## 2 Materials and Methods
### Algorithm for Dynamic Weighting Between Estimates of Kalman Filter and GERT Model
This coefficient is transmitted to the estimation fusion subsystem, which forms the final combined estimate of the target position and motion. Figure 2 shows a functional diagram of the implementation of the dynamic weighting algorithm. It reflects the information flows between the estimation, intelligent analysis and fusion subsystem blocks. The Kalman filter and the GERT model transmit their coordinate estimates to the combination module. In parallel, the intelligent module, analyzing the system state, calculates the weighting coefficient \(\alpha(t)\), which is used to combine the results. In this figure, the Kalman Filter block generates a local estimate of the position \(\hat{x}_{KF}\) and velocity. The GERT model block provides a global predicted estimate \(\hat{x}_{GERT}\) taking into account the probabilities of the states. The intelligent adaptation module (with AI elements) analyzes the input metrics (innovations, error trends, instability) and forms the value \(\alpha(t)\), which is a weighting factor. The estimate fusion block performs the mathematical operation of combining the results in real time. The output is a current estimate of the target position, which is fed to the control system or to the operator's visualization interface. As we can see in Figure 2, \(\alpha(t)\) dependence is not fixed, as its value is determined by the intelligent module based on several criteria: current filtering errors; innovation stability; the level of probability of the loss of tracking, estimated by the GERT model; and the classified level of interference in the environment. Thus, in conditions of stable tracking with low interference, the system prefers the Kalman filter, since it provides an accurate estimate of the coordinates in real time. However, in a situation where the system switches to a mode of unstable measurements or an increased probability of loss, the coefficient \(\alpha(t)\) decreases, increasing the influence of the GERT forecast, which provides global tracking logic. Figure 2: Functional diagram of the implementation of the dynamic weighting algorithm. To calculate \(\alpha(t)\), it is proposed to use the ratio:  
\[\alpha(t)=\frac{S_{KF}(t)\cdot D_{meas}(t)}{S_{KF}(t)\cdot D_{meas}(t)+\left(1-P_{ track}^{GERT}(t)\right)}, \tag{2}\]  
where \(S_{KF}(t)\) is the stability index of the Kalman filter;  
\(D_{meas}(t)\) is the confidence coefficient for measurements;  
\(P_{track}^{GERT}(t)\) is the probability of continuing to track the target according to the GERT estimate. Formula (2) implements the principle of normalized trust distribution between local (Kalman filter, measurements) and global (GERT forecast) sources of estimation. The numerator of the formula reflects the degree of reliability of local estimates; \(S_{KF}(t)\) determines the stability of the innovation process of the Kalman filter. It is introduced to quantitatively assess confidence in the recursive estimation of the target coordinates at the current cycle. The formula is built on the basis of the relative deviation of the new signal from its average value, normalized to the innovation variance. Such a structure takes into account the degree of estimation fluctuations with a constant noise background. The construction of the expression has the nature of a coefficient of variation and was formed empirically as a mechanism for the early detection of filter instability in conditions of reduced observation quality. The measurement confidence factor \(D_{meas}(t)\) is a function of the statistical characteristics of the input signals and the innovation of the Kalman filter. In particular, it takes into account the deviations of the measured values from the predicted ones and the noise-to-signal ratio. The formula was created based on the analysis of typical situations of measurement losses or interference when measurements have low reliability. The goal is to reduce the weight of \(\alpha(t)\) in such situations, even if the Kalman filter demonstrates internal stability.