On measurement structures and the maximal accuracy of linear filters

The linear filtering problem cast in convolution operator form is linked with a deterministic optimal control problem. Hilbert space analysis is employed and this permits theory for the maximal accuracy of the optimal control problem to be applied verbatim to the filtering problem. The relevance of the convolution form of the filtering problem is demonstrated by its use in specifying several output or measurement structure problems. These local and global measurement structure problems for a linear filter are exemplified.