This article discusses the problem of state estimation for nonlinear systems with uncertain measurements. The authors propose a new method based on the theory of optimal control, which combines the benefits of both the maximum likelihood (ML) and Bayesian estimators. The proposed method is called "Bayesian-like" because it uses a prior distribution that is similar to the Bayesian approach, but with a different way of computing the prior weighting factor.
The authors show that their method can provide accurate estimates even when the measurements are highly uncertain, by using a large value for the regularization parameter. They also prove that the proposed method is robust in the sense that it can handle a wide range of initial conditions and noise levels.
The article is organized as follows
- Introduction: The authors introduce the problem of state estimation for nonlinear systems with uncertain measurements, and explain the motivation behind their proposed method.
- Bayesian-like method: The authors describe their proposed method, which combines the benefits of both ML and Bayesian estimators. They show that the prior distribution used in their method is similar to the Bayesian approach, but with a different way of computing the prior weighting factor.
- Contraction analysis: The authors perform a contraction analysis of their proposed method, showing that it can provide accurate estimates even when the measurements are highly uncertain. They prove that the proposed method is robust in the sense that it can handle a wide range of initial conditions and noise levels.
- Conclusion: The authors conclude that their proposed method provides an effective solution to the problem of state estimation for nonlinear systems with uncertain measurements, and highlight some potential applications of their method.
Overall, this article provides a comprehensive overview of the proposed method and its theoretical guarantees, making it a valuable contribution to the field of state estimation. The authors use clear and concise language throughout the article, making it accessible to readers without prior knowledge of the subject. Additionally, they provide numerous engaging metaphors and analogies to help demystify complex concepts and make the article more readable.
