## 1 Introduction
The correlation estimator metric is time-efficient compared to other EMTR metrics, because, in other metrics, the time-reversed transients are injected back into the same system and a large number of simulation batches are performed after the fault's occurrence, whereas, for the correlation estimator metric, the database in the form of the transfer functions of the same system is already available to correlate with the fault-generated transfer function. Furthermore, its quantitative property outperforms other EMTR metrics in terms of offering confidence in the estimated fault candidate. For the sake of brevity, the detailed explanation of the correlation estimator is not presented here and can be found in [8; 10; 20], where different aspects of its applicability were discussed. It is worth mentioning here that a new method based on time reversal, known as the FasTR algorithm, has been proposed recently to infer the fault location while employing the optimisation algorithm, which is time-efficient as well [6]. However, it relies on the measured/recorded transients of two terminal observation probes. In the existing EMTR methods, usually, the low-impedance fault scenarios are considered. In recent times, the EMTR-III method has been proposed to accurately locate high-impedance faults [21], and another EMTR-based method, which does not require knowledge of the fault impedance, has been reported [22]. However, these methods rely on the recorded transients of multiple observation points. The correlation estimator, on the other hand, relies on a single observation point. Nevertheless, in the correlation estimator method, the data preparation analysis of the fault estimation stage is of utmost importance. Some characteristics require further investigation, such as (1) the necessity of fault impedance analysis, because the fault impedance might take on any value during the fault occurrence stage; therefore, an accurate guess of the fault impedance during the fault estimation stage is crucial. (2) Only the transfer functions of the three-phase fault scenario are stored in the existing correlation estimator approach. In this manner, errors in the fault location and the fault type have been observed. (3) The spatial step considered in the fault estimation stage is an additional key aspect that requires investigation. It has been observed that, if a larger spatial step is selected, there will be an error in the fault location. The correlation estimator method identifies this inaccuracy based on its CCv, but the traditional EMTR method does not. In order to improve the correlation estimator method and make it more adaptive while tackling the aforementioned issues, three different approaches are proposed in this study. Firstly, the impact of fault impedance mismatch between the fault occurrence and fault estimation stages was analysed. It was observed that the accuracy of the method was not affected by fault locations close to the observation probes, but when the fault position moved farther away, the error in the fault estimation increased significantly. Then, a simple approach was used to address this problem by storing the transfer functions for both the low- and high-fault-impedance scenarios during the fault estimation stage. Secondly, a so-called pseudo approach was used to accurately identify the fault type and locate the fault position, in which, in the fault estimation stage, the transfer functions are stored, taking into account all possible fault types, rather than just the three-phase fault type scenario. Finally, the efficiency of the correlation estimator increased with a feasible smaller spatial step, but at the expense of higher memory space requirements for the storage devices. This is especially the case for long transmission lines that have measuring devices with larger bandwidths. This memory problem was solved by proposing a regression-analysis-based hybrid approach, in which few fault estimation stage transfer functions were selected, instead of all the data.