Linear Estimation in Krein Spaces - Part I: Theory

We develop a self-contained theory for linear estimation in Krein spaces. The derivation is based on simple concepts such as projections and matrix factorizations, and leads to an interesting connection between Krein space projection and the recursive computation of the stationary points of certain second order (or quadratic) forms. We use the innovations process to obtain a general recursive linear estimation algorithm. When specialized to a state space structure, the algorithm yields a Krein space generalization of the celebrated Kalman lter with applications in several areas such as H 1-ltering and control, game problems, risk sensitive control, and adaptive ltering. is submitted for publication with the understanding that the US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the oocial policies or endorsements, either express or implied, of the Advanced Research Projects Agency, or the US Government.