We introduce a framework for data assimilation (DA) in which the data is split into multiple
sets corresponding to low‐rank projections of the state space. Algorithms are developed that …

This work proposes a detectability condition for linear time-varying systems based on the
exponential dichotomy spectrum. The condition guarantees the existence of an observer …

This papers shows that nonlinear filter in the case of deterministic dynamics is stable with
respect to the initial conditions under the conditions that observations are sufficiently rich …

The theory of nonlinear filtering concerns with the estimation of underlying signal (which is
Markovian) given that it has been indirectly and partially observed via. an observational …