A Novel State Estimator Based on Algebraic Parametric Method

It’s crucial to design a robust and accurate state estimator for a given observable LTI system of which the initial conditions are unknown, especially when the system is in a noisy environment. This paper handles this problem from the non-asymptotic perspective and provides a novel design process for estimators based on the algebraic parametric method. Unlike other algebraic-parametric-method-based state estimators, the proposed estimator regards the unknown initial conditions as values to be estimated, which can also provide some theoretical support for initial value settings in other estimation methods. Moreover, the separation theorem is proven to hold, so we can construct a state feedback controller based on the designed novel estimator to achieve the control objective. Finally, numerical simulations with a damping platform model illustrate that the proposed state estimator outperforms the traditional Luenberger state observer in robustness, accuracy, and fastness.