Observation strategy for a parallel connection of discrete-time linear systems

The problem of optimizing the observation structure of a complex stochastic linear discrete system is considered. The system consists of p single-output linear subsystems excited by uncorrelated noises: the output of the overall system is a linear, possibly time-varying transformation of the outputs of the subsystems. The aim is to find, for each time k, the transformation that, given the covariance of the filtered estimate at time k -1, minimizes a suitable measure of the estimation error at time k. The problem is solved by using some results from fractional programming: it turns out that one subsystem must be observed, the decision rule being extremely simple. Several numerical experiments are reported: they show that iterative application of the selection rule leads to a periodic (or constant) output transformation to which a periodic (or constant) error covariance matrix corresponds.