Radio frequency system optimization and troubleshooting remains one of the most challenging aspects of working in a cellular network. To stay competitive, cellular providers continually monitor the performance of their networks and use this information to determine where to improve or expand services. As a result, operators are saddled with the task of wading through overwhelmingly large amounts of data in order to trouble-shoot system problems. Part of the difficulty of this task is that for many complicated problems such as hand-off failure, clues about the cause of the failure are hidden deep within the statistics of underlying dynamic physical phenomena like fading, shadowing, and interference. In this research we propose that Hidden Markov Models (HMMs) be used as a method to infer signature statistics about the nature and sources of faults in a cellular system by fitting models to various time-series data measured throughout the network. By including HMMs in the network management tool, a provider can explore the statistical relationships between channel dynamics endemic to a cell and its resulting performance. This research effort also includes a new distance measure between a pair of HMMs that approximates the Kullback-Leibler divergence (KLD). Since there is no closed-form solution to calculate the KLD between the HMMs, the proposed analytical expression is very useful in classification and identification problems. A novel HMM based position location technique has been introduced that may be very useful for applications involving cognitive radios. / Ph. D.