What is the role of resampling in the particle filtering?
Particle filtering uses a set of particles (also called samples) to represent the posterior distribution of some stochastic process given noisy and/or partial observations. In the resampling step, the particles with negligible weights are replaced by new particles in the proximity of the particles with higher weights.
What is filtering in artificial intelligence?
The particle filtering algorithm generates all the samples for one variable before moving to the next variable. Given a set of samples on some of the variables, resampling consists of taking n samples, each with their own weighting, and generating a new set of n samples, each with the same weight.
How does residual resampling reduce the variance of sampling?
Residual resampling: this approach tries to reduce the variance of the sampling, by first allocating each particle their integer floor of the expected value, and leave the rest to multinomial resampling. E.g. a particle with an expected value of 2.5 will have 2 copies in the resampled set and another one with an expected value of 0.5.
What does the weight represent in the resampling step?
The principle is that the weight represents the relative probability with respect to the other particles. In the resampling step, you draw from the set of particles such that for each particle, the normalized weight times the number of particles represents the number of times that particle is drawn on average. In that your idea is correct.
How does multinomial resampling work on a strip of paper?
Multinomial resampling: imagine a strip of paper where each particle has a section, where the length is proportional to its weight. Randomly pick a location on the strip N times, and pick the particle associated with the section.
What’s the difference between stratified and systematic resampling?
Stratified resampling: same as systematic resampling, except that the marks on the ruler are not evenly placed, but added as N random processes sampling from the interval 0..1/N. So to answer your question: what you have implemented could be extended to a form of residual sampling.