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Lithium battery cells are commonly modeled using an equivalent circuit with large lookup tables for each circuit element, allowing flexibility for the model to closely match measured data. Pulse discharge curves and charge curves are collected experimentally to characterize the battery performance at various operating points. It can be extremely difficult to fit the simulation model to the experimental data using optimization algorithms, due to the number of values in the lookup tables. This challenge is addressed using a layered approach to break the parameter estimation problem into smaller tasks. The size of each estimation task is reduced to a small subset of data and parameter values, so that the optimizer can better focus on a specific problem. The layered approach was successful in fitting an equivalent circuit model to a lithium iron phosphate (LFP) cell data set to within a mean of 0.7mV residual error, and max of 9.2mV error at a transient.