# linear dynamical systems

(2.3 hours to learn)

## Summary

Linear dynamical systems (LDSs) are a kind of probabilistic model where a latent state evolves over time, all the variables are jointly Gaussian, and all the dependencies are linear. They are commonly used in robotics, computer vision (for tracking), and time series modeling. They are useful because we can perform exact posterior inference using Kalman filtering and smoothing. Algorithms for LDSs form the basis for analogous techniques in more general state space models, where some of the assumptions are not satisfied.

## Context

This concept has the prerequisites:

- multivariate Gaussian distribution (Linear dynamical systems are defined in terms of multivariate Gaussians.)
- conditional distributions (Linear dynamical systems are defined in terms of conditional distributions.)
- conditional independence (We can characterize linear dynamical systems in terms of conditional independence properties.)

## Core resources (read/watch one of the following)

## -Paid-

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 18.1-18.2, pages 631-640

## Supplemental resources (the following are optional, but you may find them useful)

## -Paid-

→ Probabilistic Robotics

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 13.3, up to 13.3.1, pages 635-637

## See also

- Other models of sequence data include: