Joint Parameter And Time Delay Estimation For State Space Models Based On Sparse Reconstruction

System identification is an effective method to establish system dynamic models based on data.However,in practical applications,it is sometimes difficult and extravagant to obtain enough input and output data.Therefore,it is necessary to study the system identification methods under small sampling data.Due to the widespread existence of time delays in the process industry and communication systems,and the widespread use of state space models in the control field,this paper focuses on the multi-variable and multi-delay systems described by the state space models,in the case of unknown time delays,based on the sparse reconstruction methods in the compressive sensing,the joint identification of the time delays and the parameters of the models under small sampling data is studied.The research mainly has the following three points.(1)For the multi-variable and multi-delay systems described by the state space models,if the time delay of each channel is unknown,based on the sparse reconstruction methods in the compressive sensing,the joint identification methods of the time delays and the parameters are studied.Firstly,the over-parameterized sparse regression equation of output,states and input is obtained by setting the regression length of the input data and the shift term transformation of the state equations.Secondly,the parameter filter technology is used to improve the basis pursuit de-noising method in the convex optimization methods,the orthogonal matching pursuit algorithm and the compressive sampling matching pursuit algorithm in the greedy algorithms,then the sparse parameter vector of the regression equation is obtained,the time delay of each channel is estimated according to the sparse structure of the parameter vector.Simulation results verify the effectiveness of the proposed algorithms.(2)For the unmeasurable states of the state-space models,the joint identification methods of the time delays,the parameters and the states of the over-parameterized models are studied.According to the iterative identification method,based on Kalman filter and the improved sparse reconstruction methods,a Kalman filter based basis pursuit de-noising iterative algorithm,a Kalman filter based orthogonal matching pursuit iterative algorithm,and a Kalman filter based compressive sampling matching pursuit iterative algorithm interactively estimate the states and the sparse parameter vector in the iterative process.Simulation results verify the effectiveness of the proposed algorithms.(3)For the state space models with the unmeasurable states and the colored noise,the problem that the information vector of the over-parameterized model contains the unknown states and the unknown noises is solved by using the iterative identification principle,Kalman filter and the improved sparse reconstruction methods.A Kalman filter based extended basis pursuit de-noising iterative algorithm,a Kalman filter based extended orthogonal matching pursuit iterative algorithm,and a Kalman filter based extended compressive sampling matching pursuit iterative algorithm are proposed,respectively.Simulation results verify the effectiveness of the proposed algorithms.In summary,this paper studies three different forms of state space models,based on the convex optimization methods and the greedy algorithms in the sparse reconstruction methods,and combining Kalman filter and the iterative identification principle,the corresponding algorithms are derived and obtained,respectively.The proposed algorithms can jointly estimate the time delays and the parameters of the state space models based on the sparse reconstruction methods with small sampling data.Simulation results verify the effectiveness of the proposed algorithms.