We address the problem of estimating the speed of a road vehicle from its acoustic signature, recorded by a pair of omnidirectional microphones located next to the road. This choice of sensors is motivated by their nonintrusive nature as well as low installation and maintenance costs. A novel estimation technique is proposed, which is based on the maximum likelihood principle. It directly estimates car speed without any assumptions on the acoustic signal emitted by the vehicle. This has the advantages of bypassing troublesome intermediate delay estimation steps as well as eliminating the need for an accurate yet general enough acoustic traffic model. An analysis of the estimate for narrowband and broadband sources is provided and verified with computer simulations. The estimation algorithm uses a bank of modified crosscorrelators and therefore it is well suited to DSP implementation, performing well with preliminary field data.