# Advanced Sensor Integration and AI Architectures for Next-Generation Traffic Navigation
## 2 Materials and Methods
### Global Route Quality Indicator Calculation  
The \(GRQ\!I_{k}\) for a specific route \(k\) is calculated using an advanced and multifaceted mathematical formula. The Equation (1) integrates five parameters: \(T\!D\!i_{k}\), \(ET_{k}\), \(T\!D\!e_{k}\), \(R\!S\!a_{k}\), and \(R\!S\!e_{k}\). The objective is to synthesize these parameters into a unique metric that ranges from 1 to 100, where 1 signifies the least favorable route, and 100 represents the most optimal one. The complexity of the formula ensures that each parameter is weighted and transformed appropriately to reflect its impact on overall route quality accurately. The \(GRQ\!I_{k}\) is proposed as a unified metric that integrates multiple parameters into a single value ranging from 1 to 100. This integration is grounded in multi-criteria decision analysis (MCDA), where each parameter is weighted based on its relative importance to balance competing objectives such as efficiency, safety, and road conditions. The \(GRQ\!I_{k}\) formula employs advanced mathematical transformations to capture the relationships between parameters. Normalization ensures that parameters with different scales contribute in proportion to their values. Nonlinear functions (e.g., logarithmic, exponential) emphasize critical factors such as delays or hazards. A sigmoid function is applied to bind the aggregated score within a user-friendly range (0-1). The value is then scaled to 1-100 for ease of interpretation. A systematic and iterative approach was employed to derive the final formula of \(GRQ\!I_{k}\). An equal-weight evaluation was initially used for each parameter, and this variant was tested on a controlled dataset. This dataset included a known correlation between inputs and outputs. The dataset included diverse scenarios, such as routes with heavy traffic, roads with significant bumps, and areas with a high frequency of traffic incidents. This initial exercise aimed to validate the basic concept of integrating multiple parameters into a single indicator. During the tests, it was observed that equal weights did not adequately reflect the relative importance of each parameter in evaluating route quality. For example, traffic  
Figure 1: GRQlk diagram. delays (\(TDe_{k}\)) and road safety (\(RSa_{k}\)) had a greater impact on user experience than total distance (\(TDi_{k}\)). As a result, the weights were adjusted through a series of iterative experiments. Thus, different combinations were tested, and the results were evaluated in comparison with human feedback and the system's performance in real-world scenarios. Subsequent adjustments included the application of mathematical transformations (such as logarithmic, exponential, and sigmoidal) to capture nonlinear relationships between parameters and route quality. These transformations were validated using the same controlled dataset. The calculated values of \(GRQI_{k}\) were compared with the qualitative scores manually assigned by experts for the same routes. The sigmoid function, for example, was introduced to normalize the scores that reflect human perception of route quality. Completing the \(GRQlk\) formula also involved consulting the specialized literature and adapting standard techniques in multi-criteria optimization and machine learning. It borrowed principles from MCDA to establish the final weights and statistical modeling to apply appropriate transformations to the raw data. The result of this iterative process is presented by Equation (1). \[GRQI_{k}=\frac{N_{k}+1.5\times\frac{RSa_{k}}{10}+1.5\times\frac{RSa_{k}}{100}} {4}\times 100, \tag{1}\]  
\[S_{k}=\frac{ET_{k}-TDe_{k}}{TDi_{k}}, \tag{2}\]  
\[N_{k}=\frac{1}{1+e^{-S_{k}}}, \tag{3}\]  
where:  
\(RSa_{k}\)--is the number of incidents normalized to 10. If the value exceeds 10, then the parameter contribution is set to 1 as the most dangerous measure;  
\(RSe_{k}\)--the number of potholes normalized to 100.