Estimation problems in an input-and-output system
The purpose of the paper is to investigate smooth and filtered estimation problems for input-and-output systems. After an introduction on stochastic operators in Hilbert space, the estimation problems are stated in the framework of input-and-output systems. One introduces the internal and external states for input-and-output systems, and the decomposition of the Hamiltonian system into two states is shown to be mathematically necessary and sufficient. It turns out that the external state is the well-known Kalman filter. The \(2\times 2\) scattering matrix is extended to the \(3\times 3\) one, and one obtains some general new results together with some well-known ones.
scientific article; zbMATH DE number 1471208
scientific article