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为使原始LTS(least trimm ed squares)方法能够处理非线性问题,研究非线性LTS稳健估计方法。说明该方法的解一定是部分观测值的非线性最小二乘估计。该方法可通过求解非线性最小二乘问题得到确切解。基于MM EA(m in im um m ax im um exchange a lgorithm)算法和非线性最小二乘技术,构建求解非线性LTS估计近似解的算法。仿真结果表明非线性LTS估计方法能够同时抵抗来自X方向和Y方向的多个异常,与传统方法相比具有更好的稳健性。
In order to make the original LTS (least trimm ed squares) method able to deal with the nonlinear problem, the nonlinear LTS robust estimation method is studied. It shows that the solution of this method must be a nonlinear least-squares estimator of some observations. This method can be solved by solving the nonlinear least squares problem. Based on MM EA (Immersion imum Exchange Algorithm) algorithm and nonlinear least squares technique, an algorithm for solving the approximate LTS estimation solution is constructed. The simulation results show that the non-linear LTS estimation method can resist multiple anomalies from X-direction and Y-direction at the same time, and has better robustness than the traditional method.