1. A method of determining and predicting a state of a rechargeable battery device in real time, comprising: via respective measuring devices, measuring a current and a voltage of the rechargeable battery in real time; via a processor operatively coupled to memory and to a computer-readable medium encoded with an algorithm for determining the state of the rechargeable battery device in real time, utilizing the measured current and voltage in the algorithm, wherein the algorithm comprises: a first mathematical model based on a direct solution of at least one differential equation characterizing an equivalent RC circuit of the rechargeable battery as a function of time, wherein the first mathematical model is configured to generate a plurality of parameters that are usable to determine the state of the rechargeable battery; and a second mathematical model configured to regress the plurality of parameters over time; and a third mathematical model configured to estimate the state of the rechargeable battery; and via the processor, applying the algorithm to determine the state of the rechargeable battery.