Driving behavior estimation in car-following scenario based on contextual traffic information is an essential capability for autonomous driving systems. Real-time motion planning based on incomplete environment perception requires complicated probabilistic model for interactions with surrounding objects and road conditions. Hidden Markov Model (HMM) with Gaussian emissions has been used to model driving behaviors for its ability of inferring unobserved states. While the high-dimensional contextual data is continuously processed, the system should be high-performance and power-efficient to make real-time decisions for safe operations. Field Programmable Gate Array (FPGA) is being increasingly used on embedded System-on-Chip (SoC) for mobile applications mainly because of its parallel computation and low-power consumption. This paper implements FAuto: the framework of HMM coupled with GMM algorithm on a Xilinx PYNQ-Z2 board for autonomous systems. We design the hybrid GMM-HMM model in python, and train the model using Next Generation SIMulation (NGSIM) trajectory data on a CPU platform. The hardware accelerator is designed through Vivado HLS 2018.2, and verified with Jupiter notebook. FAuto achieves 2.59 TOPS/W power efficiency, and 10.39x speedup compared to Python software implementation running on quad-core i7-7500U CPU.