## 7 Conclusions  
In this research, we designed a novel deep learning model for imputing missing trajectory data for autonomous cars. Trajectory data are vital for the planning, navigation, and safety of autonomous cars, but they can be damaged or lost due to many circumstances, such as sensor failures, occlusions, noise, etc. Existing methods for trajectory imputation are either too straightforward, such as linear interpolation, or too complicated, such as generative adversarial networks. We have proposed a hybrid model that incorporates LSTM and GRU to capture the temporal, spatial, and contextual characteristics of the trajectory data. Our model can handle different sorts of missing patterns and impute trajectories with excellent accuracy and efficiency. Long-short-term memory (LSTM) networks are renowned for their ability to retain long-term dependencies in sequential data. By employing an LSTM encoder,  
Figure 11: Quantile loss variation across validation epochs: tracking the model’s performance. \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **L1 Loss** \\ \hline Two-block RNN [19] & 0.363 \\ BRITS [11] & 0.312 \\ GRU based encoder–decoder & 0.306 \\
**LSTM-GRU encoder–decoder (ours)** & **0.2264** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Models and their corresponding L1 loss. our model can effectively capture the temporal dynamics of trajectories. This means it can discern patterns and trends over extended periods, crucial for understanding how trajectories evolve over time. On the decoding side, using a Gated Recurrent Unit (GRU) architecture brings its own advantages. GRUs are computationally efficient and can learn to adaptively update information in the decoding process. This helps in generating accurate predictions or reconstructions of trajectories while maintaining a balance between complexity and performance. By fusing LSTM and GRU components, our model benefits from the strengths of both architectures. LSTM excels at retaining long-range dependencies, which is crucial for understanding complex trajectory patterns. On the other hand, GRU offers computational efficiency and simpler gating mechanisms, making it well suited for decoding tasks. This hybrid approach leverages the best of both worlds to enhance the overall performance and flexibility of the model. The insights gained from trajectory analysis could be crucial for optimizing drone delivery routes in urban environments, where efficiency and safety are paramount. By leveraging trajectory analysis, logistics companies can minimize delivery times and maximize resource utilization, ultimately improving customer satisfaction and operational efficiency. In future research endeavors, an intriguing avenue for enhancement involves experimenting with transformer models in the context of trajectory imputation for autonomous cars. Another limitation, which we have already mentioned in our study, is that it solely relies on the drone dataset, which is comparatively superior to other datasets in many arenas. But many studies have been carried out with the GPS and BLE datasets, which are no less important. Our model should be utilized on these datasets as a future path of exploration and experimentation. Also, we can experiment by adding different types of embeddings, like positional embedding or graph embedding with an attention mechanism, to our proposed architecture, and anticipate better outcomes in these cases. Conceptualization, D.K.B. and M.H. ; methodology, D.K.B., M.H. and S.S.; software, S.S.; validation, D.K.B., M.H. and S.S.; formal analysis, D.K.B. ; investigation, D.K.B. ; resources, S.S; data curation, D.K.B, M.H. and S.S; writing--original draft preparation, M.H. and D.K.B. ; writing--review and editing, M.H. and D.K.B. ; visualization, S.S.; supervision, M.M.L; project administration, M.M.I. ; funding acquisition, M.M.I. All authors have read and agreed to the published version of the manuscript.