Multi-Innovation Identification Methods And Performance Analysis

The multi-innovation identification method extends the modification concept of the single-innovation identification, expands the dimension of the innovation and fully uti-lizes the characteristic that the innovation can improve the accuracy of the parameter estimates and the state estimates. This dissertation studies the multi-innovation identifi-cation methods and analyzes the convergence, thus the research has important theoretical significance and academic value. The main work is as follows.(1) For the Box-Jenkins system, this dissertation studies the convergence of the auxiliary model multi-innovation generalized extended stochastic gradient algorithm by using the stochastic martingale theory, and proves that the parameter estimates converge to their true values under the condition that the input signal is persistently exciting. In order to reduce the effect of colored noise on the system parameter estimation, this dissertation presents a data filtering based multi-innovation generalized extended stochastic gradient algorithm by filtering the measurement data, thus the parameter estimation accuracy of the multi-innovation identification algorithms can be enhanced with the same innovation length. Furthermore, the proposed algorithms are extended to the identification of the multivariable Box-Jenkins systems.(2) For the bilinear-in-parameter system, the output is expressed as the combination of the measurement data and the product of the parameters by using the over-parameterization technique, and then an over-parameterization model based multi-innovation stochastic gradient algorithm is presented by combing the multi-innovation identification theory with the negative gradient search. To overcome the problem of redundant parameter estimates causing by the over-parameterization, a hierarchi-cal multi-innovation stochastic gradient algorithm is proposed by using the multi-innovation identification theory and the convergence is analyzed. To improve the parameter estimation accuracy, a filtering based multi-innovation stochastic gradient algorithm is developed for the bilinear-in-parameter system with colored noise by combing the multi-innovation identification theory with the data filtering technique. Furthermore, the proposed algorithms are extended to estimate the parameters of the multivariable bilinear-in-parameter systems.(3) For the input nonlinear state space system, the identification model is derived based on the observability canonical of the dynamic linear subsystem. The main feature of the identification model lies in that it contains not only the parameter product of the linear subsystem and nonlinear input, but also the unknown system states. To solve this problem, the identification model is decomposed into two identification sub-models, and then the parameter estimates can be computed by replacing the unknown states in the information vectors of two identification models with the responding state estimates. According to the measurement data and the obtained parameter estimates, the state estimates can be computed by using the Kalman filter. Thus, a Kalman filtering based multi-innovation identification algorithm is proposed by implementing the interactive computation and the combined parameter and state estimation can be realized. By designing the state observer and using the data filtering technique, a state observer and data filtering based multi-innovation identification algorithm is derived for the purpose of improving the estimation accuracy.This dissertation gives the simulation examples for each proposed algorithm to test the effectiveness. The convergence for some important identification algorithms is analyzed theoretically.