In this paper, the first of a series of papers on battery fuel gauge (BFG), we present a real time parameter estimation strategy for robust state of charge (SOC) tracking. The proposed parameter estimation scheme has the following novel features: it models hysteresis as an error in the open circuit voltage (OCV) and employs a combination of real time, linear parameter estimation and SOC tracking technique to compensate for it. This obviates the need for modeling of hysteresis as a function of SOC and load current. We identify the presence of correlated noise that has been so far ignored in the literature and use it to enhance the accuracy of model identification. As a departure from the conventional “one model fits all” strategy, we identify four different equivalent models of the battery that represent four modes of typical battery operation and develop the framework for seamless SOC tracking by switching. The proposed parameter approach enables a robust initialization/re-initialization strategy for continuous operation of the BFG. The performance of the online parameter estimation scheme was first evaluated through simulated data. Then, the proposed algorithm was validated using hardware-in-the-loop (HIL) data collected from commercially available Li-ion batteries.