# Joint State Estimation and Noise Identification Based on Variational Optimization

arXiv: https://arxiv.org/abs/2312.09585 · HTML: https://mlsanity.com/paper/2312.09585/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 15 Dec 2023.

## Builds on (most cited first, 11 of 11)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models](https://mlsanity.com/paper/1703.04265/) (2017)
- [Fast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-family Approximations](https://mlsanity.com/paper/1906.02914/) (2019)
- [Handling the Positive-Definite Constraint in the Bayesian Learning Rule](https://mlsanity.com/paper/2002.10060/) (2020)
- [Nonlinear Kalman Filtering with Divergence Minimization](https://mlsanity.com/paper/1705.00722/) (2017)
- [Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances](https://mlsanity.com/paper/1412.5307/) (2014)
- [Variational Nonlinear Kalman Filtering with Unknown Process Noise Covariance](https://mlsanity.com/paper/2305.03914/) (2023)
- [Robust Kalman filters with unknown covariance of multiplicative noise](https://mlsanity.com/paper/2110.08740/) (2021)

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

- [State estimations and noise identifications with intermittent corrupted observations via Bayesian variational inference](https://mlsanity.com/paper/2604.02738/) (2026)

## Abstract (arXiv)

In this article, the state estimation problems with unknown process noise and measurement noise covariances for both linear and nonlinear systems are considered. By formulating the joint estimation of system state and noise parameters into an optimization problem, a novel adaptive Kalman filter method based on conjugate-computation variational inference, referred to as CVIAKF, is proposed to approximate the joint posterior probability density function of the latent variables. Unlike the existing adaptive Kalman filter methods utilizing variational inference in natural-parameter space, CVIAKF performs optimization in expectation-parameter space, resulting in a faster and simpler solution. Meanwhile, CVIAKF divides optimization objectives into conjugate and non-conjugate parts of nonlinear dynamical models, whereas conjugate computations and stochastic mirror-descent are applied, respectively. Remarkably, the reparameterization trick is used to reduce the variance of stochastic gradients of the non-conjugate parts. The effectiveness of CVIAKF is validated through synthetic and real-world datasets of maneuvering target tracking.