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A trajectory of (33) is simulated and a KF is used to compute the optimal variances P k|k.
The authors in [2] exploited the relationship between linear diffusion and Gaussian scale space to estimate optimal variances and window size of the Gaussian.
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We found that performance gain and information transmission can be maximized by input signals with optimal variance.
The results are used to derive the optimal variance of the best linear estimator in the continuous time model and to construct efficient estimators and corresponding optimal designs for finite samples.
No further investigation concerning optimal variance partition between spatial trend-function and random plot effects was made at this point.
This is a three-dimensional mean-variance frontier as the optimal variance now depends on the choice of both a deterministic drift m and a random drift d.
Therefore, the optimal variance window size for noise-dominated profiles should be as large as possible so as to diminish the effect of the noise spikes.
Thus, for the target profile, the optimal variance window size is expected to be less than or equal to the sub-profile length.
The optimal variance window for the overall algorithm's performance is the one offering the best compromise between the need to enhance the target profile score (i.e., as short as possible) and the need to suppress the short-term noise fluctuations (i.e., as long as possible).
Local estimates [ 14- 16] of the mean-variance relationship are likely best, but further research is needed to understand the optimal variance estimation strategy.
The method combines grid search with the Newton Raphson algorithm and can be applied, in order to find the optimal variance components.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com