The second-order least squares (SLS) estimation is a parameter estimation method for nonlinear regression model based on second-order moment information. Its optimization is a non-convex problem, even for the linear regression. Existing research does not propose a systematic and complete calculation method for the optimization corresponding to this estimation. Although this is a smooth optimization, the objective function is non-convex, which causes traditional methods to easily fall into local solutions or fail to obtain the desired accuracy. In this paper, we propose a systematic calculation method for SLS estimation, which is called alternate updating (AU) method. First, we give the assumptions needed for this estimation in linear regression and analyze some potential properties. Second, we design an alternate updating method based on a strong first-order optimality condition and establish its convergence. In the end, the effectiveness of the alternating updating method is demonstrated by numerical simulations.
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