Two new methods are presented for estimating car-following model parameters using data collected from Adaptive Cruise Control (ACC) enabled vehicles. The vehicle is assumed to follow a constant time headway relative velocity model in which the parameters are unknown and to be determined. The first technique is a batch method that uses a least-squares approach to estimate the parameters from time series data of the vehicle speed, space gap, and relative velocity of a lead vehicle. The second method is an online approach that uses a particle filter to simultaneously estimate both the state of the system and the model parameters. Numerical experiments demonstrate the accuracy and computational performance of the methods relative to a commonly used simulation-based optimization approach. The methods are also assessed on empirical data collected from a 2019 model year ACC vehicle driven in a highway environment. Speed, space gap, and relative velocity data are recorded directly from the factory-installed radar unit via the vehicle's CAN bus. All three methods return similar mean absolute error values in speed and spacing compared to the recorded data. The least-squares method has the fastest run-time performance, and is up to 3 orders of magnitude faster than other methods. The particle filter is faster than real-time, and therefore is suitable in streaming applications in which the datasets can grow arbitrarily large.