Concept of model validation and outlier detection in JAG3D (Software)

E_merlet, Mittwoch, 12. April 2017, 18:27 (vor 14 Tagen) @ Micha

To preform an outlier test, you extend (at least one equation of) the functional model e.g. δhik

\delta h_{i,k} = (H_k - H_i) + \nabla_{i,k}

Ok, and do I have to extend the model with \nabla by myself or does the software do it by itself?

For ∇ = 0 the extension is unneeded because there is no benefit to estimate this additional parameter. If ∇ ≠ 0, the extended functional model improves your solution or is more suitable. In this case, we assume that the observation, which is related to the modified equation, is an outlier.
It will be an exception that ends up to zero, if no outlier is presented. In general, ∇ ≈ 0 and a stochastic test is used for the decision.

So, it means there is always an error, for every observation. The stochastic test tells us if the error is too big and has to be corrected or not. Right?
∇ ≠ 0 means the observation is an outlier. Does it not mean it has to be removed instead of being improved?

B is a design matrix, which contains the partial deviation w.r.t. the unknown parameter ∇. In the example above, B is just a vector with zeros, that contains a one at the row that corresponds to the observation δhik

So, B is like the jacobian matrix A but with the parameter \nabla in the partial deviation.

And what is E in EPi = (E-Ri)Bi\nabla i in the section Influence on the position of a point?


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