## 3 Proposed Methodology
### Trust Value Computation  
The dependability of surrounding mobiles is determined by the extended osprey-assisted optimized link state routing protocol (EO_OLSRP), using the transmitted topology control (TC) and HELLO messages. A mobile may be chosen in a packet transmission when the trust rate is at least equal to the specified trust criteria. The collection of neighbors can be changed to include the number of messages every neighbor has sent in addition to neighbor identifiers in order to account for the newly added modules. Every time a TC and HELLO message is established, these variables are modified. The trust-based optimal routing also identifies trustworthiness in a node \(n\) controlled by a separate node \(y\) as a probability of performing a specific action expected \(y\), which is represented as \(T_{y}(n)\). Then, \(y\) may evaluate trustworthiness as a result of knowledge collected during a certain operation phase by applying a weighted average of the trust with every type of action, such as route reply, route error, route request, and data transmission. During a period, message transmissions through \(n\), in which \(p_{c}^{\prime}s\) are confirmed to be valid, the total quantity of attempts transmission is \(p_{a}\), and the total number of accurate transmissions as \(p_{s}\), is estimated by:  
\[T_{y}(n)=\frac{p_{c}+\varepsilon p_{s}}{p_{t}+\varepsilon p_{a}} \tag{11}\]  
where \(0<\varepsilon<1\) indicates the weighting factor representing a ratio of effective transmissions that shows a high probability that the transmission link can operate properly. In this case, a mathematical framework similar to that used to measure link quality is employed, which differs from the trust-level analysis. Equation (11), in addition to evaluating trustworthiness, also partially demonstrates connection quality. Other more complex measurements that describe link quality, including the collision monitoring and signal separation approach, as well as the link adjustment and power control method, may also be employed  
Figure 8: BI-GRU network.  
to produce a more precise trustworthiness rating. \(T_{x}(n;j)\) represents the trustworthiness of node \(n\) as provided by node \(y\) through the \(j^{th}\) trustworthiness update cycle. When new data arrives, the node maintains its archive and computes a trustworthiness score utilizing a weighted mean or shifting average model. Consider that the measurement of \(T_{x}(n;j)\) for the \(j^{th}\) trustworthiness update phase is designated as \(\widetilde{T}_{x}(n;j)\), which is determined by assessing \(n\)'s current behavior while \(y\) examines the correctness and authenticity of the messages that arrive. In the \((j+1)^{th}\) trustworthiness update phase, generate a number of the trustworthiness, that is indicated as \(\hat{T}_{x}(n;j)\). The moving average approach is used to generate a smooth valuation in Equation (12),  
\[\hat{T}_{y}(n;j+1)=\alpha\hat{T}_{y}(n;j)+(1-\alpha)\widetilde{T}_{y}(n;j), \quad\text{ for }n\in N_{1}(y) \tag{12}\]  
where \(0<\alpha<1\) represents a weighting factor utilized to balance the current measurement data and the previous estimation. Assume the path \(k\epsilon K_{s\to y}\), in which \(K_{s\to y}\) is a collection of pathways that begins at a source node \(s\) and ends at a destination node \(y\), for instance \(K_{s\to y}=\{\text{{all paths from $s$ to $y$}}\}\). Then, \(T_{x}(k;j)\) denotes the trustworthiness of the path specified by the node \(y\). As a result, the path's trustworthiness is described as  
\[T_{y}(p;j)=\prod_{n\in k}T_{y}(n;j) \tag{13}\]  
As a result, \(y\) can increase its reputation on a path depending on the trustworthiness of its nearby nodes. The connections in Equation (13) can be utilized as a measurement of routing by a node to determine routing decisions.