Non-iterative parameter estimation of the 2R-1C model suitable for low-cost embedded hardware

适于低成本嵌入式硬件的2R-1C模型非迭代参数估计

Parameter estimation of the 2 R-1 C model is usually performed using iterative methods that require high-performance processing units.Consequently,there is a strong motivation to develop less time-consuming and more power-efficient parameter estimation methods.Such low-complexity algorithms would be suitable for implementation in portable microcontroller-based devices.In this study,we propose the quadratic interpolation non-iterative parameter estimation(QINIPE)method,based on quadratic interpolation of the imaginary part of the measured impedance,which enables more accurate estimation of the characteristic frequency.The 2 R-1 C model parameters are subsequently calculated from the real and imaginary parts of the measured impedance using a set of closed-form expressions.Comparative analysis conducted on the impedance data of the 2 R-1 C model obtained in both simulation and measurements shows that the proposed QINIPE method reduces the number of required measurement points by 80%in comparison with our previously reported non-iterative parameter estimation(NIPE)method,while keeping the relative estimation error to less than 1%for all estimated parameters.Both non-iterative methods are implemented on a microcontroller-based device;the estimation accuracy,RAM,flash memory usage,and execution time are monitored.Experiments show that the QINIPE method slightly increases the execution time by 0.576 ms(about 6.7%),and requires 24%(1.2 KB)more flash memory and just 2.4%(32 bytes)more RAM in comparison to the NIPE method.However,the impedance root mean square errors(RMSEs)of the QINIPE method are decreased to 42.8%(for the real part)and 64.5%(for the imaginary part)of the corresponding RMSEs obtained using the NIPE method.Moreover,we compared the QINIPE and the complex nonlinear least squares(CNLS)estimation of the 2 R-1 C model parameters.The results obtained show that although the estimation accuracy of the QINIPE is somewhat lower than the estimation accuracy of the CNLS,it is still satisfactory for many practical purposes and its execution time reduces to1/45–1/30.

2R-1C模型的参数估计常运用需要高性能处理单元的迭代方法,从而激励我们研究更省时且更节能的参数估计方法。这些低复杂度的算法将更适于便携式微机设备的运行。本文提出二次插值非迭代参数估计方法(QINIPE);该方法基于测量阻抗虚部的二次插值,能够更精确地估计特征频率。运用一组封闭表达式从测量阻抗的实部和虚部计算2R-1C模型的参数。对仿真和测量获得的模型阻抗数据作对比分析;结果表明,相较于我们早前提出的非迭代参数估计方法(NIPE),QINIPE能减少80%测量点,且所有估计参数的相对估计误差低于1%。两种非迭代方法均基于一个微机设备实施;检测了估计精度、RAM、闪存使用以及运行时间。实验结果表明,相较于NIPE,QINIPE轻微增加了0.576ms运行时间(约6.7%),且需要多24%(1.2KB)闪存及多2.4%(32字节)RAM。然而,QINIPE的阻抗均方根误差分别降低至NIPE对应的42.8%(实部)和64.5%(虚部)。此外,比较了QINIPE和复杂非线性最小二乘法(CNLS)对2R-1C模型参数的估计。结果表明,虽然QINIPE估计精度稍低于CNLS,其依然适合许多实际应用,且运行时间降至原来的1/45至1/30。