**7. Conclusions**

This paper derives an AM-MIFSG estimation algorithm for Hammerstein output-error systems based on the key-term separation principle and auxiliary model identification idea. By means of the key-term separation principle, all the parameters in the linear and nonlinear blocks are separated, and the unknown variables in the identification model are replaced by the outputs of the auxiliary models. The analysis of the simulation results shows that the proposed algorithm obtains better parameter estimation performance than the AM-MISG algorithm. However, there also exist many topics that need to be further discussed. For example, is this algorithm still effective for systems with missing data? And is the performance of the algorithm can be improved by introducing a time-varying differential order *α*? These topics remain as open problems for future studies.

**Author Contributions:** Conceptualization, C.X.; methodology, Y.M.; software, C.X.; validation, C.X.; formal analysis, C.X.; investigation, C.X.; resources, Y.M.; data curation, Y.M.; writing-original draft preparation, Y.M.; writing—review and editing, C.X.; visualization, C.X.; supervision, Y.M.; project administration, Y.M.; funding acquisition, C.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported in part by the National Natural Science Foundation of China (No. 62103167), and in part by the Natural Science Foundation of Jiangsu Province (No. BK20210451), and the research project of Jiangnan University (Nos. JUSRP12028 and JUSRP12040).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
