In automated driving, the states of the target vehicle which could be used to characterize the vehicle behaviours are usually required for the host vehicle control. However, some key states of target vehicle are difficult to measure directly and accurately in all driving situations. In addition to this, it is hard to get the accurate parameters of the target vehicle to establish vehicle dynamics-based method which is commonly adopted to estimate the vehicle state. To address these problems, this paper investigated a novel methodology for estimating the states of target vehicle using the information gathered by several host vehicle sensors such as the camera, light detection and ranging (LiDAR) and the radar. A vehicle kinematic model based on Serret-Frenet equation was constructed, which could be used to interpret the target vehicle lateral motion. An improved neural network-based observer which used the Bayesian regularization backpropagation as training algorithm to improve the generalization qualities was modelled to estimate the target vehicle lateral speed, yaw rate and sideslip angle based on vehicle kinematics and road constraints. The effectiveness of the proposed methodology was validated through simulating driving tests both in straight and curve roads by CarSim/SIMULINK joint simulation on dSPACE real-time computer. Comparison of the improved recurrent neural network estimator with Kalman filter and feedforward neural network method revealed that the neural network observer established in this article provides more accurate estimates of the target vehicle states. The proposed method could provide guidance for better recognition of target vehicle behaviours in automated driving.