## 4 Results
### Correction for Unknown Parameters  
Apart from measurement correction, another important role for robust data reconciliation was to better estimate the value of the unknown parameters in the S-CO\({}_{2}\) system. For them, original error was not able to be acquired, so the comparison was simply carried out among five kinds of estimators.  
MREs of all unknown parameters in the S-CO\({}_{2}\) system under 2000 conditions were computed and are shown in Figure 15, where the performances of five estimators still followed the order mentioned above. The WLS estimator was the worst, followed by the fair and logistic robust estimators, while the Cauchy and Welsch estimators were significantly more outstanding. As the unknown parameters were inferred from the measurements, it was no wonder that such conclusions were acquired.  
Figure 14: RMSEs of each sensor with gross errors in the S-CO\({}_{2}\) system under all conditions.  
Figure 15: MREs of all unknown parameters in the S-CO\({}_{2}\) system.  
To examine the effect of robust data reconciliation on each unknown parameter, their individual results were figured out and are listed in Figure 16. For every unknown parameter studied in the S-CO\({}_{2}\) system, MREs under the five estimators were arranged in the same order, as shown in Figure 16. Such a high consistency, from a part of the system to the overall statistical results, proved that a more accurate correction of the measurements can effectively lessen the estimation error of any unknown parameters related to them, even if some of the measurement corrections are not satisfying (e.g., for Welsch estimator). In that way, for unknown parameter estimation purpose, the Welsch estimator seemed to be a more preferable choice than the Cauchy estimator, based on MRE results, which had more stable behavior in measurement correction.  
As for RMSE results, shown in Figure 17, the pattern was consistent with MRE results. The most important unknown parameter shown in Figure 17 should be RTE, where the Welsch estimator achieved the best estimation among all estimators. Therefore, in order to apply robust data reconciliation to monitor the overall performance of the system, the Welsch estimator should be applied to acquire the most precise results.  
Besides the general conclusions on the performance of the robust estimators, one can also gain insights about specific unknown parameters. The largest errors were found in two types of parameters:  
Cooling water-related: This included H13 and H14, which were the enthalpies of the inflow and outflow cooling water. Their values were decided by sensors T13 and T14, and the robust estimators failed to reduce their excessive errors under some cases, as shown in Figure 13.  
Compressor power: This included W(C1) and W(C2). Their errors may be induced by the error that happened in the corresponding mass flow sensors, mainly M3. Fortunately, the deviation for the compressor power estimation did not influence the total shaft power W, which was controlled by the high-precision measurements of generator power G.  
Figure 16: MREs of each unknown parameter in the S-CO\({}_{2}\) system under all conditions.