Least Squares Adjustment Demonstration Braced Quad Distances a graphical approach with large measurement errors © MM B.Harvey

Author & version details Written by Bruce Harvey in 2000, updated in 2004 Based on LSD.exe written by B Harvey in Authorware Pro in Feb 1995 © B Harvey More details contact author at

Raw distance data How to make them fit & what are the best coordinates? Fixed coords Known azimuth Distance obs Graphical solution: They just don’t fit!

Now lets see what Least Squares does Starting coordinates Adjustment by second iteration Adjustment by first iteration Best fit solution

Question Time Q1. Starting values for coordinates can be rough because Least Squares Adjustment will “pull them in”, provided enough iterations are calculated. A1. This is usually true, but not always. Try to use starting values for coordinates that are approximately in correct relative positions, so that a plan of them looks OK. This is especially important when direction observations are used. TRUEFALSE

Results of Least Squares Adjustment Changes to coordinates Residuals to obs Error ellipses

Question Time Q2. Least Squares gives corrections to observations (residuals) that are about the same size as the error ellipses. A2. True for this example, but not always true. Residuals depend on how well the observations fit together. Error ellipses depend on input standard deviations of observations and network geometry. Bad observations affect residuals but not error ellipses. TRUEFALSE

What does a Least Squares adjustment do? finds the best fit solution, removes miscloses, keeps changes to observations as small as possible, gives an indication of the quality of the results

Later, go and try it yourself... with a least squares program OR ?