Electrochemical impedance spectroscopy (EIS) is a widely used means for characterization of the dynamics of batteries and electrochemical energy conversion systems in general. EIS is useful for on-line condition monitoring since it contains valuable information on the internal condition of the batteries. The conventional approach to the EIS of batteries relies on their successive excitation with mono-component sinusoidal signals at the pre-defined frequencies. When inferring about the battery's state-of-health, the low-frequency part of the impedance characteristic is of particular interest. Excitation in the low-frequency region can take an excessively long time. Moreover, maintaining stable experimental conditions over long time intervals i na way that the external disturbances will not affect the estimated impedance, might be demanding, especially in the in-field applications. To alleviate the said limitations, and to minimally intrude the process operation, in this paper we apply broadband electrochemical impedance spectroscopy based on a discrete random binary sequence for perturbation of the battery input. The impedance is evaluated by processing voltage and current signals with continuous Morse wavelet transform. The main contributions of the paper refer to (i) the accurate evaluation of the impedance spectra from μHz to kHz range with high-frequency resolution (more than 200 points per decade) and (ii) the evaluation of the uncertainty region of the impedance characteristic. The entire characterisation takes only a fraction of the time required by the classical sine-based electrochemical impedance spectroscopy. The algorithm is successfully demonstrated on a commercial Li-ion battery, which, together with the all datasets are available for download at https://repo.ijs.si/gnusev/supplementary_material.git.

A new formulation of the unknown input estimation problem in presence of unknown disturbances over a frequency region is presented. Necessary and sufficient conditions for existence of a solution are given, and three estimation filters. The minimal attenuation is equal to the norm of a rational matrix over the frequency region. As a result, the minimum can be computed by solving linear matrix inequalities (LMIs). An example is given, and the estimation with the proposed filters is illustrated by a numerical simulation, and compared with some state-of-the-art estimation filters.