The difficulty in measuring certain types of process variables rapidly has encouraged the use of soft sensors, which can determine the values of difficult to measure process variables based on easily available secondary process variables. A bias update term that allows the system to take into consideration disturbances in the system is often included in such soft sensor systems. The first part of this two-part series considers the bias update for the open-loop situation, including the ideal case, the case where there is measurement delay, the case with multirate sampling, and the case where there is a combination of measurement delay and multirate sampling. Proposed tuning rules are provided for all cases in order to obtain optimal open-loop tracking of the quality variable, especially in the presence of slow or drifting disturbances. Simulation and experimental validation of the results is presented.