Lithium-ion batteries are critical to modern technologies and have experienced significant growth in recent years. This increasing usage underscores the need for efficient diagnostic methods, particularly for real-time monitoring during operation. An intuitive method for investigating internal processes, as reflected by the impedance of the cell, is the distribution of relaxation times (DRT). Often, the DRT is calculated from the impedance spectrum using Tikhonov regularization. Since this is a batch calculation, it requires a sufficient amount of memory, making it incompatible with online microcontroller calculations.

This study investigates the applicability of the Kaczmarz algorithm for estimating the DRT, as introduced by P. Büschel. A key advantage of this approach is its ability to operate in the time domain, enabling online implementation to extract critical information about cell states during operation. Hence, the efficiency, defined here as the speed of convergence, and the reliability, referring to the accuracy in resolving the peak widths in the DRT, under varying conditions remain to be evaluated. With this study, our objective is to contribute to the advancement of real-time diagnostic capabilities for next-generation battery systems.