A Unified Continuous Time Framework for Adaptive Smartphone Battery Drain Prediction with Finite Horizon Error Analysis

Smartphone battery prediction requires a consistent connection between hardware demand, electrical dynamics and capacity aging. We develop a unified continuous-time framework that integrates a second-order equivalent circuit, a temperature-dependent resistance model, empirical aging and adaptive load calibration. A finite-horizon error analysis connects current bias and capacity uncertainty to state-of-charge drift, while exact interval updates provide a reference for numerical verification. Evaluation combines new Android telemetry, 1000 public smartphone workload profiles and five laboratory cell trajectories. On a later ZTE session, static scale calibration reduces power mean absolute error from 1.582 to 0.232 W; a predict-before-update recursive comparator achieves 0.117 W. Across 17 forward temporal blocks, the recursive method yields a pooled error of 0.155 W, with condition-dependent failures. On public Pixel 8 profiles, linear hardware features explain 89.4% of variation in a nominal-voltage power proxy. Dual-exponential capacity extrapolation achieves 0.00651 Ah root-mean-square error on the UCL cell, but offers no general advantage over simpler models on four NASA cells. The results establish a reproducible route from load calibration to charge-balance error assessment and identify the conditions governing model deployment. Complete-discharge validation remains necessary to quantify end-to-end runtime accuracy.