Since the mode of the error is still slightly negative for both components, the bias compensation can be omitted in favor of the closer error mode.
We found that the bias at low CNR values is negligible in favour of a mode of the error which is close to zero.
(a) A scatter plot of 8,000 error points and additionally the mean and mode of the error as well as the mean of the error with compensated bias (Mean cp. err).
In [141, 142], based on the ensemble empirical mode decomposition, the error measurement data in contact force are eliminated and the frequency components in contact force are extracted to evaluate the catenary dynamic state.
Further, from Figure 4a, we see that there are good reasons not even to try to compensate for the bias and use the slightly biased estimator as it is: The mode of the error, which is the peak of the histogram of the error, is slightly negative (−0.5+−0.4j), and therefore, most of the estimates of x and y will be slightly negatively biased.
(2.14) In the framework of the transmission synchronization mode, the state error can be defined as ({e_{j}}(t) = {y_{j + 1}}(t) - {y_{j}}(t)), (j = 1, ldots,N -1 ), then the definition of adaptive transmissions synchronization of N systems is obtained.
Given a positive scalar γ, the filtering error system (5) is mean-square exponentially stable with (H_{infty} ) performance γ if, for every system mode and delay mode, the filtering error system (5) with (w(t) = 0) is mean-square exponentially stable, and under zero initial condition it satisfies (Vert r(t) Vert _{2} legamma Vert w(t) Vert _{2}) for any non-zero (w(t) in L_{2}[0, + infty]).
Based on comparative analysis between numerical results and experimental results, it is shown that the added mass only considering the effect of geometric shape can agree well with the test results in low-order modes, however, the error will be increased as the order of vibration modes increasing.
Furthermore, to enable error reduction to any desired level, a convergent iterative strategy is developed, where MS-DFM is employed along with a fine-scale smoother in order to resolve low- and high-frequency modes in the error.
