# An Approach to Duality in Nonlinear Filtering

arXiv: https://arxiv.org/abs/1809.10762 · HTML: https://mlsanity.com/paper/1809.10762/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2018.

## Built on by (most cited first, 1 of 1)

- [Dual Filter: A Transformer-like Inference Architecture for Hidden Markov Models](https://mlsanity.com/paper/2505.00818/) (2025)

## Abstract (arXiv)

This paper revisits the question of duality between minimum variance estimation and optimal control first described for the linear Gaussian case in the celebrated paper of Kalman and Bucy. A duality result is established for nonlinear filtering, mirroring closely the original Kalman-Bucy duality of control and estimation for linear systems. The result for the finite state-space continuous time Markov chain is presented. It's solution is used to derive the classical Wonham filter.