In this contribution, we suggest two proposals to achieve fast, real-time lane-keeping control for Autonomous Ground Vehicles (AGVs). The goal of lane-keeping is to orient and keep the vehicle within a given reference path using the front wheel steering angle as the control action for a specific longitudinal velocity. While nonlinear models can describe the lateral dynamics of the vehicle in an accurate manner, they might lead to difficulties when computing some control laws such as Model Predictive Control (MPC) in real time. Therefore, our first proposal is to use a Linear Parameter Varying (LPV) model to describe the AGV's lateral dynamics, as a trade-off between computational complexity and model accuracy. Additionally, AGV sensors typically work at different measurement acquisition frequencies so that Kalman Filters (KFs) are usually needed for sensor fusion. Our second proposal is to use a Dual-Rate Extended Kalman Filter (DREFKF) to alleviate the cost of updating the internal state of the filter. To check the validity of our proposals, an LPV model-based control strategy is compared in simulations over a circuit path to another reduced computational complexity control strategy, the Inverse Kinematic Bicycle model (IKIBI), in the presence of process and measurement Gaussian noise. The LPV-MPC controller is shown to provide a more accurate lane-keeping behavior than an IKIBI control strategy. Finally, it is seen that Dual-Rate Extended Kalman Filters (DREKFs) constitute an interesting tool for providing fast vehicle state estimation in an AGV lane-keeping application.