"A well-known challenge in estimating the distance of the antenna pair in time-of-arrival (ToA) based RF localization systems is the problem of obstruction of the direct path (DP) between transmitter and receiver. The absence of DP component in received channel profile creates undetected direct path (UDP) conditions. UDP condition, in turn, will cause occurrence of unexpected large ranging errors which pose serious challenge to precise indoor localization. Analysis of the behavior of the ranging error in such conditions is essential for the design of precise ToA-based indoor localization systems. This dissertation discusses two open problems in ToA-based indoor localization systems. The first contribution of this dissertation discusses the problem of modeling of dynamic behavior of ranging error. We propose a novel analytical framework for analysis of dynamic spatial variations of ranging error observed by a mobile user based on an application of Markov chain. The model relegates the behavior of ranging error into four main categories associated with four states of Markov process. Parameters of distributions of ranging error in each Markov state are extracted from empirical data collected from a measurement-calibrated ray tracing algorithm simulating a typical office environment. The analytical derivation of parameters of the Markov model employs the existing path-loss models for first detected path and total multipath received power in the same office environment. Results of simulated errors from the Markov model and actual errors from empirical data show close agreement. The second contribution of this dissertation discusses the problem of identification of UDP condition given an unknown channel profile. Existing of UDP condition in a channel profile poses serious degradation to ranging estimate process. Therefore, identification of occurrence of UDP condition is of our subsequent concern. After identification, the second step is to mitigate ranging errors in such conditions. In this dissertation we present two methodologies, based on binary hypothesis testing and an application of artificial neural network design, to identify UDP conditions and mitigate ranging error using statistics extracted from wideband frequency-domain indoor measurements conducted in typical office building. "