## 2 Related Work
### Data-Driven Approach  
The data-driven TSE approach, on the other hand, makes an estimate based on the data itself fusing machine learning and statistical methods. The study by [PERSON] et al., 2003 uses historical data and compares statistical methods using a data augmentation [14]. Based on information from spatial neighbor detectors, [PERSON] et al., 2003 developed a linear regression model [15], and [PERSON] et al., 2004 presented an autoregressive integrated moving average (ARIMA), based on time series data [16]. As a means to improve estimation accuracy and robustness, [PERSON] and [PERSON] (2005) proposed Bayesian networks (BN) integrated into time series models [17]. [PERSON] et al., 2014 developed a method to consider the traffic flow capacity as well as the temporal correlation based on robust principal component analysis (RPCA) [18]. Moreover, spatiotemporal information has been incorporated into tensor-based methods by utilizing Tucker decomposition [19]. As described in [PERSON] and [PERSON] 2017, they used the Bayesian particle filter (BPF) to estimate traffic states for three different regimes: free-flowing, breakdown, and recovery [20].  
[PERSON] and [PERSON] (2022) presented a new reinforced dynamic graph convolutional network model in [21] to simultaneously impute data as well as predict traffic flow at the network-wide level. To enhance the robustness of network-wide traffic flow prediction, they used a multigraph convolutional fusion network for data imputation [21]. To represent dynamic spatiotemporal dependencies between the stations, a dynamic graph learning method using deep reinforcement learning was developed to adaptably generate a graph adjacency matrix based on a dynamic graph learning approach. To impute missing traffic state data, [PERSON] et al., 2022 presented a Graph Aggregate Generative Adversarial Network (GA-GAN), consisting of graph sample and aggregate data (GraphSAGE) and a generative adversarial network (GAN) [22]. Using GAN, they generated complete traffic state data from the extracted temporal-spatial information. By capturing spatiotemporal dependencies among nodes in the graph, [PERSON] and [PERSON] (2022) presented a novel graph-attention LSTM structure to solve the traffic flow prediction problem by exploiting the strength of graph-attention for non-Euclidean structured data modeling as well as the strength of LSTM cells for time series modeling [23]. In order to accurately estimate space-time traffic speeds, [PERSON] et al. (2022) trained deep convolutional neural networks (DCNNs) and exhaustively analyzed unseen complex congestion scenarios [24]. The graph convolutional bidirectional recurrent neural network (GCBRNN) is a state-of-the-art spatiotemporal deep learning architecture that integrates network-scale data imputation and traffic prediction [25]. To capture spatial and temporal dependencies in traffic data, [PERSON] et al. (2021) further developed a graph convolutional gated recurrent unit (NGC-GRU) within the GCBRNN. In addition, studies focused on the use of convolutional autoencoders to encode and decode spatial-temporal features to reconstruct traffic state [26; 27]. In order to overcome the shortcomings of graph neural networks, [PERSON] at al., 2022 developed a deep learning framework called memory-augmented dynamic graph convolution networks (MDGCN) for imputed traffic data, utilizing an external memory network to store and share global spatial and temporal information across the traffic network, as well as a graph structure estimation technique for learning dynamic spatial dependencies directly from traffic [28].  
In addition, some other approaches are also available in the literature, however, the research on hybrid TSE methods is lacking.