Modern Military Mathematics
(http://www.nada.kth.se/~hedvig/publications/fusion_03a.pdf)
This is a paper funded by an institute for "Data Fusion". That is, you have various surveillance techniques, like satellite images and humans on the ground calling in reports, and you want to provide the bosses with reliable information.
This is called "Filtering" - which sounds reasonable if you're saying "I'm going to put a bandpass filter on this telephone so that you don't get that hissing"; but sounds odd to my ear if you're saying "I'm going to put a filter on the reports from the field to track where the target is going".
About particle filters: Do not think of coffee filters keeping particles from going through. One can represent a probability distribution by parameters (mean and standard deviation, perhaps). However, what if the correct distribution is not normal? Perhaps a weighted sum of normal distributions would be better? "Particle Filter" is a codeword meaning "we are going to represent a probability distribution by a set of samples from that distribution".
I imagine particle filters as similar to the representation of the population in genetic algorithms. In an infinite-population case, the population moves across the fitness landscape like a cloud. We approximate that (smooth) cloud by a list of individual samples from that cloud. We want to do two things to the population- one is replication (parts of the cloud get more dense according to the fitness landscape), and the other is mutation and crossover (which makes the cloud spread out in a certain way.
In the paper, the cloud is the "probability hypothesis distribution" (a function whose integral over a given region is the approximate number of targets (cars? tanks?) we expect in that region). There are two operations that one wants to do with the cloud- one is update it with new information (which pulls the cloud together into spikes), and one is evolve it forward in time (which makes the cloud spread out in a certain way).
I recommend this paper. There's a footnote which points to movies that might be entertaining even if you don't read the paper: http://www.foi.se/fusion/mpg/FUSION03
This is a paper funded by an institute for "Data Fusion". That is, you have various surveillance techniques, like satellite images and humans on the ground calling in reports, and you want to provide the bosses with reliable information.
This is called "Filtering" - which sounds reasonable if you're saying "I'm going to put a bandpass filter on this telephone so that you don't get that hissing"; but sounds odd to my ear if you're saying "I'm going to put a filter on the reports from the field to track where the target is going".
About particle filters: Do not think of coffee filters keeping particles from going through. One can represent a probability distribution by parameters (mean and standard deviation, perhaps). However, what if the correct distribution is not normal? Perhaps a weighted sum of normal distributions would be better? "Particle Filter" is a codeword meaning "we are going to represent a probability distribution by a set of samples from that distribution".
I imagine particle filters as similar to the representation of the population in genetic algorithms. In an infinite-population case, the population moves across the fitness landscape like a cloud. We approximate that (smooth) cloud by a list of individual samples from that cloud. We want to do two things to the population- one is replication (parts of the cloud get more dense according to the fitness landscape), and the other is mutation and crossover (which makes the cloud spread out in a certain way.
In the paper, the cloud is the "probability hypothesis distribution" (a function whose integral over a given region is the approximate number of targets (cars? tanks?) we expect in that region). There are two operations that one wants to do with the cloud- one is update it with new information (which pulls the cloud together into spikes), and one is evolve it forward in time (which makes the cloud spread out in a certain way).
I recommend this paper. There's a footnote which points to movies that might be entertaining even if you don't read the paper: http://www.foi.se/fusion/mpg/FUSION03
posted by Johnicholas at 8:06 AM
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