Parity space method: a continuous time approach

In this paper, the well-known parity space method is generalized to a continuous-time case both in deterministic and stochastic frameworks. As in the discrete-time case, it is shown that the parity space equations are equivalent to a continuous deadbeat observer or, taking into account measurement/process noise, to a finite-memory smoother. Both structures are infinite-dimensional by nature and can be implemented using a number of time delays. In the deterministic setting there is a significant liberty in choosing the delays. In the stochastic setting, to achieve optimality of the resulting parity equations, the delays are to be computed from the properties of noise.