  This paper describes a minimax state estimation approach for linear
Differential-Algebraic Equations (DAE) with uncertain parameters. The approach
addresses continuous-time DAE with non-stationary rectangular matrices and
uncertain bounded deterministic input. An observation's noise is supposed to be
random with zero mean and unknown bounded correlation function. Main results
are a Generalized Kalman Duality (GKD) principle and sub-optimal minimax state
estimation algorithm. GKD is derived by means of Young-Fenhel duality theorem.
GKD proves that the minimax estimate coincides with a solution to a Dual
Control Problem (DCP) with DAE constraints. The latter is ill-posed and,
therefore, the DCP is solved by means of Tikhonov regularization approach
resulting a sub-optimal state estimation algorithm in the form of filter. We
illustrate the approach by an synthetic example and we discuss connections with
impulse-observability.
