## 3 Proposed Solution
### Producer Location Prediction
Consequently, the measurement matrix \(H_{t}\) is a \(3\times 6\) matrix that maps the state vector \(X_{t}\) to a 3-dimensional measurement vector \(Z_{t}\). It is typically defined as follows: \[H_{t}= \begin{bmatrix}1&0&0&0&0\\ 0&1&0&0&0\\ 0&0&1&0&0\end{bmatrix} \] 4. The initial covariance matrix \(P_{0}\) The initial covariance matrix \(P_{0}\) is a critical component of the KF, it represents the uncertainty in the initial state estimate. In the context of our case, where the initial state estimate is acquired from GPS and IMU sensors with high accuracy, the diagonal elements of \(P_{0}\) are usually assigned small values, indicative of a high level of confidence in these estimates. Simultaneously, the off-diagonal elements are set to zero, assuming that the initial errors in different state variables are uncorrelated. The initial values for \(P_{0}\) matrices are defined as follows: \[P_{0}= \begin{bmatrix}0.01&0&0&0&0&0\\ 0&0.01&0&0&0&0\\ 0&0&0.01&0&0&0\\ 0&0&0&0&0.01&0\\ 0&0&0&0&0&0.01\end{bmatrix} \] 5. The initial values for the process noise covariance \(Q\) and the measurement noise covariance \(R\) matrices are determined as follows: \[Q= \begin{bmatrix}0.001&0&0&0&0&0\\ 0&0.001&0&0&0&0\\ 0&0&0&0.001&0&0\\ 0&0&0&0&0.001&0\\ 0&0&0&0&0&0.001\end{bmatrix} \quad R= \begin{bmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{bmatrix} \]UAV Mobility Model  
The movement of UAVs differs significantly from that of common mobile vehicles, owing to their exposure to diverse external factors, including wind speed, turbulence, and environmental conditions. To accurately represent real-world UAV movements, the mobility model must reasonably emulate UAV movement. For that purpose, we propose to use the Gauss-Markov (GM) mobility model [40] as it closely emulates the uncertain and dynamic nature of real-world UAV movements by introducing randomness into the UAV's motion. In the GM mobility model, the UAV's velocity and direction are updated at fixed intervals of time based on their previous values using Gaussian Equation (3). The model employs average velocity, direction, and Gaussian random noise to introduce randomness and emulate the uncertain nature of UAV motion. The degree of dependency on past velocity and direction is controlled by a tuning parameter \(\alpha\), which affects the persistence and smoothness of the UAV's trajectory. A higher value of \(\alpha\) indicates a stronger dependence on past values, leading to more persistent movement patterns, while a lower value results in a more dynamic and rapidly changing trajectory. In the GM mobility model, the cycle of updates for the UAV's velocity and direction is repeated throughout the simulation. The new values for these parameters are calculated as follows:  
\[ \begin{cases}V_{n}=\alpha V_{n-1}+(1+\alpha)\overline{V}+\sqrt{(1-\alpha^{2})} \end{cases} *V_{x_{n}-1} \tag{3}\]  
where \(\alpha\) is the tuning parameter, \(\overline{V}\) and \(\overline{d}\) are the mean of velocity and direction, while \(V_{x_{n}-1}\) and \(d_{x_{n}-1}\) are random variables from a Gaussian distribution that give some randomness to the new velocity and direction parameters. The parameters of the Gauss-Markov model for our scenarios are listed in Table 2.