## 4 Results and Discussion
### Localization Results Using a Combined Dictionary  
This subsection presents the localization results of our proposed methodology using a combined dictionary approach, effectively leveraging multiple static landmarks for robust AV localization. The combined dictionary enhances the filter's predictive capability under varying environmental scenarios such as simultaneous multi-track observations, periods without sensor inputs (no-observation intervals), and isolated single-track updates. Figure 13 presents a direct comparison between the predicted ego vehicle trajectory (red dashed line) and the ground truth (solid blue line). It demonstrates that the combined dictionary approach significantly reduces localization drift, particularly in comparison to periods without observations. Furthermore, Figure 14 illustrates the predicted ego states under multiple interaction scenarios, depicted in different colors to clearly differentiate state transitions. The consistency between predicted and actual trajectories validates the robustness of using a combined dictionary in complex scenarios. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Metric** & **iCAB** & **KITTI** \\ \hline Accuracy & 87\% & 82\% \\ Precision & 88\% & 80\% \\ Recall & 94\% & 89\% \\ F1 Score & 91\% & 85\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance metrics of the classification module on iCAB and KITTI datasets. Figure 12: Confusion matrix for classification. The corresponding transition matrix in Figure 15 highlights minimal off-diagonal components, signifying accurate and stable state transitions. This observation suggests that the combined dictionary is accurately capturing the relationships and maintaining consistency across multiple landmark interactions, thereby ensuring stable localization results. To provide deeper insights into localization performance, we analyzed two types of anomalies: continuous-level anomalies (CLA) and discrete-level anomalies (KLDA). In our context, continuous-level anomalies (CLA) measure the difference between the MJPF's predicted continuous states (e.g., positions of the ego vehicle derived from the combined dictionary) and the actual LiDAR measurements. Figure 16 displays the continuous-level anomalies across the test duration (41.5 s). Initially (0-2 s), a high anomaly peak exceeding 2.0 is observed due to insufficient initialization data, causing early filter misalignment. However, the anomaly reduces significantly as more measurements are integrated, indicating effective state correction by the MJPF. Notably, at approximately 15 s (frame 150), a significant spike occurs due to the ego vehicle initiating a complex  
Figure 14: Localization result of showing various scenarios in different colors. Figure 13: Localization result of comparing the predicted ego vehicle trajectory (red) with the ground truth (blue). overtaking maneuver, causing a large deviation between predicted and observed states. Subsequent spikes around 28 s and 33 s similarly indicate transitions from periods without observations to sudden reintroduction of sensor data, resulting in abrupt corrections of the filter's predictions. Discrete-level anomalies (KLDA) represent discrepancies at a higher level, specifically in the discrete state assignments or \"cluster labels\". As the MJPF uses predefined cluster assignments from the combined dictionary, KLDA measures the divergence between predicted discrete states (clusters) and observed track distributions. Figure 17 illustrates these discrete anomalies. Initially, discrete anomalies remain low (0-14 s), indicating consistent alignment between predicted and observed clusters. However, during dynamic interactions (especially the critical overtaking maneuver at 15 s), significant discrete anomalies emerge due to abrupt mismatches in cluster assignments. Subsequent spikes at 28 s and 33 s coincide again with intervals of no observations, reinforcing how intermittent sensor data availability significantly impacts discrete-state estimation consistency.