Gauss-Newton method is mainly designed and exploited to solve the nonlinear least squares problems of static overdetermined systems with order-2 precision. When the system comes to the future time-variant situation, t...
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Gauss-Newton method is mainly designed and exploited to solve the nonlinear least squares problems of static overdetermined systems with order-2 precision. When the system comes to the future time-variant situation, the disadvantages of the Gauss-Newton method in effectiveness and precision need to be overcome. On the basis of zhangneurodynamics, the first zhangneurodynamics model and the second zhangneurodynamics model are constructed and discussed to obtain the nonlinear least squares solution of the time-variant overdetermined system in the future time-variant situation. Then, we propose a novel eleven-instant zhang time discretization formula whose convergenceness and truncation errors of order-6 are proved through rigorous mathematical derivation. The proposed eleven-instant zhang time discretization formula is thus utilized to discretize the constructed first zhangneurodynamics model and second zhangneurodynamics model, respectively. Consequently, a novel discrete-time eleven-instant first zhangneurodynamics-based algorithm and a novel discrete-time eleven-instant second zhangneurodynamics-based algorithm are proposed and generalized to obtain the predictive nonlinear least squares solution of the time-variant overdetermined system in the future time-variant situation. Furthermore, the precisions of the proposed discrete-time eleven-instant first zhangneurodynamics-based and second zhangneurodynamics-based algorithms are proved to be of order-6 through mathematical derivation. Moreover, this work reveals the facts that the Gauss-Newton method is actually the simplified version of the discrete-time two-instant first zhangneurodynamics-based algorithm and the discrete-time two-instant second zhangneurodynamics-based algorithm, respectively. Finally, five challenging numerical experiments, including the problem-solving of the critical force of a crane in a complicated environment, are carried out. The experimental results further substantiate the appli
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