Random process reconstruction from multiple noisy source observations

Abstract

The problem addressed in this paper is the reconstruction of a continuous-time stationary random process from noisy sampled observations coming from different sources. An optimal solution in terms of linear filtering of observed samples is derived and the expression of the corresponding minimum reconstruction error power is given. Moreover, two equivalent reconstruction schemes are given. The first one is recursive, involving two filter banks. Its main interest is that adding or suppressing an input does not affect the whole scheme. The second scheme is symmetric and uses only one filter bank. However, to add a new input requires a complete modification of all the filter transfer functions. Simulation examples are given to prove the application of the reconstruction scheme