Answers.Body: <p><a href="https://en.m.wikipedia.org/wiki/Kalman_filter" rel="nofollow noreferrer">Kalman filter</a> is what you're looking for.</p>
  <p>According to Wikipedia:</p>
  <blockquote>
  <p>The Kalman filter may be regarded as analogous to the hidden Markov model, with the key difference that the hidden state variables take values in a continuous space (as opposed to a discrete state space as in the hidden Markov model).</p>
  </blockquote>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-10-22T05:31:17.630Z
Answers.LastActivityDate: 2020-10-22T05:31:17.630Z
Answers.UserDisplayName: Miguel Rochefort
Body: <p>I understand that Hidden Markov Models are used to learn about hidden variables <span class="math-container">$z_i$</span> with the help of observable variables <span class="math-container">$\xi_i$</span>. On Wikipedia, I read that while the <span class="math-container">$\xi_i$</span>'s can be continuous (say Gaussian), the <span class="math-container">$z_i$</span>'s are <strong>discrete</strong>. Is this necessary, and why? Are there ways in which I could extend this to continuous domains?</p>
  
Tags: <machine-learning><hidden-markov-model><kalman-filter>
Title: Is there an equivalent model to the Hidden Markov Model for continuous hidden variables?
UserDisplayName: stoic-santiago
ThreadText: # Is there an equivalent model to the Hidden Markov Model for continuous hidden variables?
  
  (Asked by: username_0 on 2020-10-21)
  
  I understand that Hidden Markov Models are used to learn about hidden variables $z\_i$ with the help of observable variables $\xi\_i$. On Wikipedia, I read that while the $\xi\_i$'s can be continuous (say Gaussian), the $z\_i$'s are **discrete**. Is this necessary, and why? Are there ways in which I could extend this to continuous domains?
  
  **Tags:** machine-learning, hidden-markov-model, kalman-filter
  
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  ## 1 answers
  
  ### Answer by username_1 on 2020-10-22. Score: 2 | Accepted answer
  
  [Kalman filter](https://en.m.wikipedia.org/wiki/Kalman_filter) is what you're looking for.
  
  According to Wikipedia:
  
  > The Kalman filter may be regarded as analogous to the hidden Markov model, with the key difference that the hidden state variables take values in a continuous space (as opposed to a discrete state space as in the hidden Markov model).
  
  
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