When designing a robust total least-squares(RTLS) estimation algorithm based on M-estimation theory, the total least-squares(TLS) estimation is not suitable for residual prediction, and reweighting based on individual random variable residuals has theoretical flaws. We derive the TLS estimation iteration formula based on multiplicative error model, theoretically explain the equation residuals or total residuals, and explain that this residual has the properties of least-squares(LS) estimation residuals. Then, considering the robustness in both observation space and structural space, an RTLS estimation algorithm is designed based on equation residuals or total residuals. Finally, through Monte Carlo experiments, the RTLS algorithm is compared with other reweighting strategies in terms of robustness, efficiency, and iteration speed, demonstrating the advantages of the proposed RTLS algorithm.

equation residuals  /  total least-squares(TLS)  /  robust estimation  /  multiplicative error