## 1 Introduction  
The integration of an inertial navigation system (INS) and a Global Navigation Satellite System (GNSS) is an essential technique for delivering accurate position, velocity, and attitude estimates in both civil and military navigation applications. Effective state estimators are crucial to ensuring the accuracy of these estimates, with the Extended Kalman Filter (EKF) being one of the most widely adopted methods. The EKF can be used for nonlinear systems, where the model equations are linearized locally around the current state estimate during each iteration. The EKF assumes that both process noise and measurement noise are Gaussian, with zero mean [1]. Furthermore, it assumes that the covariance matrices of the process noise \(\mathbf{Q}\) and the measurement noise \(\mathbf{R}\) are known [2]. However, in real-world systems, these conditions are not always met, especially in INS/GNSS integration scenarios, leading to potential degradation in estimation accuracy. The tuning of an EKF involves optimizing matrices \(\mathbf{Q}\) and \(\mathbf{R}\) to accurately estimate the states of a nonlinear system. This process starts with defining the initial state and covariance estimates, often based on system knowledge and initial measurements. The process noise covariance matrix \(\mathbf{Q}\) and measurement noise covariance matrix \(\mathbf{R}\) are crucial for the EKF performance and require careful tuning. These matrices are usually derived from empirical data or through iterative experimentation. Fine tuning involves adjusting \(\mathbf{Q}\) and \(\mathbf{R}\) to balance responsiveness to new measurements with stability against noisy data. Extensive simulation and field testing are typically required to ensure robustness across various operating conditions [3, 4, 5, 6]. In INS/GNSS integration, the tuning process for an EKF is iterative and time-consuming. It usually begins with a static error estimate obtained through Allan variance analysis [7; 8]. This initial estimate is often optimistic and requires extensive static data collection over many hours or even days, serving as a starting point for further adjustments. Subsequent tuning involves discrete parameter adjustments and evaluating the position drift during GNSS outages [7]. To establish the order of parameter tuning, the priority can be set by evaluating the drift caused by them during GNSS signal interruptions. These parameters need to be tested in various scenarios with variable dynamics, which is challenging without extensive field test data. Additionally, the size of the discrete steps chosen in their adjustments influences their final optimization. Consequently, the ideal parameters are rarely known, and those selected are often non-ideal [7; 9; 10]. Since the 1970s, various methods for estimating the covariance matrices \(\mathbf{Q}\) and \(\mathbf{R}\) have been proposed. [PERSON] [11; 12] was a pioneer in this field, followed by [PERSON] et al. [13] and [PERSON] [14]. Despite these initial advances, progress in tuning the covariance matrices stagnated for almost three decades. In 2006, [PERSON] et al. introduced the ALS (Autocovariance Least Squares) method for the estimation of \(\mathbf{Q}\) and \(\mathbf{R}\), with subsequent improvements presented by [PERSON] et al. [15] and [PERSON] et al. [16]. However, these methods presented limitations in Multiple-Input Multiple-Output (MIMO) systems, as demonstrated by [PERSON] [17]. In recent years, traditional methods have been refined, and new methods have been developed to improve the tuning of the Kalman filter. Allan variance, for example, has been used to characterize and model noise in inertial sensors, allowing for a better estimation of the \(\mathbf{Q}\) matrix [18; 19; 20]. Additionally, neural networks have been employed to dynamically adjust the tuning parameters of the Kalman filter, adapting to changes in system characteristics and noise in real time [21; 22; 23].