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This paper examines the problem of estimating the states, including state of charge, of battery cells connected in parallel. Previous research highlights the importance of this problem, and presents multiple approaches for solving it. Algorithm scalability and observability analysis can both be challenging, particularly because the underlying pack dynamics are governed by differential algebraic equations. Our work addresses these challenges from a novel perspective that begins by inverting the causality of parallel pack dynamics, which breaks the pack model's underlying algebraic loop. This simplifies observability analysis and observer design significantly, leading to three novel contributions. First, the paper derives mathematical conditions for state observability that apply regardless of the number of battery cells and the order of their individual dynamics. Second, the paper presents an approach for grouping battery cells such that their lumped dynamics are observable. Finally, the paper presents a novel pack state estimator that achieves computational tractability by employing inverse dynamic modeling. We conclude by presenting a Monte Carlo simulation study of this estimator using experimentally-parameterized models of two battery chemistries. The simulation results highlight the computational benefits of both the clustering strategy and inverse dynamics approach for state estimation.