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I've used them in robotics and for tracking satellites going overhead via radar. Apparently they're also used by economists for guessing the state of the econo

I've used them in robotics and for tracking satellites going overhead via radar. Apparently they're also used by economists for guessing the state of the economy, along with other filters in the standard robotics toolkit.

mesofile 3y ago
Purely idle curiosity – I've heard a lot about the Kalman filter over the years, it's a popular subject here, but what are the other filters in the standard robotics toolkit?
- Symmetry 3y ago
  Particle filters would be the main other one I'd reach for. The ability to represent multiple hypotheses is a big advantage they have.
  - dplavery92 3y ago
    You can also construct multiple hypothesis trackers from multiple Kalman Filters, but there is a little more machinery. For example, Interacting Multiple Models (IMM) trackers may use Kalman Filters or Particle Filters, and a lot of the foundational work by Bar-Shalom and others focuses on Kalman Filters.
- elbear 3y ago
  Someone in another comment mentioned a book called Probabilistic Robotics. I think that covers everything.
- dplavery92 3y ago
  The Kalman filter has a family of generalizations in the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF.) Also common in robotics applications is the Particle Filter, which uses a Monte Carlo approximation of the uncertainty in the state, rather than enforcing a (Gaussian) distribution, as in the traditional Kalman filter. This can be useful when the mechanics are highly nonlinear and/or your measurement uncertainties are, well, very non-Gaussian. Sebastian Thrun (a CMU robotics professor in the DARPA "Grand Challenge" days of self-driving cars) made an early Udacity course on Particle Filters.
- mesofile 3y ago
  Thanks to everyone who replied.
bafe 3y ago
Ensemble kalman filter (and similar techniques like variational assimilation) are also used heavily in the geosciences to assimilate measurements and model data in order to obtain a "posterior observation" which can be understood intuitively as an interpolation between model and observation weighted by their relative uncertainty (and covariance)

mesofile 3y ago

Purely idle curiosity – I've heard a lot about the Kalman filter over the years, it's a popular subject here, but what are the other filters in the standard robotics toolkit?

Symmetry 3y ago
Particle filters would be the main other one I'd reach for. The ability to represent multiple hypotheses is a big advantage they have.
- dplavery92 3y ago
  You can also construct multiple hypothesis trackers from multiple Kalman Filters, but there is a little more machinery. For example, Interacting Multiple Models (IMM) trackers may use Kalman Filters or Particle Filters, and a lot of the foundational work by Bar-Shalom and others focuses on Kalman Filters.
elbear 3y ago
Someone in another comment mentioned a book called Probabilistic Robotics. I think that covers everything.
dplavery92 3y ago
The Kalman filter has a family of generalizations in the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF.) Also common in robotics applications is the Particle Filter, which uses a Monte Carlo approximation of the uncertainty in the state, rather than enforcing a (Gaussian) distribution, as in the traditional Kalman filter. This can be useful when the mechanics are highly nonlinear and/or your measurement uncertainties are, well, very non-Gaussian. Sebastian Thrun (a CMU robotics professor in the DARPA "Grand Challenge" days of self-driving cars) made an early Udacity course on Particle Filters.
mesofile 3y ago
Thanks to everyone who replied.

bafe 3y ago

Ensemble kalman filter (and similar techniques like variational assimilation) are also used heavily in the geosciences to assimilate measurements and model data in order to obtain a "posterior observation" which can be understood intuitively as an interpolation between model and observation weighted by their relative uncertainty (and covariance)