This paper introduces a new method to monitor battery state of health (SOH) by estimating the side reaction current density as a direct SOH indicator. The estimation is formulated as an inaccessible subsystem identification problem, where the side reaction current density is treated as the output of an inaccessible battery health subsystem. Inaccessiblity in this context refers to the fact that the inputs and outputs of the subsystem are not measurable in-situ. This subsystem is identified using retrospective-cost subsystem identification (RCSI), and the output of the identified subsystem provides an estimate for the side reaction current density. Using an example parameter set for a LiFePO4 battery, simulations are performed to obtain estimates under various current profiles. These simulations show promising results in identifying the battery health subsystem and estimating the side reaction current density with RCSI under ideal conditions. Robustness of the algorithm under non-ideal conditions is analyzed. Estimation of the side reaction current density using RCSI is shown to be sensitive to non-ideal conditions that cause errors in the measurement or estimation of the battery voltage. A method for quantitatively assessing the impact of non-ideal conditions on the side reaction current estimation accuracy is provided. The proposed estimation technique, including the method for estimating the side reaction current density and the framework analyzing its robustness, can also be applied to other parameter sets and other battery chemistries to monitor the SOH change resulting from any electrochemical-based degradation mechanism that consumes cyclable Li-ions.