December 1, 2023

Each year, connected and autonomous driving [ 1], as well as self-driving robotic taxis, become more common. In [ 2] is a survey of common autonomous driving practices. References [ 34, and 5] review motion planning, motion planning, and control methods used for autonomous driving. Reference [ 6] deals with maneuver-based trajectory plans for highly automated vehicles. Reference [ 7] provides a survey of deep-learning applications for autonomous driving. Reference [ 8] examines automated driving in unreliable environments. Reference [ 9] is devoted to empirical decision-making for autonomous vehicles. Reference [ 10] is focused on the real-time nature in which their motion planning occurs for autonomous driving within urban environments. In the references cited above, autonomous driving systems, feedback control loops, and decision-making systems depend on information collection, vehicle motions, and knowledge. This includes the ego vehicle as well as other vehicles nearby. This information allows autonomous vehicles to estimate future positions and behaviors of other vehicles in order to determine how they should behave within their current traffic situation.

The sensor suite used by on-road autonomous cars includes GPS (Global Positioning System), IMUs (Inertial Measurement units), lidars, cameras, and radars. The ego vehicle is able to measure its current state using the GPS and IMU information. This includes its global position, heading angle, linear velocity, angular speed, and acceleration. The ego vehicle can compute and estimate its current state and future trajectory using the data collected by these sensors. The case for other vehicles is different from the ego vehicle. Due to the following factors, estimating real object states and predicting the future trajectory of other road users may be a challenging task. Perception sensors like lidar, cameras, and radar indeed provide information on position and velocity. Still, unlike ego vehicles with an onboard IMU system, it’s difficult to determine angular acceleration and velocity based solely on the observations of these sensors. Sensor-based detections are also not precise in autonomous vehicles. Data collection on other road users, objects, and traffic is noisy and leads to sensor errors. Moreover, not all states of other vehicles are observed and measured.

The motion of road users, particularly in urban traffic, is not known. In urban environments, traffic can be complex, which means that the speed, acceleration, and heading angle of vehicles can suddenly change. In urban scenarios, road users must be alerted immediately when an unexpected event occurs. This is especially true when traffic density is high. Vehicle estimation and future state predictions have been a research problem of focus for many years, and several solutions have been suggested. Estimation is useful for predicting future vehicle behavior and for obtaining information about nearby vehicles, particularly for states that are not directly measured. We call these internal states. There are several methods for determining the internal states based on the measured vehicle trajectory. By assuming that the vehicle tires are in pure rolling contact with the road, the authors of [ 11] calculated lateral velocity based on longitudinal velocity and steering angles using the single-track or bicycle model. The authors of [ 12] compared motion models and used Kalman filtering to generate an estimated trajectory. This was done in order to demonstrate the accuracy of the motion models when describing vehicle movement while eliminating sensor noise. The reference [ 12] is a useful tool for choosing the best motion model that describes vehicle motions in different road conditions.

In [ 13], Real Time Kinematics (RTK) based GPS correlation for vehicle position data is used to estimate vehicle internal states, which increases the precision of collected information. Image-based trajectory predictions are also gaining popularity with the rapid development of artificial intelligence methods and neural networks. A graph-LSTM-based trajectory-prediction method is presented in [ 14] by using a series of images and a weighted geometric graph to represent the distance between road agents. A spatio-temporal convolutional graph neural network for predicting road users’ safety is presented in [ 15]. Other neural network-based prediction methods utilizing LSTM and Recurrent Neural Networks are [ 16]. Kalman filter-based estimation of state and change point detection-based policy is introduced. The combined method of vehicle trajectory prediction will help the ego vehicle make better decisions at the round intersection. We assume, without losing generality, that other road users are also vehicles that the ego car encounters. This paper does not consider vulnerable road users like bicyclists or pedestrians. This paper presents a Bayesian policy prediction method based on change point detection. Here, a change point detection method that was previously used is modified by Kalman filter state estimation to generate a clean vehicle history and assist in behavior prediction. The likelihood value is computed using a new method. This modified method predicts future dynamic behavior using vehicle hidden states estimated with the Kalman filter. The vehicle motion model is used to predict vehicle behavior in the future. This combined method helps in making decisions. In Section 2, state estimation using the unscented Kalman Filter is presented. For the simulation experiments in Section 2, the microscopic traffic sim SUMO was used to create realistic traffic at the round intersection. Section 4 introduces a change point detection-based approach to driving behavior prediction. This is evaluated using the round intersection as an example. Section 5 combines methods from section 2section 3, and section 4 to estimate vehicle trajectory based on UKF. The last section of the paper concludes with the usual conclusions.

Kalman Filter State Estimation

Onboard sensors, such as GPS or IMU, can provide information about the position, motion, velocity, acceleration, and angular speed. In the event that we don’t have information on vehicle motion or measurements, it is essential to have an estimation tool to calculate and estimate the internal states. Our sensors cannot access this data. In these cases, the Kalman filter is an effective and widely used estimation algorithm. The Kalman filter’s central idea and operation is to propagate the Gaussian random variables through the dynamic system model. 17 ]. The original Kalman Filter can be used to solve the problem when the dynamic equations of the system are linear. The vehicle models, however, are nonlinear. Therefore, the original Kalman Filter is not suitable to solve the problem of trajectory tracking and motion estimation. For the nonlinear cases, several Kalman filter variations have been proposed. The extended Kalman Filter (EKF), for example, is one of the suggested variations. 18 The unscented Kalman Filter (UKF) 19 ]. The EKF approximates states by using Gaussian random variable and introduces first-order linearization to the system dynamics of the nonlinear systems. The UKF handles nonlinearity using sampling points called sigma-points that capture the true mean and covariance for the Gaussian random variable that describes the states and propagation of the nonlinear function. Both Kalman filters work well in the nonlinear situation. The EKF is a better option; however, as it was discussed in 19 [], it has some disadvantages. When the linearized equation propagates the Gaussian random variable, the first-order linearization can introduce large errors in the posterior mean and the covariance. In addition to this linearization error, estimations based on EKF can also be suboptimal and may not always converge. In the UKF, however, the propagation of sample points through dynamic equations will not introduce additional errors. In the UKF, the unscented transform will still capture the posterior mean and covariance. It outperforms EKF, and this paper implements it to estimate the internal states of vehicles based on observable measurements.

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