Hidden Markov Models have many applications in signal processing and pattern recognition, but their convergence-based training algorithms are known to suffer from oversensitivity to the initial random model choice. This paper focuses upon the use of model averaging, ensemble thresholding, and random relative model permutations for improving average model performance. A method is described which trains by searching for the best relative permutation set for ensemble averaging. This uses the fit to the training set as an indicator. The work provides a simpler alternative to previous permutation-based ensemble averaging methods
