In this section
@article{Astolfi:2026:10.1109/TAC.2026.3681142,
author = {Astolfi, A and Bhattacharjee, D and Manca, G and Sassano, M},
doi = {10.1109/TAC.2026.3681142},
journal = {IEEE Transactions on Automatic Control},
title = {Steady-state optimal filtering for linear and nonlinear systems},
url = {http://dx.doi.org/10.1109/TAC.2026.3681142},
year = {2026}
}
TY - JOUR
AB - The steady-state optimal filtering problem for linear systems is revisited with the objective of establishing further insights on the structure of the underlying solution. It is shown that, in addition to the invariance property of a suitably defined hyperplane, the optimal filter is related to a triangularizing change of coordinates for certain Hamiltonian dynamics associated to the filtering problem. The implication of the above observation is twofold. First, the novel interpretation admits a conceptually straightforward counterpart in the nonlinear setting in terms of invariant distributions. The latter then permit the design of local steady-state optimal filters for nonlinear systems that only rely upon the solutions of linear partial differential equations, the solution of which is independent from the specific time history of the measured output. The conditions may be further leveraged to determine a polynomial algebraic equation, which characterizes the solution of the filtering problem and which is expressed in the entries of the optimal filter gain alone, hence circumventing the need for solving the underlying Riccati equation.
AU - Astolfi,A
AU - Bhattacharjee,D
AU - Manca,G
AU - Sassano,M
DO - 10.1109/TAC.2026.3681142
PY - 2026///
SN - 0018-9286
TI - Steady-state optimal filtering for linear and nonlinear systems
T2 - IEEE Transactions on Automatic Control
UR - http://dx.doi.org/10.1109/TAC.2026.3681142
ER -