**7. Conclusions**

The estimation of the wheel loads is formulated as an input estimation problem. A quarter-car model with load transfer and tire normal force is used as the estimation model. Two observers are designed. A Youla controller is designed to minimize the error between the measurement and the estimated model output in the Youla Controller Output Observer framework. Similarly, unobservable states of the quarter-car model are removed to use the Unbiased Minimum Variance Filter. Since the design of the YCOO is based on the frequency domain and the closed-loop transfer functions *Tu*, *Su*, and *Y*, it directly addresses the trade-off among noise rejection, high bandwidth, and good robustness when tuning the observer.

Both observers were tested in simulation and provide good estimates as long as the model possesses a good enough representation of the suspension. Moreover, the anti-roll bar introduces coupling between the two wheels of the same axle. In this case, the quarter-car estimation model cannot be used and should be replaced by a half-car model. Despite using different approaches to solve the input estimation problem and different design methods, both controllers give similar performance and robustness, but the proposed YCOO provides better noise rejection than the UMVF. The YCOO provides a much simpler structure and observer tuning than the UMVF as it does not require the system to be observable and requires only two measurement when the UMVF needs a third measurement with additional signal processing.

**Author Contributions:** Conceptualization, L.F. and F.A.; methodology, L.F., F.A. and J.V.A.; software, L.F.; validation, L.F. and F.A.; formal analysis, L.F., F.A., and J.V.A.; supervision: M.K. and R.J.; writing—original draft preparation, review and editing: L.F. and F.A.; funding acquisition: F.A. and M.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded under grant Ford Motor Company: AFFORDM.

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

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** The authors thank Ford Motor Company for its support of this work.

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

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**

