# Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances

arXiv: https://arxiv.org/abs/1412.5307 · HTML: https://mlsanity.com/paper/1412.5307/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2014.

## Built on by (most cited first, 4 of 4)

- [Automated Controller Calibration by Kalman Filtering](https://mlsanity.com/paper/2111.10832/) (2021)
- [Variational Nonlinear Kalman Filtering with Unknown Process Noise Covariance](https://mlsanity.com/paper/2305.03914/) (2023)
- [Joint State Estimation and Noise Identification Based on Variational Optimization](https://mlsanity.com/paper/2312.09585/) (2023)
- [State estimations and noise identifications with intermittent corrupted observations via Bayesian variational inference](https://mlsanity.com/paper/2604.02738/) (2026)

## Abstract (arXiv)

We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.