2 research outputs found
Exact linear modeling using Ore algebras
Linear exact modeling is a problem coming from system identification: Given a
set of observed trajectories, the goal is find a model (usually, a system of
partial differential and/or difference equations) that explains the data as
precisely as possible. The case of operators with constant coefficients is well
studied and known in the systems theoretic literature, whereas the operators
with varying coefficients were addressed only recently. This question can be
tackled either using Gr\"obner bases for modules over Ore algebras or by
following the ideas from differential algebra and computing in commutative
rings. In this paper, we present algorithmic methods to compute "most powerful
unfalsified models" (MPUM) and their counterparts with variable coefficients
(VMPUM) for polynomial and polynomial-exponential signals. We also study the
structural properties of the resulting models, discuss computer algebraic
techniques behind algorithms and provide several examples