Parameters Estimation of Cole-Cole Bio-Impedance Model with a Minimum Number of Frequencies

Wearable bioimpedance devices are becoming increasingly popular due to their portability and non-invasiveness. However, these devices consume a lot of energy during measurement time, limiting the operating time. The number of frequencies must be reduced to reduce the measurement time and energy. In this paper, we propose using three frequencies and investigating their optimal values for accurate measurement. The remaining two frequencies at high frequencies are chosen by eliminating the high frequencies that have a high deviation. Lastly, a third frequency is optimally chosen based on a combination of the frequencies whose non-linear least-squares fitting parameters results lead to the smallest deviations. First, a simulation is used to validate the results, where a Cole-Cole model is used with different noise levels. Two high frequencies in combination with a frequency close to the characteristic frequency yielded the best results, regardless of the presence of noise. Second, the measurement was experimentally validated in STM32 with a physical Cole-Cole model, which confirmed the results, where 7.94 kHz, close to the characteristic frequency, had mean deviations of 2.43% in
$R_{l}$
, 3.7% in
$R_{E}$
, and 2.55% in C. Using three points reduces the measurement time from 9.7 ms to 0.41 ms.