## 1 Introduction
The study [21] investigates methods for estimating the inertia of power systems, a critical aspect in the era of increasing renewable energy sources. It applies swing equation polynomial approximation and RV methods to evaluate power system inertia. The research includes an analysis of frequency and RoCoF data from power disturbances in Taiwan, utilizing noise filters to enhance data accuracy. While it introduces innovative approaches relevant to modern power systems and has practical applications in improving power system stability and efficiency, it faces challenges in complexity, its reliance on high-quality data, and potential limitations in its scope. Exploring methods for wind speed forecasting, the article [22] examines the application of Empirical Mode Decomposition (EMD) along with its refined variations: Ensemble EMD (EEMD), Complete Ensemble EMD (CEEMD), and Completed Ensemble EMD with Adaptive Noise (CEEMDAN). The study found EEMD most effective in preprocessing for wind speed forecasting. The paper presented an innovative approach combining Adaptive Robust Extreme Learning Machine (ARELM) with signal decomposition algorithms like EMD, EEMD, CEEMD, and CEEMDAN, showing improved forecasting accuracy by effectively managing complex data features and outliers. However, the complexity of implementation, limitations under specific conditions, potential for overfitting, and the need for further improvement in loss functions are acknowledged as challenges. Examining advanced decomposition techniques like EMD, ensemble EMD, and variational mode decomposition (VMD) in the context of wind prediction, one study specifically looks at their utilization within extreme learning machine (ELM)-based models [23]. These techniques are primarily utilized to remove redundant noise or to amalgamate multiple models for enhanced forecasting accuracy. The use of EMD is central to the approach presented in [24], offering significant advantages due to its fully data-driven nature, which allows adaptability to different types of signals. This is crucial in handling the non-linear and non-stationary data commonly found in natural phenomena like wind speed. Moreover, EMD's proficiency in extracting features from complex data is a key factor in improving the accuracy of forecasts. EMD can suffer from mode mixing, where a single intrinsic mode function (IMF) could contain signals of widely different scales. Additionally, the subjective nature of selecting IMFs for further analysis can affect the reproducibility and consistency of the results. Despite these challenges, the study's proposed method stands out for its adaptability and efficiency in the complex task of wind speed forecasting. The paper [25] explores the use of [PERSON]'s Empirical Mode Decomposition for estimating the rate of change of frequency (\(df/dt\)) and active power imbalance in power systems. The research demonstrates that the EMD approach, along with other methods like the Discrete Wavelet Transform and the Least Squares Method, can accurately estimate CoI RoCoF. It was found that the differences in the estimation of \(df/dt\) at different buses in the power system are small enough not to limit the choice of measurement buses and signal analysis. This finding suggests the EMD method's effectiveness for power system analysis, especially in the context of non-linear and non-stationary signal processing. The research emphasizes the capabilities of the approach for supervising contemporary electrical power systems and recommends its application in creating sophisticated protection systems. Inspired by the robust adaptive EMD, this paper is designed as an approach for estimating power system inertia based on swing equation and signal decomposition algorithms. Contributions are summarized as follows:  
* This study introduces an approach for estimating CoI RoCoF in power systems. This innovative approach leverages the EMD technique, enabling a more accurate estimation of frequency change rates, which is crucial for assessing the stability and reliability of power systems.