Talk:Particle filter

From Wikipedia, the free encyclopedia

Nice work but...

Quoting: "They are something like an Extended Kalman filter (EKF)"

They are NOTHING like an EKF!

  • The EKF:
  1. uses a 1st order linearisation around the current estimate.
  2. assumes that the process and measurement noise of the system are Gaussian.
  • The particle filter:
  1. uses the actual nonlinear dynamics for propagating the system.
  2. it can deal with extreme non-Gaussian and multimodal noise distributions.
  3. since it is a Monte Carlo based technique, it can incorporate easily and accurately in its structure any non-standard information (like hard/soft constrains, a-priori knowledge), improving thus its performance.

and many more...

(if I will have time I might add some new things in the article)

Have changed the offending phrase, hope it's an improvement.
As to why it's a valid comparison in the first place,
* It's in an encyclopedia article. That means it must be useful to non-specialists.
* The EKF does solve a related problem and it's probably the best known filtering algorithm after the Kalman filter itself, and the best known one for nonlinear state-space models (if there's a better known one put that in instead).  : * It's in an introductory paragraph, and an appropriate place for an informal introduction.
Of course there are major differences compared with the EKF, but it's still a worthwhile comparison for anyone new to particle filters.
I'm with the original author on this one. It's pedantic at best to say that particle filtering is "nothing" like EKF. Both exist to solve nonlinear estimation problems. Particle filtering, of course, goes about this in a very different way in trying to approximate important samples of the density rather than forcing a Gaussian estimate via linearization. But the general purpose and scope of the two approaches is quite similar. Mateoee 20:42, 4 November 2006 (UTC)

[edit] missing probability symbol

The definition could be clearer. For example, what is \beta \mid \beta_k in the definition? It means conditional probability of β, so why not say P(\beta \mid \beta_k)?

Not necessarily. If you're talking about:
\beta_k|\beta_{k-1} \sim p_{\beta_k|\beta_{k-1}}(\beta|\beta_{k-1})
then that means βk | βk − 1 is a distribution, not a probability. Cburnett July 8, 2005 16:05 (UTC)

[edit] Choice of P

How is the number of particles (P) normally chosen? Is it a necessarily large number and does each state have the same number of particles?

This number is picked based on the problem it's trying to solve, most importantly on the number of dimensions X models. The bigger the possible range of X, the more samples you need.

[edit] Eh?

I find this article too hard to understand right now. Examples could help. Thanks, --Abdull 14:52, 28 February 2006 (UTC)

Retrieved from "http://en.wikipedia.org../../../p/a/r/Talk%7EParticle_filter_e844.html"