Convergence analysis of the guaranteed parameter estimation algorithm for models of one-dimensional chaotic systems

This paper considers the parameter estimation problem for models of one-dimensional chaotic systems. The guaranteed algorithm is proposed in the context of set-membership approach, which assumes that only intervals of possible values are known for the uncertain variables in the model (initial condition, parameter and measurement errors). The algorithm recursively computes the interval estimates of the parameter at every time step. If the prior information is correct, found interval estimates always contain the true value of the parameter. For certain models of measurement errors the result of the algorithm is the exact value of the parameter (the final interval estimate contains a single point). The goal of this study is to derive conditions under which the guaranteed algorithm improves the interval estimate of the parameter.