# On stability of a class of filters for non-linear stochastic systems

arXiv: https://arxiv.org/abs/1809.05667 · HTML: https://mlsanity.com/paper/1809.05667/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2018.

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

- [Probabilistic Estimation of Instantaneous Frequencies of Chirp Signals](https://mlsanity.com/paper/2205.06306/) (2022)

## Abstract (arXiv)

This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under certain strong assumptions. The class of filters encompasses the extended and unscented Kalman filters and most other Gaussian assumed density filters and their numerical integration approximations. The stability results are in the form of time-uniform mean square bounds and exponential concentration inequalities for the filtering error. In contrast to existing results, it is not always necessary for the model to be exponentially stable or fully observed. We review three classes of models that can be rigorously shown to satisfy the stringent assumptions of the stability theorems. Numerical experiments using synthetic data validate the derived error bounds.