Develop the observation equations for the given baseline vectors T h e o b s e r v a t i o n e q u a t i o n s f o r b a s e l i n e c o m p o n e n t s a r e : X B − R = 1 , 164 , 499.387 + v 1 Y B − R = − 4 , 660 , 600.879 + v 2 Z B − R = 4 , 182 , 158.213 + v 3 X T − H = 1 , 168 , 947.841 + v 4 Y T − H = 4 , 650 , 766.249 + v 5 Z T − H = 4 , 191 , 851.263 + v 6 Given that Baseline vector are given as Explanation: Writing observation equation for X coordinate for jim to troy: X B − R = X B + Δ X B − R + v 1 WHERE X B = X coordinate of the station bonnie = 1 , 161 , 121.599 m ∆X B - R = X component in baseline vector = 3.377.788 m ∆ 1 = residual X B − R = 1 , 161 , 121.599 + 3.377.788 + v 1 = 1 , 164 , 499.387 + v 1 Writing observation equation for Y coordinate for Bonnie to Ray: Y B − R = Y B + Δ Y B − R + v 2 WHERE Y B = Y coordinate of the station BONNIE = − 4 , 655 , 872.977 ΔY B-R = Y component in baseline vector = − 4 , 727.902 ∆ 2 = residual Y B − R = − 4 , 655 , 872.977 + − 4 , 727.902 + v 2 = − 4 , 660 , 600.879 + v 2 Writing observation equation for Y coordinate for Bonnie to Ray: Z B − R = Z B + Δ Z B − R + v 3 WHERE Z B = Z coordinate of the station bonnie = 4 , 188 , 330.232 m ∆Z B - R = Z component in baseline vector = − 6 , 172.019 m ∆ 3 = residual Z B − R = 4 , 188 , 330.232 + − 6 , 172.019 + v 3 = 4 , 182 , 158.213 + v 3 Writing observation equation for X coordinate for tom to herb: X T − H = X T + Δ X T − H + v 4 WHERE X T = X coordinate of the station Tom = 1 , 176 , 398.558 m ∆X T - H = X component in baseline vector = − 7 , 450.717 m ∆ 4 = residual X T − H = 1 , 176 , 398.558 − − 7 , 450.717 + v 4 = 1 , 168 , 947.841 + v 4 Writing observation equation for y coordinate for tom to herb: Y T − H = Y T + Δ 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 Y T − H = − 4 , 653 , 039.613 + 2 , 273.364 + v 5 = − 4 , 650 , 766.249 + v 5 Writing observation equation for Z coordinate for tom to herb Z T − H = Z T + Δ 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 Z T − H = 4 , 187 , 198.360 m + 4652.903 + v 6 = 4 , 191 , 851.263 + v 6 Conclusion: Hence, the observation equations for baseline components are: X B − R = 1 , 164 , 499.387 + v 1 Y B − R = − 4 , 660 , 600.879 + v 2 Z B − R = 4 , 182 , 158.213 + v 3 X T − H = 1 , 168 , 947.841 + v 4 Y T − H = 4 , 650 , 766.249 + v 5 Z T − H = 4 , 191 , 851.263 + v 6

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Question

Chapter 16, Problem 16.24P

To determine

Develop the observation equations for the given baseline vectors

The observation equations for baseline components are:XB−R= 1,164,499.387+ v1YB−R= −4,660,600.879+ v2ZB−R= 4,182,158.213+ v3XT−H= 1,168,947.841+ v4YT−H= 4,650,766.249+ v5ZT−H= 4,191,851.263+ v6

Given that

Baseline vector are given as

Explanation:

Writing observation equation for X coordinate for jim to troy:

XB−R= XB+ ΔXB−R+v1

WHERE

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

∆X_B_-_R= X component in baseline vector = 3.377.788m

∆₁= residual

XB−R=1,161,121.599+3.377.788+v1          = 1,164,499.387+ v1

Writing observation equation for Y coordinate for Bonnie to Ray:

YB−R= YB+ ΔYB−R+v2

WHERE

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

ΔYB-R = Y component in baseline vector = −4,727.902

∆₂= residual

YB−R=−4,655,872.977+−4,727.902+v2          = −4,660,600.879+ v2

Writing observation equation for Y coordinate for Bonnie to Ray:

ZB−R= ZB+ ΔZB−R+v3

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

ZB−R=4,188,330.232+−6,172.019+v3          = 4,182,158.213+ v3

Writing observation equation for X coordinate for tom to herb:

XT−H= XT+ ΔXT−H+v4

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

XT−H=1,176,398.558 −−7,450.717+v4          = 1,168,947.841+ v4

Writing observation equation for y coordinate for tom to herb:

YT−H= YT+ ΔYT−H+v5

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

YT−H=−4,653,039.613+2,273.364+ v5          = −4,650,766.249+ v5

Writing observation equation for Z coordinate for tom to herb

ZT−H= ZT+ ΔZT−H+v6

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

ZT−H=4,187,198.360m +4652.903+v6          = 4,191,851.263+ v6

Conclusion:

Hence, the observation equations for baseline components are:

XB−R= 1,164,499.387+ v1YB−R= −4,660,600.879+ v2ZB−R= 4,182,158.213+ v3XT−H= 1,168,947.841+ v4YT−H= 4,650,766.249+ v5ZT−H= 4,191,851.263+ v6

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