An adaptive formulation of the smooth variable structure filter based on static multiple models

The Kalman filter (KF) is the most well-known estimation strategy that yields the optimal solution to the linear quadratic estimation problem. The system in such applications shall be well modelled assuming the presence of Gaussian noise. While the KF is effective under the stated conditions, it lacks robustness to other types of disturbances. Therefore, numerous variants of the KF have been developed to accommodate its limitations. The smooth variable structure filter (SVSF) is an alternative solution with improved robustness, especially in the case of modelling uncertainties. It is based on a sliding-mode technique that offers robustness at the cost of optimality. On the other hand, some algorithms and solutions involve with several possible operating modes and generate an estimation based on the output of these models, i.e., the static multiple models (SMMs) that obtain the estimates based on the weighted statistical fusing of the outputs of the models depending on the likelihood of each mode. This paper introduces an adaptive formulation of the SVSF that is reformulated based on SMMs. The proposed model is applied and tested on an electro-hydrostatic actuator (EHA). The proposed method takes the advantages of the SVSF's robustness and stability while reducing the estimation error due to the use of an adaptive modelling structure. The results show an improvement on the SVSF performance, where the root mean-squared errors are reduced by 41%, 99%, and 75% for the position, velocity, and acceleration estimated states. Therefore, the proposed method is a good candidate for parameter and state estimation problems.