Chapter 16, Problem 16.24P

To determine

Develop the observation equations for the given baseline vectors

   $\begin{array}{l}Theobservationequationsforbaselinecomponentsare:\\ \begin{array}{l}{X}_{B-R}=1,164,499.387+{\text{ v}}_1\hfill \\ Y_{B-R}=-4,660,600.879+{\text{ v}}_2\hfill \\ Z_{B-R}=4,182,158.213+{\text{ v}}_3\hfill \\ X_{T-H}=1,168,947.841+{\text{ v}}_4\hfill \\ Y_{T-H}=4,650,766.249+{\text{ v}}_5\hfill \\ Z_{T-H}=4,191,851.263+{\text{ v}}_6\hfill \end{array}\end{array}$

Given that

Baseline vector are given as

Explanation:

Writing observation equation for X coordinate for jim to troy:

   $X_{B-R}=X_B+\Delta X_{B-R}+v_1$

WHERE

X_B= X coordinate of the station bonnie = $1,161,121.599m$

∆X_B-R= X component in baseline vector = $\mathrm{3.377.788}m$

∆₁= residual

   $\begin{array}{l}{X}_{B-R}=1,161,121.599+\mathrm{3.377.788}+v_1\hfill \\ {}_{ } =1,164,499.387+{\text{ v}}_1\hfill \end{array}$

Writing observation equation for Y coordinate for Bonnie to Ray:

   $Y_{B-R}=Y_B+\Delta Y_{B-R}+v_2$

WHERE

Y_B= Y coordinate of the station BONNIE = $-4,655,872.977$

${\text{ΔY}}_{\text{B-R}}$ = Y component in baseline vector $=-4,727.902$

∆₂= residual

   $\begin{array}{l} Y_{B-R}=-4,655,872.977+-4,727.902+v_2\hfill \\ {}_{ } =-4,660,600.879+{\text{ v}}_2\hfill \end{array}$

Writing observation equation for Y coordinate for Bonnie to Ray:

   $Z_{B-R}={\text{ Z}}_B+\Delta Z_{B-R}+v_3$

WHERE

Z_B= Z coordinate of the station bonnie = $4,188,330.232m$

∆Z_B-R= Z component in baseline vector = $-6,172.019m$

∆₃= residual

   $\begin{array}{l}{Z}_{B-R}=4,188,330.232+-6,172.019+v_3\hfill \\ {}_{ } =4,182,158.213+{\text{ v}}_3\hfill \end{array}$

Writing observation equation for X coordinate for tom to herb:

   $X_{T-H}=X_T+\Delta X_{T-H}+v_4$

WHERE

X_T= X coordinate of the station Tom = $1,176,398.558m$

∆X_T-H= X component in baseline vector = $-7,450.717m$

∆₄= residual

   $\begin{array}{l} X_{T-H}=1,176,398.558--7,450.717+v_4\hfill \\ {}_{ } =1,168,947.841+{\text{ v}}_4\hfill \end{array}$

Writing observation equation for y coordinate for tom to herb:

   $Y_{T-H}=Y_T+\Delta Y_{T-H}+v_5$

WHERE

Y_T= Y coordinate of the station tom = -4,653,039.613m

∆Y_T-H= Y component in baseline vector = 2,273.364m

∆₅= residual

   $\begin{array}{l}{Y}_{T-H}=-4,653,039.613+2,273.364+{\text{ v}}_5\hfill \\ {}_{ } =-4,650,766.249+{\text{ v}}_5\hfill \end{array}$

Writing observation equation for Z coordinate for tom to herb

   $Z_{T-H}=Z_T+\Delta Z_{T-H}+v_6$

WHERE

Z_T= Z coordinate of the station tom = 4,187,198.360m

∆Z_T-H= Z component in baseline vector = 4652.903m

∆₆= residual

   $\begin{array}{l}{Z}_{T-H}=4,187,198.360m+4652.903+v_6\hfill \\ {}_{ } =4,191,851.263+{\text{ v}}_6\hfill \end{array}$

Conclusion:

Hence, the observation equations for baseline components are:

   $\begin{array}{l}{X}_{B-R}=1,164,499.387+{\text{ v}}_1\hfill \\ Y_{B-R}=-4,660,600.879+{\text{ v}}_2\hfill \\ Z_{B-R}=4,182,158.213+{\text{ v}}_3\hfill \\ X_{T-H}=1,168,947.841+{\text{ v}}_4\hfill \\ Y_{T-H}=4,650,766.249+{\text{ v}}_5\hfill \\ Z_{T-H}=4,191,851.263+{\text{ v}}_6\hfill \end{array}$