Time Constant Estimation on a Low-Cost, Low-Power Microcontroller Using the Matrix Pencil Method

An algorithm to accurately determine the time constant of a circuit simplifies reading out resistive and capacitive sensors. However, implementing such an algorithm on low-cost, low-power microcontrollers requires overcoming hardware limitations, such as analog-to-digital converter (ADC) noise, limited memory, and the lack of a floating-point unit. This work utilizes the matrix pencil method to estimate the time constant of a decaying exponential signal and outlines the nontrivial firmware implementation of the algorithm on a low-cost, low-power microcontroller. Experimental results show that time constants over more than two orders of magnitude can be accurately estimated to be within around 2% of the nominal value with a standard error of about 0.2% of the nominal value, despite the hardware limitations. This is a significant improvement over previous methods for accurately determining the time constant of a circuit using subpar hardware.