A classification algorithm is presented that uses hidden Markov models (HMMs) to carry out recognition between three classes of targets: personnel, tracked vehicles and wheeled vehicles. It exploits the time-varying nature of radar Doppler data in a manner similar to techniques used in speech recognition, albeit with a modified topology, to distinguish targets with different Doppler characteristics. The algorithm was trained and tested on real radar signatures of multiple examples of moving targets from each class, and the performance was shown to be invariant to target speed and orientation and was able to be generalised with respect to variants within a class.