# 2D Network Simulation

Hello, I hope that you can help me. I have task to create 2D network for building purposes and it contains 5 points. It is not "perfect" geometry of network, but I only want on this example to see how this great software works. I did calculations in Excel, and results are good in a mathematical sense, so I tried the same thing in JAG, and did not get same results. I will screen record what I did and also attach Excel results. Please help me, I have a deadline to do this, and also I have 1D network in project, but for 1D you have youtube tutorials. I am new on this forum, so please tell me how to upload results in this thread.

Thanks!

## 2D Network Simulation

Hello Zaklina,

the forum does not support the upload of external files. However, there are a lot of services like Dropbox, Google Drive, Nextcloud etc. to upload data.

If the network is quite small, as in your case, simply include the network data in your answer, as shown here.

All the best
Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## 2D Network Simulation

Thanks Micha a lot!!!
I need to do simulation of 2D free network. All points are datum points. I propose use of instrument 3" accuracy for directions, and 2+2ppm for distances. Approximate coordinates are:

S1 5442.34 3926.15
S2 5503.94 3951.27
S3 5563.70 3920.66
S4 5513.12 3899.66
S5 5452.25 3880.17

Input file for observations - directions is:
S1 S2 0.00000
S1 S5 0.00000
S2 S1 0.00000
S2 S4 0.00000
S2 S3 0.00000
S3 S2 0.00000
S3 S4 0.00000
S4 S5 0.00000
S4 S2 0.00000
S4 S3 0.00000
S5 S1 0.00000
S5 S4 0.00000

Input file for observations - distances is:
S1 S2 0.0000
S1 S5 0.0000
S2 S1 0.0000
S2 S4 0.0000
S2 S3 0.0000
S3 S2 0.0000
S3 S4 0.0000
S4 S5 0.0000
S4 S2 0.0000
S4 S3 0.0000
S5 S1 0.0000
S5 S4 0.0000

Results that i get in Excel are:
PointID A [mm] B [mm] angle myi mxi
S1 0.94 0.77 344.3853168 0.41 0.34
S2 0.74 0.70 8.394335191 0.32 0.31
S3 1.12 0.47 352.0845818 0.48 0.21
S4 0.72 0.58 330.685026 0.30 0.27
S5 1.00 0.75 340.6293756 0.43 0.34

A and B and angle are parametars od ellipses and myi and mxi are a-posteriori uncertainty for Y and X component.
I also get 0 results for a-posteriori uncertainty for directions, so I dont know what I missed.
I will attach via google drive JAG3D project and video what I did, can you give me an e-mail for sharing these files?

Zaklina

## 2D Network Simulation

Hello Zaklina,

I created a project using your data but I cannot confirm your results. My project can be found here. The differences can arise for various reasons. One of the most common reasons is a different stochastic model - especially for the distances. 2mm + 2ppm can be interpreted differently, see for instance Shih (2013) On accuracy specifications of electronic distance meter, Survey Review, 45(331), 281-284.

Kind regards
Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## 2D Network Simulation

Thanks Micha.
Can you tell me how to specify stochastic model for directions which are we assume to measure in 3 gyruses (in my Excel I divided 3" with √3 (square root) and for distances we assume to measure twice every direction (in my Excel I divided 2 + 2ppm with √2, ppm part depends on approximate distance value). That is probably reason why I get different results. Can you also tell me why is a posteriori uncertainty zero value for directions?
If you have least square root concepts that you implemented in software, please give me link.

## 2D Network Simulation

Hi Zaklina,

Can you also tell me why is a posteriori uncertainty zero value for directions?

I am not sure which value you mean, because no residuals can be estimated in the simulation. Therefore, no a-posteriori values can be calculated.

If you have least square root concepts that you implemented in software, please give me link.

The stochastic model of the terrestrial observation can be found in the Wiki (German only).

Kind regards
Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## 2D Network Simulation

Thanks Micha. Can you only tell me is there any way to present results in seconds for uncertainties?

## 2D Network Simulation

Hello Zaklina,

Can you only tell me is there any way to present results in seconds for uncertainties?

You can switch the units and change the resolution of numeric values via Properties → Formatter preferences, see screenshot

/Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## 2D Network Simulation

Hello Micha.
Thanks for all notes. I successfully simulated 2D network, I have only one question, and I will maybe have one more later (about "reading" some report values). Is there any chance to calculate RELATIVE ellipses parameters? Also, can you help me put instrument centering error in stochastic model? I put these values in stochastic model: 1" for δa for directions, and for distances δa 1mm, and δc(d) 1.5ppm (declared accuracy of instument). I need to put value
0.8mm for instrument centering error, can you help me? What means δb√d in stochastic model also?

## 2D Network Simulation

Hello Zaklina,

I successfully simulated 2D network

Perfect!

Is there any chance to calculate RELATIVE ellipses parameters?

Yes, there is a - let's say - workaround. You can use a part of the implemented deformation analysis because the estimation procedure is identical. To obtain the confidence region between any two points, you must specify both points as a so-called point nexus, cf. the bottom screenshot in the right figure. The relative confidence region is shown in the plot in yellow (default color) together with an arrow. As already mention, the function is designed for deformation analysis, so the arrows indicate the direction of deformation. So, please ignore the arrows. In the Figure, relative confidence regions are depicted between S1 and S4 as well as S2 and S3.

