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The rapid introduction of electric vehicles (EVs) in the transportation market has initiated the concept of vehicle-to-grid (V2G) technology in smart grids. However, where V2G technology is intended to facilitate the power grid ancillary services, it could also have an adverse effect on the aging of battery packs in EVs. This is due to the instant depletion of power during the charge and discharge cycles, which could eventually impact the structural complexity and electrochemical operations in the battery pack. To address this situation, a median expectation-based regression approach is proposed for parameter estimation of vehicle batteries in V2G systems. The proposed method is built on the property of uncertainty prediction of Gaussian processes for parameter estimation while considering the cell variations as an exogenous function. First, a median expectation-based Gaussian process model is derived to predict the fused and individual cell variations of a battery pack. Second, a magnitude-squared coherence model is developed by the error matrix to detect and isolate each variation. This is obtained by extracting the cross-spectral densities for the measurements. The proposed regression-based approach is evaluated using experimental measurements collected from lithium-ion battery pack in EVs. The parametric analysis of the battery pack has been verified using D-SAT Chroma 8000ATS hardware platform. Performance evaluation shows an accurate estimation of these dynamics even in the presence of injected faults. [ABSTRACT FROM AUTHOR]