Simulation, MMSE estimation, and interpolation of sampled continuous-time signals using factor graphs

Abstract

The paper proposes a factor graph representation of finite-dimensional continuous-time linear systems /filters driven by white Gaussian noise. Applications of such factor graphs include (i) simulation of the output signal at arbitrary discrete instants and (ii) MAP /MMSE /LMMSE estimation of the input signal, or of the state, or of the output signal at arbitrary discrete instants from noisy observations of the output signal at arbitrary discrete instants. Moreover, it is suggested that the MMSE estimate of the input signal from the output signal may be viewed as a generalization of a bandlimited estimate that is suited for real filters.