A Review of Least Squares Theory Applied to Traverse Adjustment
A Technical paper published in two parts in The Australian Surveyor, Vol. 36, No. 3, pp. 245-253 and Vol. 36, No. 4, pp. 281-290, 1991.
Travad.pdf
AppendixA.pdf
AppendixB.pdf
Traverse Network Adjustment Program HAVOC
HAVOC (Horizontal Adjustment by Variation Of Coordinates) is a 2D least squares adjustment program for traverse networks that runs in a MATLAB or OCTAVE environment. The theory behind the program is provided in A Review of Least Squares Theory Applied to Traverse Adjustment (see Travad.pdf above) and the program consists of 10 Matlab files (filename.m) that can be copied onto your system. Three data files (filename.txt) are supplied together with some brief notes on the operation of the program.
decdeg.m deg2dms.m ellipse.m Havoc.m HavocPlot.m
join.m readdata.m results.m solve.m status.m
Survad.txt Broadford.txt Free_Broadford.txt
HAVOC Notes (new).pdf
Combined Least Squares
Notes on the combined least squares adjustment model, including the derivation of equations, covariance matrices (propagation of covariances) and the connection with parametric least squares (21 pages)
Combined Least Squares.pdf
Constrained Least Squares
Notes on the addition of constraint equations in parametric least squares (7 pages).
Constrained Least Squares.pdf
Free Net Level Adjustment
Notes on the application of inner constraints to overcome datum deficiency problems in level network adjustments (6 pages).
Free Net Level AdjustmentV2.pdf
Inner Constraints in Least Squares Adjustment
Notes on the development of inner constraint equations for 3D survey network adjustments (12 pages)
Inner Constraints.pdf
The Kalman Filter: A Look Behind The Scene
Paper presented at the Victorian Regional Survey Conference, Mildura, 23-25 June, 2006 (12 pages).
Kalman Filter Mildura Conference.pdf
Kalman Filter and Surveying Applications
Technical paper (30 pages) explaining the Kalman Filter with surveying application. Includes Matlab functions.
Kalman Filter and Surveying Applications.pdf
Kalman Filtering
A set of large print lecture notes (74 pages) suitable for PowerPoint presentation outlining the least squares principle and its application in the development of combined least squares, indirect least squares (parametric least squares), observations only least squares and Kalman Filtering.
Kalman Filtering Lectures.pdf
Least Squares and Kalman Filtering
Technical document covering Least Squares and Kalman Filtering from a surveying/geodesy perspective (91 pages). Notes include a concise explanation of Combined Least Squares with general formula for solutions of particular cases. Examples of different problems are given with solutions and MATLAB functions given in an Appendix. The usual least squares approach (minimizing sum of squares of weighted residuals) is extended Primary and Secondary (or dynamic) measurement models at discrete time intervals to obtain the Kalman Filter equations (the derivation of equations is set out). Examples are given (EDM measurement, Position and Velocity of a Ship in a Navigation channel, global warming: estimating trends from temperature anomalies) and MATLAB functions given in an Appendix.
Least Squares and Kalman Filtering.pdf
edm.m
global_warming_filter.m
kalship3.m
least_squares.m
linear_regression_CLS.m
Anomalies_NASA_1880_2014.txt
Anomalies_US_Surface_Air_Temp_1880_2014.txt
Example_1.txt
Example_2.txt
Example_3.txt
Example_4.txt
kalshipdata3.txt
Level Network Adjustments
Notes (including worked examples) of different methods of adjusting a level network using least squares (21 pages)
Yarra Bend Level Net Adjustment Exercise.pdf
Linear Regression (Line of Best Fit using Least Squares)
Fitting a straight line through X,Y data is a common problem in estimation. Using a data plot and a ruler, the problem is solved by slowly moving the ruler to a position that visually minimizes the perpendicular distances between the data points and the ruler. A mathematical solution can be determined using the theory of least squares that supposes the most probable ‘answer’ is one that minimizes the sum of the weighted squares of residuals, where residuals are small corrections to the X,Y data and weights are numbers reflecting the precision of measurements.
York (1966, 1968) solved this problem for uncorrelated and correlated data, but unfortunately, his solution is not well known and scientists and engineers often use inappropriate methods embedded in software products and calculators. This paper will show, in detail, how York solved this problem of estimation.
A MATLAB function and ASCII text data are also provided.
Fitting a straight line.pdf
linear_regression_YORK.m
Neri_Line_Data_2.txt
Notes on Least Squares
Lecture notes on the topic of least squares with plane surveying applications (222 pages). These notes contain 10 chapters plus an appendix on matrix algebra.
Notes on Least Squares 2005.pdf
Rank of a Matrix
Notes on matrix Rank including methods of elimination to determine matrix rank (8 pages).
Rank of a Matrix.pdf
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