An identification approach to dynamic errors-in-variables systems with a preliminary clustering of observations

Errors-in-variables models are statistical models in which not only dependent but also independent variables are observed with error, i.e. they exhibit a symmetrical model structure in terms of noise. The application field for these models is diverse including computer vision, image reconstruction, speech and audio processing, signal processing, modal and spectral analysis, system identification, econometrics and time series analysis. This paper explores applying the errors-in-variables approach to parameter estimation of discrete-time dynamic linear systems. In particular, a framework is introduced in which a preliminary separation step is applied to group observations prior to parameter estimation. As a result, instead of one, two sets of estimates are derived simultaneously, comparing which can yield estimates for noise parameters. The proposed approach is compared to other schemes with simulation examples