Precision of Adjusted Variables by Least Squares

The principles of least squares adjustment of observations are described in this paper through the use of matrix algebra. Six possible cases of adjustment of observations are presented and completely solved. The precision estimates of the adjusted variables are being considered a part of the solution of each case. The general problem of least squares adjustment is then derived and solved through a simple approach. The solutions for two additional problems of adjustment are extracted from the solution of the general problem. In the same way, the solution of any particular case of adjustment can easily be found from that of the general problem. A summary for the equations which give the solution of most of the adjustment cases presented in this paper is given in tabulated form. A numerical example which solidifies the solution of the general problem of least squares is presented.