Acoustic vehicle classification is a difficult problem due to the non-stationary nature of the signals, and especially the lack of strong harmonic structure for most civilian vehicles with highly muffled exhausts. Acoustic signatures will also vary largely depending on speed, acceleration, gear position, and even the aspect angle of the sensor. The problem becomes more complicated when the deployed acoustic sensors have less than ideal characteristics, in terms of both the frequency response of the transducers, and hardware capabilities which determine the resolution and dynamic range. In a hierarchical network topology, less capable Tier 1 sensors can be tasked with reasonably sophisticated signal processing and classification algorithms, reducing energy-expensive communications with the upper layers. However, at Tier 2, more sophisticated classification algorithms exceeding the Tier 1 sensor/processor capabilities can be deployed. The focus of this paper is the investigation of a Gaussian mixture model (GMM) based classification approach for these upper nodes. The use of GMMs is motivated by their ability to model arbitrary distributions, which is very relevant in the case of motor vehicles with varying operation modes and engines. Tier 1 sensors acquire the acoustic signal and transmit computed feature vectors up to Tier 2 processors for maximum-likelihood classification using GMMs. In a binary classification task of light-vs-heavy vehicles, the GMM based approach achieves 7% equal error rate, providing an approximate error reduction of 49% over Tier 1 only approaches.