非線形最小2乗問題に対する一手法

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The nonlinear least square (NLS) problem often appears in the scene of problem solving that uses a mathematical model when the model parameter is decided. Various methods are designed for the solving. When these methods are classified from the standpoint where the problem is taken up and the standpoint of execute form of the solving, the execute form of a deterministic standpoint or the stochastic standpoint or the solving can divide the treated standpoint roughly like the batch processing form or the serial processing form, etc. At this time, the method in the batch processing form from a deterministic standpoint is treated as nonlinear programming problem of objective function, and a lot of methods that make a gradient method system algorithm a center are designed. It is very difficult the problem of the local minimum point aversion a difficult thing, and to solve this in this case systematically. It is often treated to depend as minimization problem of objective function as a state estimation problem of the non-linear system or a parameter estimation problem. On the other hand, there is an estimation method and recursive maximum a posteriori (MAP) estimation method in maximum likelihood (ML) as a typical method at this time when treating by the serial processing form from the stochastic standpoint. When recursive ML or recursive MAP estimation method (RMAP) was used for the solving of a former problem, the solving of a former problem was able to be done if the consistent estimator was able to be obtained because a former problem was reduced to the problem of the conformity securing of the estimator. In this paper, convergence analysis of RMAP estimator, when used as a solver for NLS problem, is presented. Based on a quadratic representation without residue for the value of the object function at true parameters, sufficient conditions to ensure asymptotic convergence are established. Furthermore, it is shown that the design parameter in the paper plays an important role for convergence of the RMAP. Also, it is shown that the setting of is given as the solution of a continuous-time algebraic Riccati equation (CARE). Moreover, the conformity of Recursive Gauss-Newton (RGN) Method that is one of the standard solutions of the NLS problem is considered, and RGN is shown that the conformity is not secured. Numerical example indicates that the proposed method gives acceptable performance.
徳島文理大学の論文

非線形最小2乗問題に対する一手法

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