The Cole model is widely used in bioimpedance spectroscopy (BIS) applications for evaluating the contents and status of biological tissues. Traditional frequency-domain fitting methods for Cole parameter estimation (CPE) often need wideband direct or indirect BIS measurements. The newly emerged time-domain fitting methods do not require BIS measurement, but they usually have unsatisfactory estimation accuracy and heavily rely on some specific excitations. This paper proposes a novel time-domain fitting method based on the fractional operational matrix (FOM) for CPE. First, the Cole model is represented as a FOM-based algebraic equation. Then, the model-based voltage response can be calculated as the product of the sampled current excitation and the FOM-based Cole equation. Finally, the Cole parameter can be estimated by minimizing the sum of squares error between the sampled voltage response and the model-based voltage response using an iterative nonlinear least-squares fitting algorithm. Experimental measurements are verified on three 2R1C circuits and in vivo leg muscle of a healthy volunteer. The results show that the Cole parameter can be accurately estimated by the proposed FOM-based fitting method directly using the sampled current and voltage signals. This paper establishes an effective time-domain fitting method for CPE, which could greatly simplify the hardware and software designs without the need for the BIS measurement.

中文翻译：

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一种基于分数运算矩阵的Cole参数估计简化时域拟合方法

Cole 模型广泛用于生物阻抗谱 (BIS) 应用，以评估生物组织的内容和状态。用于科尔参数估计 (CPE) 的传统频域拟合方法通常需要宽带直接或间接 BIS 测量。新出现的时域拟合方法不需要 BIS 测量，但它们通常具有不令人满意的估计精度，并且严重依赖于某些特定的激励。本文提出了一种新的基于分数运算矩阵 (FOM) 的 CPE 时域拟合方法。首先，Cole 模型表示为基于 FOM 的代数方程。然后，基于模型的电压响应可以计算为采样电流激励和基于 FOM 的 Cole 方程的乘积。最后，Cole 参数可以通过使用迭代非线性最小二乘拟合算法最小化采样电压响应和基于模型的电压响应之间的平方误差总和来估计。实验测量在三个 2R1C 电路和健康志愿者的体内腿部肌肉上得到验证。结果表明，Cole 参数可以通过所提出的基于 FOM 的拟合方法直接使用采样的电流和电压信号准确估计。本文建立了一种有效的 CPE 时域拟合方法，可以大大简化硬件和软件设计，而无需进行 BIS 测量。实验测量在三个 2R1C 电路和健康志愿者的体内腿部肌肉上得到验证。结果表明，Cole 参数可以通过所提出的基于 FOM 的拟合方法直接使用采样的电流和电压信号准确估计。本文建立了一种有效的 CPE 时域拟合方法，可以大大简化硬件和软件设计，而无需进行 BIS 测量。实验测量在三个 2R1C 电路和健康志愿者的体内腿部肌肉上得到验证。结果表明，Cole 参数可以通过所提出的基于 FOM 的拟合方法直接使用采样的电流和电压信号准确估计。本文建立了一种有效的 CPE 时域拟合方法，可以大大简化硬件和软件设计，而无需进行 BIS 测量。