Blind Identification Methods For Linear Systems

This thesis is based on the project "Study of Modelling and Identification of a Class of Nonlinear Systems" (The National Nature Science Foundation of China). The author searches and read some references in the literature and aims to identify the characteristics of a system only by using measured outputs and not using input signals. After a deep research, the main contributions in the thesis are as follows.1. Studying blind identification methods for deterministic systems. By normalizing the model parameters or the input signals, the conditions for identificability are gained. Further, a multi-innovation least squares, multi-innovation stochastic gradient and multi-innovation projection based lind identification algorithms are derived. The simulation results indicate that these methods proposed are effective.2. This paper studies the blind identification problem for stochastic systems by sampling the output with a higher frequency than that of the input and presents a least square identification algorithm. The system parameters are estimated only from the fast output measurements by properly choosing the sampling rate and normalizing the model parameters or the input signals and discretitzing a continuous-times system by impulse-invariance-transform or step-invariance-transform. Furthermore, we derive two stochastic gradient blind identification algorithms to compare with the least squares blind identification algorithms. The simulation results show that the algorithms can produce highly accurate parameter estimation.3. For single-input multi-input systems, this thesis studies blind identification methods using the instrumental variable technique by assuming that the subsystem transfer functions are coprime each other. The key is how to choose the instrumental variables to generate the instrumental matrixes. In the traditional identification approaches with known input signals, the instrumental variables are formed by using the input signals, but for blind system identification, difficulty arises in that the system inputs are unavailable. Therefore, the basic idea is to simultaneously identify two combined subsystems using the outputs of the third subsystem as the instrumental variables, and to present the instrumental variable least squares blind identification algorithm and to give its recursive form and to analyze convergence of the algorithm involved. A simulation example is included.4. In additions, another instrumental variable method generalized Yule-Walker algorithms is proposed to identify the single-input multi-input systems with the proper transfer functions for each subchannel, the kernel of this algorithm is to calculate the correlation functions of the inputs and outputs to estimate the system parameters. Usually, these approaches are easy to approximate the correlation functions with known input signals, however, for blind system identification, it is impossible without the system inputs. Here, it is to simultaneously identify two combined subsystems which do not include the inputs, and to seeks for the correlation functions between two output signals to avoid the computation of the input signals, forming the generalized Yule-Walker algorithm. A simulation example is given.As a bisc signal processing technique with the purpose of identifying the characteristics of a system and its input by the system's output measurements only, blind system identification methods are desired in wide applications where the input signals are not measured. Therefore, the research on blind identification is not only significant in theory, but also potentially values in applications. In this thesis, the blind identification algorithms for sevral models are obtained under proper conditions. Some algorithms are given from other existing ones without any proof. Moreover, the applications of the proposed algorithms are deserved study deeply.