  In this paper we study observation problem for linear 2-point BVP Dx=Bf
assuming that information about system input f and random noise \eta in system
state observation model y=Hx+\eta$ is incomplete (f and M\eta\eta' are some
arbitrary elements of given sets). A criterion of guaranteed (minimax)
estimation error finiteness is proposed. Representations of minimax estimations
are obtained in terms of 2-point BVP solutions. It is proved that in general
case we can only estimate a projection of system state onto some linear
manifold $F$. In particular, $F=L_2$ if $dim N(D H) = 0$. Also we propose a
procedure which decides if given linear functional belongs to $F$.
