Some LMS-based algorithms for impedance measurements

The properties of some algorithms based on digital signal processing for the impedance components determination in circuits with sampling sensor have been analysed. It is supposed that the voltage and current are sampled in a synchronous way with a fundamental frequency of the generated sinusoidal signal. Two groups of fitting sine wave algorithms, which are based on the least mean square (LMS) technique, have been described. The first group of algorithms implements an indirect measurement method. The algorithms of the second group estimate the unknown impedance components using a direct measurement method. In order to simplify the calculations in all of these algorithms, different forms of input matrix have been used. The propagation of the uncertainty in the described algorithms can be analysed by means of a covariance matrix. In order to verify the performance of the considered algorithms (e.g., accuracy, estimator bias and convergence) the Monte Carlo simulations have been performed in MATLAB environment. It has been shown that these algorithms provide the minimisation of the uncertainty for selected numbers of samples and phase angles.