Here is the translation:

"Dear,

I use the Jag3D program for the adjustment of both 1D and 2D networks. I have a question to which I couldn't find an answer on the forum. What do the parameters sigma a, sigma b, and sigma c mean?
As far as I understand, if the accuracy of the instrument we use is 1mm, sigma b should have a value of 1. Sigma c is always zero, but what is sigma a? Is it the a priori standard deviation that is by default 1, or is it something else?
If it is, should sigma a be 1? If not, what is it, and where is the a priori standard deviation set?
Thank you."

Hello,

What do the parameters sigma a, sigma b, and sigma c mean?

These parameters have different meanings depending on the type of observation.

As far as I understand, if the accuracy of the instrument we use is 1mm, sigma b should have a value of 1. Sigma c is always zero, but what is sigma a?

Both, σb and σc, depend on the distance between the start-point and the end-point. Contrary, σa is independent from the distance and can be interpreted as some random background noise of the measurement process having the same unit as the measured itself. Moreover, σa cannot be set to zero by convention. In a leveling network, σa refers to the uncertainty of a single measurement setup.

All the best
Micha

Dear
I am interested in the values of the parameters sigma a, sigma b, and sigma c in a 1D network (Leveling measurements). How do sigma b and sigma c depend on the distance between points? For example, if the leveling distances are between 100 and 200 meters, what should be the value of sigma b? In one of your previous responses, I found that sigma b is actually the accuracy of the instrument we use for leveling. For instance, if the instrument’s accuracy is 1mm/km, then sigma b is 1. Is this correct?

I am most interested in the value of the sigma a parameter. What should its value be and what does it depend on? Does sigma a represent an a priori standard deviation or not? If it refers to the uncertainty of a single measurement, does that mean it is the expected error value?

Thank you

Hello aleksandar95,

How do sigma b and sigma c depend on the distance between points?

I already posted a link to the documentation. The equation reads

${\sigma }_{\delta h}=\sqrt{{\sigma }_a^2+{\sigma }_b^{2}d+({\sigma }_{c}d{)}^2}$

where d is the distance.

For example, if the leveling distances are between 100 and 200 meters, what should be the value of sigma b?

The value you expect for this type of a-priori uncertainty.

For instance, if the instrument’s accuracy is 1mm/km, then sigma b is 1. Is this correct?

It is a good starting value to define this component of the stochastic model, yes.

I am most interested in the value of the sigma a parameter. What should its value be and what does it depend on?

Like σb and σc, σa depends on the assumed uncertainty of your measurement procedure.

Does sigma a represent an a priori standard deviation or not?

Again, like σb and σc, σa is an a-priori uncertainty, too.

If it refers to the uncertainty of a single measurement, does that mean it is the expected error value?

No. It is the assumed distance-independent part of the combined uncertainty of the measurement procedure. However, in case of σb=σc=0, σa defines the assumed a-priori uncertainty of a single observation δh, cf. the equation above.

Kind regards
Micha

Dear,
I will send you an example of a 1D network project I have worked on. Based on that, can you tell me what the values of the parameters sigma a, sigma b, and sigma c should be? Can You give me your mail adres to send you a project?
Thanks

Hello aleksandar95,

I will send you an example of a 1D network project I have worked on. Based on that, can you tell me what the values of the parameters sigma a, sigma b, and sigma c should be? Can You give me your mail adres to send you a project?

No, I'm, sorry. I developed the software for free, I support the software for free, but I will not analyse someone else's data or network for free.

Kind regards
Micha

Dear,
I am not asking you to do the project for me. I would like to send you the project I have already done, where I have input the values for sigma a, sigma b, and sigma c based on my experience and the explanations from the website. I would appreciate it if you could review it and tell me whether these values are suitable for this type of project. What I am most interested in is what sigma a represents. Is it the a priori standard deviation or not? Since we have concluded that sigma b is the instrument's accuracy.

What interests me the most is what sigma a represents, because this parameter is very important, and as it changes, so do the results, both when performing the alignment and when conducting the preliminary accuracy analysis
Thank you.

Hello aleksandar95,

I would like to send you the project I have already done, where I have input the values for sigma a, sigma b, and sigma c based on my experience and the explanations from the website. I would appreciate it if you could review it and tell me whether these values are suitable for this type of project.

A common approach to evaluate the a-priori stochastic model (i.e. σa, σb, and σc) is the variance-component estimation. The following image shows an example of the estimation results.

The most popular variance-component is the estimated a-posteriori variance of the unit weight. This variance is evaluated within the global test. However, the residuals and redundancies of the network can be grouped in order to derive sub-components. In JAG3D, the components refer to the observation type. Since the stochastic model for each terrestrial observation type consists of up to three components (i.e. σa, σb and σc), JAG3D derives sub-components of these variances. Each specific variance-component can be analysed in the same way as the global variance-component. The expectation value for each variance-component is $E\{{\hat{\sigma }}^2\}={\sigma }^2$ (by convention, ${\sigma }^2=1$ in JAG3D).

What I am most interested in is what sigma a represents.

I have already answered this question and I am not sure how this question can be answered if you make your project available.

Is it the a priori standard deviation or not?

Have you read my answer to the same question? The answer is still yes.

Since we have concluded that sigma b is the instrument's accuracy.

The σb is an a-priori standard deviation which depends on the length d.

What interests me the most is what sigma a represents

It is not helpful if you ask me the same question over and over again without responding to my answer. In summery, σa is an a-priori standard deviation. It is independent of the length and is a random error of each single observation. This value is derived from empirical values for the instrument and the measurement process.

Kind regards
Micha

Dear, I just have one more question. When the JAG is opened for the value sigma a it says 0.1, is that the actual value, or is 0.1 actually 1, 0.2 is 2, or are the values correct as they are? Thank you."

Hello,

When the JAG is opened for the value sigma a it says 0.1, is that the actual value, or is 0.1 actually 1, 0.2 is 2, or are the values correct as they are? Thank you.

Sorry, this question cannot be answered seriously because important information about the measuring unit is missing. Since JAG3D specifies the unit used for each value (see the following screenshot), I will return the question to you.

Kind regards
Micha

I set sigma a to 0.1mm and sigma b to 1mm (this is the accuracy of my instrument) and got the following results. Then I set sigma a to 1 and sigma b to 1 and got the following results. What is correct if it is assumed that sigma a priori is 1 and the instrument's accuracy is 1?

When I set sigma a to 0.1mm and sigma b to 1mm, the sigma h values for each measurement are between 0.2 and 0.4, while when I set sigma a to 1mm and sigma b also to 1mm, I get sigma h values between 0.8 and 0.9.
Whats is correct?
Thanks.

Hello,

When I set sigma a to 0.1mm and sigma b to 1mm, the sigma h values for each measurement are between 0.2 and 0.4, while when I set sigma a to 1mm and sigma b also to 1mm, I get sigma h values between 0.8 and 0.9.
Whats is correct?

Your question cannot be answered in this way. It depends on your assumption and experience.
How do you evaluate the value for σb? The value may be specified by the manufacturer of the instrument, but this does not mean that you have reached this value.

Have a nice weekend
Micha