Quantitative Evaluation of Observability for Batteries in Electric Aircraft Using Gramian-Based Methods

Reliable thermal state estimation is fundamental to safe and efficient Battery Thermal Management Systems (BTMS) for electrified aviation. This paper develops a systematic observability analysis framework for lumped parameter thermal models of Lithium-ion batteries and quantifies the effect of temperature sensor placement using Gramian based degree of observability (DoO) metrics. Specifically, we construct the observability matrix and Gramian for linear time invariant (LTI) unit cell and module models and evaluate the condition number of the observability Gramian as a DoO measure to compare sensor layouts. We determine the minimum number of sensors required to give full system observability for a unit cell and a module. And establish configurations that provide the strongest observability among minimal sets. A Pareto analysis of the number of sensors versus normalized DoO (with proxy cost) reveals diminishing returns beyond a threshold, emphasizing that strategic placement governs observability and cost. The proposed framework enables design phase optimization of sensor layouts to improve thermal estimation fidelity under realistic financial, packaging, and manufacturing constraints.