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Exact(4)
The true direction of nonlinearity is a.
We chose to use split into three components, and the direction of nonlinearity was computed using the eigendecomposition.
For F&K, [7] gives two alternatives for choosing the number of components and for computing the direction of nonlinearity.
For computing the direction of maximum nonlinearity, the sigma points (mathcal {X}_{i}) are weighted by the norm of their associated residual (||Amathcal {X}_{i} + mathbf {b} - mathcal {Y}_{i} ||) and the direction of nonlinearity is the eigenvector corresponding to the largest eigenvalue of the second moment of this set of weighted sigma points.
Similar(55)
This causes fewer problems with AS, because AS splits only in the direction of maximum nonlinearity and then re-evaluates the nonlinearity for the resulting components.
The good performances of the proposed method and AS in Figure 5 are partly due to the algorithm for estimating the direction of maximum nonlinearity, because they have clearly the most accurate nonlinearity direction estimates.
In the table, Δ θ is the average error of the direction of maximum nonlinearity.
In the paper, there are two alternatives for choosing the direction of maximum nonlinearity.
AS and BinoGMF use the same algorithm for computing the direction of maximum nonlinearity.
In [9], the splitting direction is computed by finding the direction of maximum nonlinearity of the following transformed version of criterion (15) for one-dimensional measurements: text{tr},, PHPH>{R}.
It is shown that the direction of the maximum nonlinearity is aligned with the eigenvector corresponding to the largest absolute eigenvalue of PH.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com