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Due to growing interest in hybrid and electric vehicles, the battery, being one of the critical components, is receiving a lot of attention from designers and researchers. Two battery-modeling approaches, though seemingly different, share the same mathematical challenge of robust non-linear curve-fitting. The two methods are battery equivalent circuit model and battery system level thermal modeling using the linear time-invariant (LTI) method. Both modeling approaches involve curve-fitting testing data or data from advanced models to identify four parameters in a circuit model consisting of two pairs of RC elements. Such curve-fitting is mathematically a non-linear least-squares (LS) problem. Standard methods like the Levenberg-Marquardt (LM) method can be used for non-linear curve-fitting, but the LM method is known to be sensitive to initial conditions.