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

Micha ⌂, Bad Vilbel, Mittwoch, 12. April 2017, 17:42 (vor 14 Tagen) @ E_merlet
bearbeitet von loesler, Mittwoch, 12. April 2017, 18:20

Hi Etienne,

I wondered what is the design matrix B and what is the model failure ∇. What does it look like?

The parameters in vector contains additional parameters that are introduced to the functional model. Sometimes, these parameters are called "estimated gross errors". A simple example may be a levelling network. In this case, the functional model reads

\delta h_{i,j} = H_j - H_i
\delta h_{i,k} = H_k - H_i
\delta h_{i,l} = H_l - H_i
\delta h_{j,l} = H_l - H_j
...

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}

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.

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

B^T = 
 \begin{bmatrix}
0 & \cdots & 0 & 1_{\delta h_{i,k}} & 0 & \cdots & 0
\end{bmatrix}

kind regards
Micha

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Tags:
Modelstörung, Outlier, Matrix, Stochastic test


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