I have known that Particle filter is suitable for non-linear non-Gaussian systems. Kalman filter is optimal in linear Gaussian system. However, I have no evidence that Kalman filtering is better than particle filtering in linear Gaussian systems.
So I hope someone can help me , such as a paper that Kalman filtering is better than particle filtering in linear Gaussian systems, or something.
Yes, Kalman filter is one of the best filters for the linear Gaussian system.
Hi Santhakumar Mohan ,Do you have some paper about this answer? or other something is ok.
If by Linear Gaussian system you mean a linear dynamic system with Gaussian process noise and Gaussian measurement noise, then Boris Blagov has answered your question precisely.
In many other situations, e.g., say the noise is from a Rayleigh distribution, and the dynamics are linear, the Kalman filter will still be the best linear estimator, but it is no longer the maximum likelihood estimator.
For nonlinear dynamic systems, the filtering problem is far more involved, and there are in general no proofs of optimality or even efficient calculation. The Extended Kalman Filter only provides local convergence of state estimates, provided the initial conditions are set in the correct neighborhood.
Hi Kartik B Ariyur , Particle filter is suitable for non-linear non-Gaussian systems .so if the noise is from a Rayleigh distribution or others, and the dynamics are linear , is particle filter worse than kalman filter ??
In the scenario where noise and actual signal have same frequency practical filters fail to work which lead to the emergence of prediction(Kf)
They are both the same in that case because both are baysian estimator. For simplicity KF is directly effective in linear systems associated with Gaussian noise
But if your system doesn't fit nicely into a linear model, or your sensor uncertainty doesn't look very gaussian, a particle filter lets you handle almost any kind of model, by discretizing the problem into individual "particles" -- each one is basically one possible state of your model, and a collection of a sufficiently large number of particles lets you handle any kind of probability distribution, the particle filter is your estimator of choice.
Problem is, you may have a helluva lot of particles, and it gets exponentially worse as you have a model with more state variables. And there are other funny problems, like "particle depletion" -- once you've run out of particles in one area of the solution space, it's hard to get them back, so the correct estimate may just drop out permanently unless you have a very large number of particles. This is an active area of research, with a lot of great work all the time, so these problems will be mitigated. Also, it's hard to allocate the correct amount of computation in advance, the only decent way I know of to know how many particles you'll need is with lots of data and simulation or test.
But it's kinda like using a heuristic vs. an algorithm -- particle filters won't always guarantee your answer, and may take more computation than you have available, while Kalman filters will terminate and give a decent answer, so long as your model fits.
*good luck
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