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The predicted covariance is (P_{(t)} = {FP}_{ t-1)}^F^{ t-1 W), where W is the covariance of the state transition error.
Besides, it can be discovered in [7] that there is an implicit assumption is that transmitters should know transition error probabilities.
This allows us to define the most error-prone information symbols and find the highest transition error probability p, which yields a vanishing output error probability on long codes.
Group mean transition error rates, sorted in order of increasing value, are displayed in Fig. 2B.
We then measured the transition error rates on the first three post-sleep trials but ordered them in two different ways first, by the subject's pre-sleep transition error rates, and separately, by the subject's post-sleep error rates.
The profile of pre-sleep transition error rate was monotonic (Fig. 2B, black), indicating that, in general, subjects' accuracy across the four transitions of the sequence differed substantially.
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On the other hand, if the state transition errors happen far away from the actual transition moment, the detection performance would decline by 0.75 dB.
This may be sufficient for those applications that do not need the precise breaking spots and that are tolerant to the transition errors described above.
If the measurement and state transition errors are independent, white, and Gaussian processes, the KF computes the posterior mean that is the optimal estimator in minimum mean square error sense (i.e., the KF is the exact Bayesian filter) [12].
Following Freeland & Hurst [ 2], we will use a form of the error probability matrix that makes transition errors more frequent than transversion errors and makes 2nd position errors less frequent than 1st and 3rd position errors.
It is shown that, when the state transition point error estimation gets earlier, the sensing performance will be declined by 0.61 dB compared to the ideal situation that the state transition moment has been precisely identified.
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