This paper is concerned with the finite-time filtering problem for linear continuous time-varying systems with uncertain observations and ℒ 2-norm bounded noise. The design of finite-time filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein state-space model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite-time filtering problem is solved. A numerical example is given to illustrate the performance of the filter.
Huihong Zhao. Chenghui Zhang. "Finite-Time Filtering for Linear Continuous Time-Varying Systems with Uncertain Observations." J. Appl. Math. 2012 (SI08) 1 - 11, 2012. https://doi.org/10.1155/2012/710904