Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems

This paper is concerned with the joint estimation of states and parameters of a special class of nonlinear systems, ie, bilinear systems. The key is to investigate new estimation methods for interactive state and parameter estimation of the considered system based on the interactive estimation theory. Because the system states are unknown, a bilinear state observer is established based on the Kalman filtering principle. Then, the unavailable states are updated by the state observer outputs recursively. Once the state estimates are obtained, the bilinear state observer-based hierarchical stochastic gradient algorithm is developed by using the gradient search. For the purpose of improving the convergence rate and the parameter estimation accuracy, a bilinear state observer-based hierarchical multi-innovation stochastic gradient algorithm is proposed by expanding a scalar innovation to an innovation vector. The convergence analysis indicates that the parameter estimates can converge to their true values. The numerical example illustrates the effectiveness of the proposed algorithms.