Innovation-Based Subspace Identification in Open- and Closed-Loop

The applicability of subspace-based system identification methods highly depends on the disturbances acting on the system. It is well-known, e.g., that the standard implementations of the MOESP, N4SID or CVA algorithms yield biased estimates when closed-loop noisy data is considered. In order to bypass this difficulty, we follow the recent trends for closed-loop subspace-based model identification and suggest, in a first step, pre-estimating the innovation term from the available data. By doing so, the initial subspace-based identification problem can be written as a deterministic problem for which efficient methods exist. Once the innovation sequence is estimated, the second step of our subspace-based identification procedure focuses on the estimation of the open-loop and closed-loop system's Markov parameters. A constrained least-squares solution is more precisely considered to guarantee structural constraints satisfied by Toeplitz matrices involved the open-loop and closed-loop data equations, respectively. The performance of the methods is illustrated through the study of simulation examples under open-loop and closed-loop conditions.