Accurate estimation of State of Charge (SOC) and State of Health (SOH) is critical for safe and reliable operation of lithium-ion batteries under temperature variations and long-term aging. Most existing approaches estimate SOC and SOH independently using separate models validated under limited thermal conditions, restricting practical applicability. This paper argues that battery aging through a single solid-electrolyte interphase (SEI) growth mechanism physically couples all equivalent circuit model (ECM) parameters including \(R_0\), \(R_1\), \(C_1\), and OCV making multicollinearity among these features structurally inevitable, and therefore requiring a linear decorrelation stage as a necessary architectural constraint preceding any nonlinear regressor. Motivated by this argument, a PCA-enhanced XGBoost hybrid framework is proposed for simultaneous SOC and SOH estimation using task-appropriate input features. For SOC estimation, cycle number (n) and ambient temperature (T) are polynomially expanded to five dimensions \(\{n,\, T,\, n^2,\, T^2,\, nT\}\), z-score normalized, and projected via PCA to a four-dimensional latent representation (\(k = 4\) components, \(99.37\%\) cumulative variance retained); terminal voltage, current, and time serve exclusively as sources for Coulomb Counting SOC reference labels and do not enter the regression model. For SOH estimation, the four HPPC-derived ECM parameters ohmic resistance \(R_0\), polarization resistance \(R_1\), diffusion capacitance \(C_1\), and open-circuit voltage (OCV) extracted at six cycle intervals (0, 100, 200, 300, 400, and 500 cycles) serve as direct regression inputs; these features are polynomially expanded, z-score normalized, and projected via PCA to a four-dimensional latent representation (\(k = 4\) components, \(99.20\%\) cumulative variance retained), with SOH labels derived from experimentally measured discharge capacity normalized by initial cell capacity. Both tasks share the same PCA–XGBoost architectural pipeline with task-specific input feature sets, and the Variance Inflation Factor (VIF) analysis directly justifies the mandatory PCA decorrelation stage for the SOH task, where \(R_0\) exceeds the severity threshold at cycle 200 (\(\text {VIF} = 12.57\)), confirming that passing raw ECM features into any regressor without prior decorrelation would produce unstable predictions. The framework is validated on a \(2.6\,\text {Ah}\) NMC cell discharged under five temperatures (\(-20^{\circ }\text {C}\) to \(30^{\circ }\text {C}\)) for SOC estimation and cycled over 500 charge–discharge cycles at \(25^{\circ }\text {C}\) for SOH estimation. Comparative evaluation against nine machine learning models achieves minimum RMSE values of 0.00871 for SOC and 0.00847 for SOH, with pack-level scalability confirmed through a \(16\text {S}12\text {P}\) simulation study (test \(\text {RMSE} = 0.00831\)).
