Minimum variance constrained estimator

Mishra, Prabhat K.; Chowdhary, Girish; Mehta, Prashant G.

doi:10.1016/j.automatica.2021.110106

Cited by 4 publications

(1 citation statement)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [29], it is used to obtain the solution to a class of singular regulator problems, and in [30], the Lagrangian dual for an MEE problem with truncated measurement noise is considered. Numerical algorithms for (2) and its extensions appear in [31]- [34]. Prior to our work, it was widely believed that the nonlinear extension of minimum variance duality is not possible [4].…”

Section: A Background and Literature Reviewmentioning

confidence: 99%

Duality for Nonlinear Filtering II: Optimal Control

Kim¹,

Mehta²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

This paper is concerned with the development and use of duality theory for a nonlinear filtering model with white noise observations. The main contribution of this paper is to introduce a stochastic optimal control problem as a dual to the nonlinear filtering problem. The mathematical statement of the dual relationship between the two problems is given in the form of a duality principle. The constraint for the optimal control problem is the backward stochastic differential equation (BSDE) introduced in the companion paper. The optimal control solution is obtained from an application of the maximum principle, and subsequently used to derive the equation of the nonlinear filter. The proposed duality is shown to be an exact extension of the classical Kalman-Bucy duality, and different from other types of optimal control and variational formulations given in literature.

show abstract