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As you say, measurements with multimodal error, but also measurements with horribly non linear observation or time models. It has to be pretty bad though, other

As you say, measurements with multimodal error, but also measurements with horribly non linear observation or time models. It has to be pretty bad though, otherwise a UKF would be better.

credit_guy 7y ago
For those not familiar, UKF = unscented Kalman filter. And by the way, there is no such thing as "scented" KF. The inventor of the UKF, whose name was Jeff Uhlmann, didn't want this method to be called after his name, so he picked a random word in the dictionary. [1] https://en.wikipedia.org/wiki/Unscented_transform https://en.wikipedia.org/wiki/Unscented_transform
jvanderbot 7y ago
UKF is, in my mind, a principled version of the particle filter. Its a really clean way of operating and I cant emphasize enough the power of explicitly conditioning on decision variables, i.e. multi hypothesis formulations of UKF, EKF, or even Batch filters, all of which require orders of magnitude less CPU / mem. (e.g. I'm not sure about this echo or that, so I'll propegate explicitly conditioned on those unknowns two reasonable hypotheses that are effectively unimodal rather than sampling the entire posterior probability space). The exponential set of probabilities then allows you to take action to remove hypotheses or trim by weight. And, this is only required when you encounter huge uncertainties nonlinearities or multimodalities, so it is explicitly adaptive to the situation. I've never seen a sampling or reweighting strategy that provides a decent job of this. PF is throwing CPU and memory at the problem, and it does reasonably well but for anything Ive worked on or dug into, the CPU and Memory is alwayd better used elsewhere in the system.
- galangalalgol 7y ago
  Agreed, by using PF you are throwing your hands up and admitting you have no idea how to model your observations. If you can correctly model any aspect of the problem that will be both better performing and more efficient. I use PF to help me figure out a distribution mostly. Even UKF is usually overkill for me. Anything less than 2n+1 sigma points gets beat by a 1st order ekf.

As you say, measurements with multimodal error, but also measurements with horribly non linear observation or time models. It has to be pretty bad though, otherwise a UKF would be better.

credit_guy 7y ago

For those not familiar, UKF = unscented Kalman filter. And by the way, there is no such thing as "scented" KF. The inventor of the UKF, whose name was Jeff Uhlmann, didn't want this method to be called after his name, so he picked a random word in the dictionary. [1] https://en.wikipedia.org/wiki/Unscented_transform https://en.wikipedia.org/wiki/Unscented_transform

jvanderbot 7y ago

UKF is, in my mind, a principled version of the particle filter. Its a really clean way of operating and I cant emphasize enough the power of explicitly conditioning on decision variables, i.e. multi hypothesis formulations of UKF, EKF, or even Batch filters, all of which require orders of magnitude less CPU / mem. (e.g. I'm not sure about this echo or that, so I'll propegate explicitly conditioned on those unknowns two reasonable hypotheses that are effectively unimodal rather than sampling the entire posterior probability space). The exponential set of probabilities then allows you to take action to remove hypotheses or trim by weight. And, this is only required when you encounter huge uncertainties nonlinearities or multimodalities, so it is explicitly adaptive to the situation. I've never seen a sampling or reweighting strategy that provides a decent job of this. PF is throwing CPU and memory at the problem, and it does reasonably well but for anything Ive worked on or dug into, the CPU and Memory is alwayd better used elsewhere in the system.

galangalalgol 7y ago
Agreed, by using PF you are throwing your hands up and admitting you have no idea how to model your observations. If you can correctly model any aspect of the problem that will be both better performing and more efficient. I use PF to help me figure out a distribution mostly. Even UKF is usually overkill for me. Anything less than 2n+1 sigma points gets beat by a 1st order ekf.