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In terms of the computational cost, the time consumed for a one-year period is shown in Table 5. Similar to the case study of the hypothetical bay experiment, the UKF approach is computed based on the sigma points. Although the Kalman gain is updated at each time step, such implementation is rapid because it is not necessary to evaluate the Jacobians required for an EKF. However, the implementation of GP would demand extra computational cost. Therefore, in the case of short time correction, the UKF can provide accurate results with less time, while the UKF-GP is more useful for the long time correction. In the two-SKF approach, the constant Kalman gain is based only on two forecast realizations and can be computed offline until it reaches a constant solution. Such steady gain application can greatly reduce the computational demands, resulting in lower computational cost compared to the UKF. In this case, since the state vector consists of small variables, their computational differences can be negligible. However, the computational load will be substantial when applied to a large-scale system where there exist thousands or even tens of thousands of states. Therefore, in terms of the computational time, using the two-SKF is more efficient for large-scale problems.

Table 5

The time consumed for the two-SKF, UKF and UKF-GP for the case of SRM

 Two-SKFUKFUKF-GP
Time (mins) 33 36 39 (UKF) + 20 (GP) 
 Two-SKFUKFUKF-GP
Time (mins) 33 36 39 (UKF) + 20 (GP) 

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