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The proposed modified Kalman filter framework consists of two loops: a loop to estimate the state, and a loop to estimate the disturbance generated by the modeling errors (a dual-loop Kalman filter).
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In the future work, we will improve the performance of the proposed control design by compensating the modeling errors and external disturbances.
In addition, a robust state estimator that we previously proposed is adopted to compensate for the estimation error caused by the modeling error.
The smaller eigenvalues are particularly affected by the modeling error.
This indicates that the localization errors of shallow sources are mainly influenced by the modeling error.
As mentioned before, obviously, the localization errors are also mainly determined by the modeling error for the shallow sources.
Therefore, when using high density electrode montage, the localization errors are not primarily generated by the noise but determined by the modeling error for the deep sources.
Even though each coefficient (a, b, and H) is expressed by the fifth-order polynomial functions, the modeling errors are very big and worse than those of the LSM shown in Fig. 4.
A comparison of a preliminary slip distribution result obtained by Nishimura and Yagi (2008), neglecting the modeling errors due to the Green's function uncertainty, with the result obtained in this study (Fig. 3(b)) shows that the broad pattern of two major slip areas was estimated by both methods.
The modeling errors are attenuated by a well-designed robust controller with a control accuracy measured by a design parameter.
The adequacy of these models was judged by comparing the modeling error to the known measurement error of the quality variables.
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