Fisher Ratio Optimization under Volterra Filtering Model for Identification of Polarimetric Air/Air Range Profiles of Aircrafts

This paper introduces an original supervised classification method based on the optimization of the Fisher ratio under the Volterra filtering model. Optimum Volterra filters are derived for the problem of discriminating 2 classes. They have properties yielding some decision strategy that aims to reject (i.e. take no decision) data corresponding to unlearned classes. An original extension of this solution is then proposed for the problem of discriminating more than 2 classes. Performances of our method are evaluated by classifying real data of jet fighters range profiles. Influence of the filtering model order is investigated. Interest of the waveform polarization states is also analyzed. Results obtained show that our method outperforms the nearest neighbor classification method in term of error probability, while yielding equivalent performances in term of correct identification probability. Moreover, it is shown that good rejection probability of unlearned classes can be obtained, particularly with fully-polarized data.