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It is shown that the resulting mixture converges weakly to the prior component.
So far, we have discussed the update of a prior component with a measurement at a single time step.
The mean is preserved by choosing μ in (21b) to be the mean of the prior component.
In splitting a prior component, the parameters are chosen such that the mean and covariance are preserved.
This work also advances prior component and transfer path type studies by providing an improved multi-degree of freedom system perspective.
The BinoGM is based on splitting a normal distributed prior component into smaller ones using weights and transformed locations from the binomial distribution.
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In the particular case of Madrid there are no previous studies calculating prior components, so they were all unknown.
Finally, parameter values from Table 1 were introduced as new prior components to design the definitive survey.
In this section, we present BinoGMF, which uses BinoGM for splitting prior components when nonlinear measurements occur.
Gaussian mixture filters (GMFs) work in such a manner that the prior components are split, if necessary, into smaller components to reduce the linearization error within a component.
The splitting direction is chosen to be the eigenvector of the prior covariance closest to this direction, and the prior components are split into two or three components that preserve the mean and covariance of the original component.
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