## 2 Related Work  
Missing value handling is one of the most difficult problems in the field of time series data. A wide variety of approaches, from complex convolutional recurrent encoder-decoder architectures to recurrent dynamical systems, have been thoroughly explored by researchers. By studying the literature, we have examined different approaches used to fill the gaps in work related to time series datasets, exposing the advantages and disadvantages of each. Using a bidirectional recurrent dynamical system, [PERSON] et al. [11] described a technique for inferring time series data that can directly estimate the missing value. There was no significant presumption about the underlying data generation method. The majority of the other current systems, according to the paper, made significant assumptions about the data generation process. According to [PERSON] et al. [12], there was no abrupt spike in the data and the data were smoothable while generating the missing data. Therefore, smoothing the surrounding data could produce missing values. Some current methods have used interpolation to infer missing values; however, local interpolation has generated missing values without taking into account the relationship between the variables over time. The model BRITS, devised in the literature, has outperformed all baseline models in terms of mean absolute error and mean relative error. [PERSON] et al. [13] introduced a deep learning-based convolutional recurrent encoder-decoder architecture to address the GPS trajectory imputation problems. There were temporal and spatial components to GPS trajectory data. While recurrent neural networks such as LSTM were effective in predicting consecutive time series, convolutional neural networks excelled at extracting the spatial aspect from data. They were used by the suggested ConvLSTM to achieve better results in trajectory imputation tasks. The authors used GPS trajectories with transportation mode labels from the Microsoft Geolife trajectory dataset [14; 15; 16] and employed the Average Displacement Error (ADE) as an evaluation metric. \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Meaning** \\ \hline \(X(t)\) & Trajectory of a entity at time \(t\), consisting of spatial coordinates, velocity, \\ \((x(t),y(t))\) & Position of the entity at time \(t\) \\ \(v(t)\) & Velocity of the entity at time \(t\) \\ \(\theta(t)\) & Heading of the entity at time \(t\) \\ \(\mathbf{T_{complete}}\) & Complete trajectory comprising all data points \\ \(p-1\) & Number of missing points in the trajectory to be imputed \\ \(\mathbf{T_{incomplete}}\) & Incomplete trajectory with missing points \\ \(\alpha\) & Masking ratio for simulating missing data in trajectory sequences \\ \(X_{i}\) & Trajectory of the \(i\)-th example \\ \hline \(T_{i}\) & Length of the trajectory \(X_{i}\) \\ \(T_{\max}\) & Maximum length across different trajectories \\ \(M_{i}\) & Binary mask indicating observed and missing points in a trajectory \\ \(H^{\text{enc}}\) & Hidden state sequence of the LSTM encoder \\ \(H^{\text{dec}}\) & Hidden state sequence of the GRU decoder \\ \(Y\) & Input sequence for the GRU decoder \\ \(Y^{\prime}\) & Output sequence of the GRU decoder \\ \(r_{t}\) & Reset gate at time step \(t\) \\ \(z_{t}\) & Update gate at time step \(t\) \\ \(\tilde{I}_{t}\) & Candidate hidden state at time step \(t\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Glossary of symbols and their definitions. [PERSON] et al. [17] proposed a novel deep neural network approach to address the human trajectory imputation problem, which is a crucial step in the COVID-19 contact tracing process. The representation process using graph embedding was the first component of the solution, and the transformer model was the second. The formation of the human trajectory sequence occurred in a high-dimensional environment, making it difficult to extract significant information. The nodes were mapped from high-dimensional to low-dimensional vector space using the graph embedding model to remove the challenges.