# Nonlinear Kalman Filtering with Divergence Minimization

arXiv: https://arxiv.org/abs/1705.00722 · HTML: https://mlsanity.com/paper/1705.00722/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2017.

## Built on by (most cited first, 6 of 6)

- [Variational Nonlinear Kalman Filtering with Unknown Process Noise Covariance](https://mlsanity.com/paper/2305.03914/) (2023)
- [Distributed Variational Inference for Online Supervised Learning](https://mlsanity.com/paper/2309.02606/) (2023)
- [Joint State Estimation and Noise Identification Based on Variational Optimization](https://mlsanity.com/paper/2312.09585/) (2023)
- [BOLT: Block-Orthonormal Lanczos for Trace estimation of matrix functions](https://mlsanity.com/paper/2505.12289/) (2025)
- [Nonlinear Kalman Filtering with Reparametrization Gradients](https://mlsanity.com/paper/2303.04450/) (2023)
- [Generative Bayesian Filtering for State Estimation](https://mlsanity.com/paper/2607.20521/) (2026)

## Abstract (arXiv)

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and α-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper we propose novel algorithms to optimize the forward and reverse forms of the KL divergence, as well as the alpha-divergence which contains these two as limiting cases. Unlike previous approaches, our algorithms do not make approximations to the divergences being optimized, but use Monte Carlo integration techniques to derive unbiased algorithms for direct optimization. We assess performance on radar and sensor tracking, and options pricing problems, showing general improvement over the UKF and EKF, as well as competitive performance with particle filtering.