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is I believe explained in the first complete paragraph in the second page (page number 1645) of Dietrich and Newsam 1995
Second, in practice, measurements z₂* of Z on Ω are likely to be noisy. This is usually modelled by assuming that [z₂*]ₖ = Z(xₖ, yₖ) + εₖ, where the errors εₖ, are zero mean Gaussian random variables which may be correlated among themselves with correlation matrix Σ, but are independent of the vectors z₁ and z₂. This extension can be easily accommodated in the results presented above by simply replacing the matrix R₂₂ in (3) and subsequent equations by R̅₂₂ = R₂₂ + Σ.
In our case we are assuming Σ = σ²I (that is the observation errors / noise variables are independent zero-mean Gaussian random variables with standard deviation σ) so R̅₂₂ = R₂₂ + σ²I.
If that answers the question I can create a PR to update the comment to summarize the above.
The text was updated successfully, but these errors were encountered:
The answer to the question in
ParticleDA.jl/src/OptimalFilter.jl
Lines 114 to 122 in c278bbc
is I believe explained in the first complete paragraph in the second page (page number 1645) of Dietrich and Newsam 1995
In our case we are assuming Σ = σ²I (that is the observation errors / noise variables are independent zero-mean Gaussian random variables with standard deviation σ) so R̅₂₂ = R₂₂ + σ²I.
If that answers the question I can create a PR to update the comment to summarize the above.
The text was updated successfully, but these errors were encountered: