# Reinforcement Solver for H-infinity Filter with Bounded Noise

arXiv: https://arxiv.org/abs/2008.00674 · HTML: https://mlsanity.com/paper/2008.00674/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2020.

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

- [Smoothing Policy Iteration for Zero-sum Markov Games](https://mlsanity.com/paper/2212.01623/) (2022)

## Abstract (arXiv)

H-infinity filter has been widely applied in engineering field, but copping with bounded noise is still an open problem and difficult to solve. This paper considers the H-infinity filtering problem for linear system with bounded process and measurement noise. The problem is first formulated as a zero-sum game where the dynamic of estimation error is non-affine with respect to filter gain and measurement noise. A nonquadratic Hamilton-Jacobi-Isaacs (HJI) equation is then derived by employing a nonquadratic cost to characterize bounded noise, which is extremely difficult to solve due to its non-affine and nonlinear properties. Next, a reinforcement learning algorithm based on gradient descent method which can handle nonlinearity is proposed to update the gain of reinforcement filter, where measurement noise is fixed to tackle non-affine property and increase the convexity of Hamiltonian. Two examples demonstrate the convergence and effectiveness of the proposed algorithm.