Also, can you help me put instrument centering error in stochastic model? I put these values in stochastic model: 1" for δa for directions, and for distances δa 1mm, and δc(d) 1.5ppm (declared accuracy of instument). I need to put value 0.8mm for instrument centering error, can you help me?

The coefficients σa, σb and σc have no physical meaning. They differ only in the way the distance between the standpoint and the target point is taken into account. For this reason, you must consider how a centering error will affect a measurement. For a distance measurement, the centering error refers to the line of sight but is independent of the distance between the standpoint and the target point. Thus, σa should be used to specify the centering error by applying uncertainty propagation, i.e. $\sigma_a = \sqrt{1.0^2 + 0.8^2}$. For a angle measurement, the centering error is transverse to the line of sight. Moreover, the unit of the centering error is usually not an angle unit, like your specified 0.8 mm. To convert the transverse error component to an angle unit, the distance between the standpoint and the target point is needed, i.e. $\frac{σ}{d}$. Thus, the centering error is part of σc for angle measurements.

What means δb√d in stochastic model also?

Typically, leveling networks are specified for 1 km double measuring a line. Here, the σb must be used to specify the stochastic model.

Best regards
Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## 2D Network Simulation

Hello Micha,
I calculated standard deviation for easch direction, according to horizontal distance.

I got these results:

standard deviation of direction in "

distance value from        distance value to standard deviation of direction in "
0                        20                     80
20                        30                     60
30                        40                     42
40                        60                     28
60                        70                     21
70                        100                     15
100                        120                     10
120                        150                      7

I have small distances in network, so I got these results. For example, if distance is between 0m and 20m, standard deviation of direction is 80" etc.
How to define that in stochastic model - martix P, since I have various weights for almost each direction. For distance weights, I have no problem to define.
For this calculation I used formula
σ_α=arcsin⁡((σ_DV×√n)/(d[mm]))×ρ"

σ_D is standard deviation of points (needed to be)
n - number of directions from one point to destination points in network configuration
d - distance in mm

Is that possible to define in JAG, or I need to use some averaged value (in this case of various distance, averaged value wont respresent network model satisfactory)

I hope that you can help me.
Best regards,
Zaklina

## 2D Network Simulation

Hello Zaklina,

If I understand your answer correctly, you want to specify individual uncertainties (one specific uncertainty per observation) instead of using a group model. If this is the case, then these individual uncertainties must be entered in the observation tables. Please use the column denoted by σ0.

All the best
Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## 2D Network Simulation

Thanks Micha.
That was very helpful. I almost finished all that. But can I put these uncertainty values in txt file for importing? I have 164 rows in observations. Example of input file is:

S1 S4 0.00000 7
S1 S2 0.00000 9
S1 T1 0.00000 31
S1 T8 0.00000 17
Third column is distance, and fourth is uncertainty of one direction in SECONDS.

I have problem for import, since uncertainty in not loaded into right column in JAG.

That is last question, I promise! :D
T

## 2D Network Simulation

Hej Zaklina,

I have problem for import, since uncertainty in not loaded into right column in JAG.

The uncertainties must be specified in the same unit as the observations. If the distance is in meter, so the uncertainties must be specified in the ASCII file in meter.

That is last question, I promise! :D

This is a support forum. There is no question limit per person.

/Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## 2D Network Simulation

Great Micha, thanks.
One question for relative ellipses. I put imported nexus points (network simulation, not deformation analysis).
from to
S1 S2
S2 S3
S3 S4
S4 S1
etc.
I have 42 rows.
Problem is that I did not got all relative ellipses.
Look at image:
https://ibb.co/Fq3KRG3

For most directions, these is missing relative confidence info.
Here are results:
https://ibb.co/6yk9Chq

I cant figure out what is problem to get results for all nexus points.
Zaklina

## 2D Network Simulation

Hello Zaklina,

I have 42 rows.
Problem is that I did not got all relative ellipses.
For most directions, these is missing relative confidence info.

You can not specify one point twice. For example, if you have specified S1 - S2, S1 - S3 will be ignored. Please note that the procedure is part of a deformation analysis and it is not usually useful to check whether the point S1 is congruent to S2 AND S3. So, you have to restrict the point nexuses.

/Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## 2D Network Simulation

Thanks for all informations, I did project successfully.
I only have one more question. What is ∇(1)″ in report? I mean, what math formula is implemented in software to get this value?

Zaklina

## 2D Network Simulation

Hello Zaklina,

I only have one more question. What is ∇(1)″ in report? I mean, what math formula is implemented in software to get this value?

In JAG3D, the Maximum Tolerable Bias (MTB) denoted by ∇(1) is a further metric to analyse the reliability of the observations in a geodetic network, cf. 10.1080/00396265.2021.1924003

All the best
Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## 2D Network Simulation

Thanks, but I cant open annotated link to see detailed explanation.

## 2D Network Simulation

Hello,

Thanks, but I cant open annotated link to see detailed explanation.

I've corrected the link to the paper called "Maximum Tolerable Biases (MTBs) and hardly detectable points in least-squares adjustment".

/Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences