# On Kalman-Bucy filters, linear quadratic control and active inference

arXiv: https://arxiv.org/abs/2005.06269 · HTML: https://mlsanity.com/paper/2005.06269/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2020.

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

- [Predictive Coding: a Theoretical and Experimental Review](https://mlsanity.com/paper/2107.12979/) (2021)
- [Active Inference in Robotics and Artificial Agents: Survey and Challenges](https://mlsanity.com/paper/2112.01871/) (2021)
- [Neural Kalman Filtering](https://mlsanity.com/paper/2102.10021/) (2021)
- [World models of environment, agent and joint agent-environment systems](https://mlsanity.com/paper/2608.20401/) (2026)

## Abstract (arXiv)

Linear Quadratic Gaussian (LQG) control is a framework first introduced in control theory that provides an optimal solution to linear problems of regulation in the presence of uncertainty. This framework combines Kalman-Bucy filters for the estimation of hidden states with Linear Quadratic Regulators for the control of their dynamics. Nowadays, LQG is also a common paradigm in neuroscience, where it is used to characterise different approaches to sensorimotor control based on state estimators, forward and inverse models. According to this paradigm, perception can be seen as a process of Bayesian inference and action as a process of optimal control. Recently, active inference has been introduced as a process theory derived from a variational approximation of Bayesian inference problems that describes, among others, perception and action in terms of (variational and expected) free energy minimisation. Active inference relies on a mathematical formalism similar to LQG, but offers a rather different perspective on problems of sensorimotor control in biological systems based on a process of biased perception. In this note we compare the mathematical treatments of these two frameworks for linear systems, focusing on their respective assumptions and highlighting their commonalities and technical differences.