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A sufficient condition for almost-sure asymptotic stability is derived and numerical results are presented for the cases of Gaussian noise and periodic noise coefficient.
The experimental method used the "cavitation noise coefficient" defined as the sum of the energy at different scales (or levels) in the wavelet transform of the measured signal containing the subharmonic and harmonics of the fundamental frequency.
Finally, the result is asymptotically valid only if the noise coefficient, α, is small.
To test whether a given X is a noise coefficient or not, we test its significance by binary hypothesis test: H 0 is the hypothesis that X is a noise coefficient, and H 1 is a significant one.
The window size centered at a wavelet coefficient is 21×21, and the threshold T α for classifying a noise coefficient is set as 0.3.
where represents the channel vector of the th user, is the vector containing the transmit antenna symbols, and is the independent complex circularly symmetric additive Gaussian noise coefficient.
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Table 2 Stochastic noise coefficients before and after Kalman filtering Noise coefficient Before filtering After filtering Q 1.50e-3 1.01e-5 1.01e-5-5 1.26e-6 B 4.74e-4 4.74e-4 K 7.5.66e-5.89e-4 R 4.31e-2 5.10e-3 Fig. 5 Total variance analysis before and after Kalman filter.
Finally, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients to illustrate the performance of the theoretical results.
To illustrate the performance of the theoretical results, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients.
In order to illustrate the dynamic difference between the deterministic system and the stochastic system, there have been given a series of numerical simulations by using different noise disturbance coefficients.
Analytical moment solutions are obtained for white noise coefficients while hybrid computer simulation was used for correlated stochastic coefficients.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com