and estimation of precision; an error ellipse describes positional uncertainty.
Worked example
A five-angle closed traverse has observed angle sum 540 degrees 00 minutes 20 seconds; theoretical sum is 540 degrees 00 minutes 00 seconds. Angular misclosure is +20 seconds. If the allowable is 30 seconds x sqrt(5) = 67 seconds, the traverse passes the angular test. Apply a correction of -20/5 = -4 seconds to each angle before computing bearings. Do not adjust coordinates until the angular misclosure is accepted.
Traps
Applying Bowditch to a GNSS network; ignoring weights; adjusting before checking angular closure; treating a small misclosure as proof of no blunder; forgetting that least squares needs a functional model and a stochastic model.