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Particle Filter

leimao.github.io

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Re: Particle Filter

#11

Post by cityroasted »

blauditore wrote: post #10

The term "monte carlo methods" in statistics/probability bothers me, since it literally just means trying out, or simulating. I can't help but think someone started using it to just sound smart. Such shenanigans seem make science harder to grasp especially for newcomers, so I think it would be better to keep naming simple and obvious where possible. There are enough topics that are too abstract, so it can't be done t…

My understanding is Monte Carlo method refers to sampling using a random component, evoking the casinos of the real Monte Carlo

Re: Particle Filter

#12

Post by isatty »

jvanderbot wrote: post #4

Ive never found a practical implementation of particle filters that was deployed on a real system. PF are a poor choice for tracking a solution that does not have wildly divergent measurements that can cause "lost robot" types of situations. Even then, PF is a fine temporary and high cost stopgap to converge to a "filterable" solution with only one predominant mode / a tight cluster of oarticles. At that point, a clo…

It’s definitely a high cost implementation but it’s worked well as a brute force solution for multiple non linear measurements like multiple cameras + sonar etc.

Re: Particle Filter

#13

Post by n3ur0n »

blauditore wrote: post #10

The term "monte carlo methods" in statistics/probability bothers me, since it literally just means trying out, or simulating. I can't help but think someone started using it to just sound smart. Such shenanigans seem make science harder to grasp especially for newcomers, so I think it would be better to keep naming simple and obvious where possible. There are enough topics that are too abstract, so it can't be done t…

> just means trying out

this statement trivializes a very hard problem.

> literally just means trying out, or simulating

Simulating is an incredibly hard problem and MC methods and theory is an incredibly rich area of study. Some tools I use for my work in probabilistic machine learning models are MCMC techniques like HMC (Hamiltonian Monte Carlo), variance reduction techniques (Rao Blackwellization). If you would like to learn more, here is a great course: https://statweb.stanford.edu/~owen/mc/ -- you can take a look at the syllabus. Also, Casella Berger is a standard MC method book.

Re: Particle Filter

#14

Post by jvanderbot »

galangalalgol wrote: post #6
jvanderbot wrote: post #4

Ive never found a practical implementation of particle filters that was deployed on a real system. PF are a poor choice for tracking a solution that does not have wildly divergent measurements that can cause "lost robot" types of situations. Even then, PF is a fine temporary and high cost stopgap to converge to a "filterable" solution with only one predominant mode / a tight cluster of oarticles. At that point, a clo…

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.

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.

Re: Particle Filter

#15

Post by jvanderbot »

isatty wrote: post #12
jvanderbot wrote: post #4

Ive never found a practical implementation of particle filters that was deployed on a real system. PF are a poor choice for tracking a solution that does not have wildly divergent measurements that can cause "lost robot" types of situations. Even then, PF is a fine temporary and high cost stopgap to converge to a "filterable" solution with only one predominant mode / a tight cluster of oarticles. At that point, a clo…

It’s definitely a high cost implementation but it’s worked well as a brute force solution for multiple non linear measurements like multiple cameras + sonar etc.

MH EKF has worked much better for range, bearing, and visual association in TRL 9 applications I've worked on.

Re: Particle Filter

#16

Post by phreeza »

blauditore wrote: post #10

The term "monte carlo methods" in statistics/probability bothers me, since it literally just means trying out, or simulating. I can't help but think someone started using it to just sound smart. Such shenanigans seem make science harder to grasp especially for newcomers, so I think it would be better to keep naming simple and obvious where possible. There are enough topics that are too abstract, so it can't be done t…

The alternative would be calling it something like stochastic methods, which would probably be even more confusing. Monte Carlo is a convenient term to make it clear the stochastic part is in the method itself, and not in the measurements or the modeled system.

Re: Particle Filter

#17

Post by kkylin »

blauditore wrote: post #10

The term "monte carlo methods" in statistics/probability bothers me, since it literally just means trying out, or simulating. I can't help but think someone started using it to just sound smart. Such shenanigans seem make science harder to grasp especially for newcomers, so I think it would be better to keep naming simple and obvious where possible. There are enough topics that are too abstract, so it can't be done t…

I don't think there's universal agreement about terminology, but to many of us who work in the area, Monte Carlo (MC) means specifically using random sampling to estimate a deterministic quantity. For example, MC methods can be used to compute the ground state energy of atoms and molecules. This in principle can also be done by solving the many-body Schroedinger equation, but direct numerical solution is simply not feasiable except for systems with very few degrees of freedom. In contrast, the term "simulation" often (but not always) means to simulate to take a look.

As is usual with these things, the boundary is not sharp. One selling point of sampling is that with greater expense you also get more information about the "energy landscape," can do uncertainty quantification, etc.

Re: Particle Filter

#18

Post by galangalalgol »

jvanderbot wrote: post #14
galangalalgol wrote: post #6

Earlier quoted context omitted.

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.

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…

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.

Re: Particle Filter

#20

Post by mturmon »

blauditore wrote: post #10

The term "monte carlo methods" in statistics/probability bothers me, since it literally just means trying out, or simulating. I can't help but think someone started using it to just sound smart. Such shenanigans seem make science harder to grasp especially for newcomers, so I think it would be better to keep naming simple and obvious where possible. There are enough topics that are too abstract, so it can't be done t…

Those “someones” who started using it were Stan Ulam and John von Neumann: https://en.wikipedia.org/wiki/Monte_Carlo_method#History

It’s a beautiful piece of math history.

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