Three objects are located on a line at points p1 < p2 <

Chapter , Problem 5

(choose chapter or problem)

Three objects are located on a line at points \(p_1<p_2<p_3\). These locations are not precisely known. A surveyor makes the following measurements:

a. He stands at the origin and measures the three distances from there to \(p_1, p_2\), \(p_3\). Let these measurements be denoted by \(Y_1, Y_2, Y_3\).

b. He goes to \(p_1\) and measures the distances from there to \(p_2\) and \(p_3\). Let these measurements be denoted by \(Y_4, Y_5\).

c. He goes to \(p_2\) and measures the distance from there to \(p_3\). Denote this measurement by \(Y_6\).

He thus makes six measurements in all, and they are all subject to error. In order to estimate the values \(p_1, p_2, p_3\), he decides to combine all the measurements by the method of least squares. Using matrix notation, explain clearly how the least  squares  estimates  would  be  calculated  (you  don’t  have  to  do  the actual calculations).