This paper presents a vehicle-independent, non-intrusive, and light monitoring system for accurately measuring fuel consumption in road vehicles from longitudinal speed and acceleration derived continuously in time from GNSS and IMU sensors mounted inside the vehicle. In parallel to boosting the transition to zero-carbon cars, there is an increasing interest in low-cost instruments for precise measurement of the environmental impact of the many internal combustion engine vehicles still in circulation. The main contribution of this work is the design and comparison of two innovative black-box algorithms, one based on a reduced complexity physics modeling while the other relying on a feedforward neural network for black-box fuel consumption estimation using only velocity and acceleration measurements. Based on suitable metrics, the developed algorithms outperform the state of the art best approach, both in the instantaneous and in the integral fuel consumption estimation, with errors smaller than 1\% with respect to the fuel flow ground truth. The data used for model identification, testing, and experimental validation is composed of GNSS velocity and IMU acceleration measurements collected during several trips using a diesel fuel vehicle on different roads, in different seasons, and with varying numbers of passengers. Compared to built-in vehicle monitoring systems, this methodology is not customized, uses off-the-shelf sensors, and is based on two simple algorithms that have been validated offline and could be easily implemented in a real-time environment.