## 1 Introduction  
Pedestrian trajectory unpredictability has presented a formidable challenge for autonomous vehicles, necessitating sophisticated trajectory imputation techniques. The erratic and dynamic nature of pedestrians' movement makes it challenging to accurately predict their future paths. Factors such as sudden changes in direction, varying speeds, and unexpected interactions with the environment contribute to this unpredictability. Figure 1 Bearing this unpredictability in mind, autonomous vehicles have transformed transportation by utilizing state-of-the-art technologies like artificial intelligence, sensor fusion, and machine learning to navigate safely and independently. Central to their operation is the ability to efficiently plan and follow trajectories while adapting to changing environments. In this context, a trajectory refers to the path an entity takes over time, including its spatial coordinates, velocity, and orientation. Mathematically, a trajectory \(X(t)=(x(t),y(t),v(t),\theta(t))\) describes the vehicle's state in a specific coordinate system, where \((x(t),y(t))\) denotes its position, \(v(t)\) represents its velocity, and \(\theta(t)\) indicates its heading at time \(t\). Trajectory imputation is a critical aspect of motion prediction, focusing on filling in missing points within incomplete trajectories to create a comprehensive representation of an object's movement. Essentially, trajectory imputation involves using existing trajectory data to interpolate or extrapolate missing segments, compensating for factors like sensor errors, occlusions, or data loss. By integrating predictive models with historical trajectory information, trajectory imputation facilitates the reconstruction of a coherent and uninterrupted trajectory, vital for applications such as autonomous navigation and activity recognition. The primary objective of trajectory imputation is to estimate the missing points inside the incomplete trajectory to yield a complete trajectory represented as follows:  
\[\mathbf{T}_{complete}=\{(x_{1},y_{1},t_{1}),(x_{2},y_{2},t_{2})\dots(x_{n},y_{n},t_ {n})\}\]  
and  
\[\mathbf{T}_{incomplete}=\{ (x_{1},y_{1},t_{1}),(x_{2},y_{2},t_{2})\dots\] \[(x_{n-m-1},y_{n-m-1},t_{n-m-1}),\] \[(x_{n-m},y_{n-m},t_{n-m}),\] \[(x_{n-m+p},y_{n-m+p},t_{n-m+p})\dots\] \[(x_{n},y_{n},t_{n})\}\]  
where \(p-1\) represents the number of missing points to be imputed, n denotes the total points of a complete trajectory, and m is a variable providing the continuity of sequential points. Since the early days of trajectory imputation, several techniques have been employed, each with its advantages and limitations. These techniques include Kalman filtering [1], which is widely used for state estimation and trajectory prediction in autonomous vehicles. It provides a recursive solution for predicting the phase of a dynamic system dependent on noisy sensor measurements. Kalman filters are particularly effective in scenarios with linear dynamics and Gaussian noise distributions. Particle filters, also known as Monte Carlo localization [2], are probabilistic algorithms used for non-linear and non-Gaussian state estimation. They represent the posterior distribution of the vehicle's state using a set of weighted particles. These particles are sampled and propagated based on motion models and sensor measurements. Bayesian inference provides a principled framework for updating beliefs about the vehicle's state based on observed data and prior knowledge. It  
Figure 1: Humans are unpredictable, a critical security concern for autonomous vehicles. Image courtesy of coursera.org accessed on 25 June 2024.  
allows for the incorporation of uncertainty into trajectory prediction and facilitates decision making under uncertainty. In recent times, machine learning methodologies, like support vector machines [3], neural networks, and Gaussian processes, have been increasingly employed for trajectory imputation in autonomous vehicles.