Comparing Open-loop Subspace System Identification Methods: The DSR and MOESP Methods

Abstract

This thesis presents a comparative analysis of two subspace system identification algorithms—Deterministic and Stochastic Realization (DSR) and Multivariable Output Error State Space (MOESP)—focusing on their performance in open-loop identification of discrete-time, linear time-invariant systems. Subspace identification methods are widely used for deriving state-space models from measured input-output data, offering robustness in noisy conditions and efficient computation. The study addresses a critical research gap by evaluating algorithms’ accuracy, computational speed, and noise resilience through structured Monte Carlo simulations using MATLAB. The simulations employed pseudo-random binary sequence (PRBS1) inputs and randomized system models to ensure statistical robustness. Evaluation criteria included Root Mean Square Error (RMSE), Mean Absolute Error (MAE), mean error, computational time, parameter variance for matrices and scaling criterion. The results demonstrate that under noisy conditions, DSR outperforms MOESP in key areas: it achieved lower RMSE (0.5044 vs. 0.5131), lower MAE (0.3913 vs. 0.4004), and significantly lower parameter variance, particularly for matrix A. Additionally, DSR was approximately three times faster than MOESP across all simulations, making it particularly suitable for real-time and resource-constrained applications. Although MOESP showed a slightly lower mean error (58.85%) than DSR (58.93%), this difference was marginal. In noise-free conditions, MOESP slightly outperformed DSR in RMSE and MAE suggesting it may be better suited for high-precision applications with minimal measurement noise. Overall, the findings position DSR as a robust and computationally efficient method in noisy environments, while MOESP offers marginal advantages in noise-free scenarios requiring precision