A geometric approach to the reciprocal realization problem

A reciprocal realization of a stationary process {y(t )} is a stochastic system of the form y(t)=Cx (t), Mx(t)=N´x(t -1)+Nx(t+1)+e(t), where the state process {x(t)} is a reciprocal process. The minimality and observability of reciprocal realizations are analyzed by geometric methods analogous to those of A. Lindquist and G. Picci (1985). In particular, the concept of splitting subspaces plays a central role