Filtering discrete-time systems with multiplicative noise in L2 spaces with applications

In this work we adopt a novel formulation of thedistributed parameters recursive filter for discrete-time systemsevolving in L 2 spaces to widen the class of systems that canbe processed by a state estimation algorithm. Starting froma rigorous definition of Kronecker algebra on L 2 spaces thatinvolves both elements and bounded operators of L 2 , we providea computationally efficient solution in the case of linear systemswith multiplicative noises. We illustrate the potential applicationof the approach by developing a case-study concerning theconceptual design of a distributed thermo-couple in the presenceof the Nyquist–Johnson noise.