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 [1] for estimating
the DRT, as introduced by P. B¨uschel [2]. 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 conver-
gence, and the reliability, referring to the accuracy in resolving the peak widths in the DRT,
under varying conditions remain to be evaluated. Our current work focuses on analyzing the
convergence of the algorithm under shifting operating points. With this study, our objective
is to contribute to the advancement of real-time diagnostic capabilities for next-generation
battery systems.