What is the Lagrangian for Nonlinear Filtering

Jin Won Kim, Prashant G. Mehta, Sean P. Meyn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Duality between estimation and optimal control is a problem of rich historical significance. The first duality principle appears in the seminal paper of Kalman-Bucy, where the problem of minimum variance estimation is shown to be dual to a linear quadratic (LQ) optimal control problem. Duality offers a constructive proof technique to derive the Kalman filter equation from the optimal control solution.This paper generalizes the classical duality result of Kalman-Bucy to the nonlinear filter: The state evolves as a continuous-time Markov process and the observation is a nonlinear function of state corrupted by an additive Gaussian noise. A dual process is introduced as a backward stochastic differential equation (BSDE). The process is used to transform the problem of minimum variance estimation into an optimal control problem. Its solution is obtained from an application of the maximum principle, and subsequently used to derive the equation of the nonlinear filter. The classical duality result of Kalman-Bucy is shown to be a special case.

Original languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1607-1614
Number of pages8
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period12/11/1912/13/19

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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