A recursive subspace based method for errors-in-variables model identification of time-varying systems

Deepanjhan Das, Shankar Narasimhan

The Subspace-based Model Identification algorithm using a modified Iterative Principal Component Analysis (SMI-IPCA) is a theoretically rigorous method for identifying a linear state-space model of a multi-input multi-output (MIMO) process, in an errors-in-variables (EIV) setting. The method can simultaneously estimate unknown heteroskedastic noise variances corrupting the input and output measurements, along with the state space model. This work proposes a recursive formulation of SMI-IPCA (RSMI-IPCA) enabling online identification and adaptive model updates as and when new data arrive. By maintaining a fixed length lag window rather than storing the complete historical data, RSMI-IPCA estimates measurement noise variances, process order, while simultaneously identifying the state-space matrices, making it suitable to monitor time-varying systems, whether the induced changes are slow or abrupt. The algorithm gradually adapts to slow sensor degradation (time-varying noise variances), changes in process operating conditions (time-varying model parameters), and structural modifications (varying model order). Simulation studies are presented to demonstrate the efficacy and practical applicability of the proposed algorithm.