A measurement is a dynamical process that aims to estimate the true value of a measurand. The measurand is the input that excites a sensor, and, as a consequence, the sensor output is a transient response. The main approach to estimate the input is applying the sensor transient response to another dynamical system. This dynamical system is designed by deconvolution to invert the sensor dynamics and compensate the sensor response. Digital signal processors enable an alternative approach to estimate the unknown input. There exists a data-driven subspace-based signal processing method that estimates a measurand, assuming it is constant during the measurement. To estimate the parameters of a measurand that varies at a constant rate, we extended the data-driven input estimation method to make it adaptive to the affine input. In this paper, we describe the proposed subspace signal processing method for the measurement of an affine measurand and compare its performance to a maximum-likelihood input estimation method and to an existing time-varying compensation filter. The subspace method is recursive and allows real-time implementations since it directly estimates the input without identifying a sensor model. The maximum-likelihood method is model-based and requires very high computational effort. In this form, the maximum-likelihood method cannot be implemented in real-time, however, we used it as a reference to evaluate the subspace method and the time-varying compensation filter results. The effectiveness of the subspace method is validated in a simulation study with a time-varying sensor. The results show that the subspace method estimation has relative errors that are one order of magnitude smaller and converges two times faster than the compensation filter.
- Affine input estimation
- Subspace estimation method
- Maximum-likelihood estimation method
- Recursive least squares
- Dynamic weighing