This paper presents a memristive device model capable of accurately matching a wide range of characterization data collected from a tantalum oxide memristor. Memristor models commonly use a set of equations and fitting parameters to match the complex dynamic conductivity pattern observed in these devices. Along with the proposed model, a procedure is also described that can be used to optimize each fitting parameter in the model relative to an I-V curve. Therefore, model parameters are self-updated based on this procedure when a new cyclic I-V sweep is provided for model optimization. This model will automatically provide the best possible match to the characterization data without any additional optimization from the user. In this paper, multiple cyclic I-V characterizations are modeled from ten different tantalum oxide devices (on the same wafer). Additionally, studies were completed to demonstrate the amount of variation present between devices on a wafer, as well as the amount of variation present within a single device. Methods for modeling this variation are then proposed, resulting in an accurate and complete, automated, memristor modeling approach.