Unknown input and state estimation for linear discrete-time systems with missing measurements and correlated noises

Abstract

This paper is concerned with the problem of simultaneous input and state estimation for a class of linear discrete-time systems with missing measurements and correlated noises. The missing measurements occur in a random way and are governed by a series of mutually independent random variables obeying a certain Bernoulli distribution. The process and measurement noises under consideration are correlated at the same time instant. Our attention is focused on the design of recursive estimators for both input and state such that, for all missing measurements and correlated noises, the estimators are unbiased and the estimation error covariances are minimized. This objective is achieved using direct algebraic operation and the design algorithm for the desired estimators is given. Finally, an illustrative example is presented to demonstrate the effectiveness of the proposed design scheme.

Keywords:

• State and input estimation
• unbiasedness
• minimum variance
• missing measurements
• correlated noises

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61134009], [grant number 61473076]; the Shu Guang project of Shanghai Municipal Education Commission and Shanghai Education Development Foundation [grant number 13SG34]; the Fundamental Research Funds for the Central Universities, the DHU Distinguished Young Professor Program and the Alexander von Humboldt Foundation of Germany.