## 1 Introduction  
As a new type of energy medium, supercritical carbon dioxide (S-CO\({}_{2}\)) has gained the prevailing interests of researchers. It has excellent fluidity and thermal conductivity [1], and it is easy to produce and use due to its relatively low critical parameters [2]. Researchers have regarded it as an ideal working fluid for thermodynamic cycles, especially suitable for Brayton cycles. Currently, various thermodynamic cycle designs using S-CO\({}_{2}\) as the working fluid have been proposed by the academic community and applied to nuclear power systems [3], solar power systems [4], gas turbine systems [5], and energy storage systems [6]. Among the common S-CO\({}_{2}\) thermodynamic cycle designs, the recompression cycle has a higher thermal efficiency and is widely used as the subject of various theoretical and applied studies. For example, [PERSON] and [PERSON] [4] designed multiple S-CO\({}_{2}\) thermodynamic cycles for solar systems, and the recompression cycle gained the highest round-trip thermal efficiency (RTE) of 52%. [PERSON] et al. [7] demonstrated that an S-CO\({}_{2}\) recompression cycle with both inter-cooling and reheating structures can achieve a maximum RTE of 60%, proving the superiority of the recompression design. [PERSON] and [PERSON] [8] came up with an optimization analysis on the supercritical carbon dioxide recompression cycle, which focused on the effect of the pressure ratio on the thermal efficiency and energetic efficiency of the system. Similarly, [PERSON] et al. [9] carried out the optimization of a S-CO\({}_{2}\) recompression Brayton cycle as well, though they were more concerned about the condensation margin for the system in order to apply the S-CO\({}_{2}\) cycle in shipboard usage. [PERSON] et al. [10] carried out a comparative study on the control strategies of a supercritical carbon dioxide recompression Brayton cycle, which aimed for actual usage in GEN-IV nuclear reactors. Apart from the classical optimal analysis, [PERSON] et al. [11] applied deep neural network and data mining techniques in the S-CO\({}_{2}\) recompression cycle to achieve higher efficiency, which resulted in a high-efficiency and compact design of S-CO\({}_{2}\) systems for shipboard usage. As summarized by [PERSON] and [PERSON] [12], recompression design (with flow diving) offered better results for S-CO\({}_{2}\) Brayton cycles. Existing research mainly focuses on the thermodynamic design and optimization of S-CO\({}_{2}\) thermal systems, which are mostly confined to the design stage. As for a constructed S-CO\({}_{2}\) power plant, however, it would be more crucial to capture its actual operation status, with various measurement sensors deployed around the system. Due to precision limitations, errors always exist in the measurement results. When the error of measurements exceeds the normal range, evaluation of the system would be unreliable. To overcome the problem, it is necessary to utilize the data reconciliation method in S-CO\({}_{2}\) systems. It is a technique for measurement correction in the real-world industrial system, based on the physical model of systems and statistical principles. It was introduced by [PERSON] and [PERSON] [13] in 1961 for data correction in chemical engineering control systems, and later, it was accepted in various industrial sectors, including the chemical industry [14], mining industry [15], and energy industry [16]. Specific to the energy and power engineering sector, several studies have been carried out to apply data reconciliation to various types of systems. [PERSON] [17] implemented data reconciliation in nuclear power plants for power recapture and power uprate for the reactors, based on VDI 2048 [18], a technical standard on data reconciliation proposed by the Association of German Engineers (VDI). [PERSON] et al. [19] developed a data reconciliation framework for a double reheat power plant, significantly reducing the uncertainty of mass flow measurements and the calculation result of the heat rate.