In this article we describe the incoherent and coherent spin and charge dynamics of a single electron quantum dot. We use a stochastic master equation to model the state of the system, as inferred by an observer with access to only the measurement signal. Measurements obtained during an interval of time contribute, by a past quantum state analysis, to our knowledge about the system at any time t within that interval. Such analysis permits precise estimation of physical parameters, and we propose and test a modification of the classical Baum-Welch parameter re-estimation method to systems driven by both coherent and incoherent processes.