Estimation of Humidity Sensor Equivalent Circuit Parameters Utilizing Frequency Response Measurements Combined with Subspace Identification and Similarity Transformations

This article presents an algorithm to estimate the impedance parameters of a humidity sensor from the measured frequency response data. The sensor is modeled as a multielement two-terminal network. The procedure accurately identifies the impedance parameters using a noniterative algorithm. Traditional nonlinear least-squares procedures rely on having initial parameter values close to the actual values for converging. We approach the problem in two steps: a black-box system identification and a physical parameter extraction step. Based on the first principles, a physical state-space model is developed, where the system matrices contain the impedance parameters in very complicated ways. By strategically introducing extra variables that are a function of these problematic parameters, the state-space model is converted into an observable canonical form. Using frequency response data, a subspace algorithm identifies a model of the same order as the physical model. An unknown similarity transformation matrix is then used to establish the relationship between the identified model and the canonical model. In the first step, we determine the additional variables and the transforming matrix. The impedance parameters are obtained from the relationship between the additional variables and the physical parameters. Simulations and experiments validate the proposed algorithm.