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Math newbie here. Does 'filter' (as it is used here) have a precise mathematical definition? The only other place where I've seen this word used is the 'bloom

Math newbie here. Does 'filter' (as it is used here) have a precise mathematical definition? The only other place where I've seen this word used is the 'bloom filter', which according to Wikipedia is not an algorithm like the Kalman filter but a data structure.

mbrudd 5y ago
In general, filters do what their names suggest -- they filter out noise or unwanted components of signals. The simple Kalman filter filters out white noise to estimate parameters that describe a system; other filters use things like the Fourier or wavelet transform to, say, select certain frequencies and remove others.
SimplyUnknown 5y ago
It is a filter in the sense that it can track the system state from one (or more) noisy measurements. The filter part thus reflects the input denoising.
sceadu 5y ago
In signals it's a term used to mean a processing step that removes unwanted parts of a signal, e.g. measurement noise
mpmpmpmp 5y ago
The wikipedia page for Kalman filter says it's also known as "linear quadratic estimation" so that might be a good place to start.
alanbernstein 5y ago
IIRC, The kalman filter has a state-space formulation, in which it is clear that it is equivalent to an LTI filter (https://en.m.wikipedia.org/wiki/Linear_filter https://en.m.wikipedia.org/wiki/Linear_filter). However, I believe updating the statistics of the system in response to updated measurements breaks the "time invariant" part. This is precisely the classic concept of an audio filter, which is, I believe, the inspiration for the term "filter" in other contexts. Bloom filters and selfie filters don't have much in common in a technical sense, but if you squint you can see the connection.
billfruit 5y ago
Filter has very established definition in Signal Processing, and covers things which can do a lot of things, essentially something that can manipulate how energy or power is distributed over a set of frequencies. A common analogy is yo imagine it as an entity that can turn a block of stone to a sculpture, by removing material.

mbrudd 5y ago

In general, filters do what their names suggest -- they filter out noise or unwanted components of signals. The simple Kalman filter filters out white noise to estimate parameters that describe a system; other filters use things like the Fourier or wavelet transform to, say, select certain frequencies and remove others.

SimplyUnknown 5y ago

It is a filter in the sense that it can track the system state from one (or more) noisy measurements. The filter part thus reflects the input denoising.

sceadu 5y ago

In signals it's a term used to mean a processing step that removes unwanted parts of a signal, e.g. measurement noise

mpmpmpmp 5y ago

The wikipedia page for Kalman filter says it's also known as "linear quadratic estimation" so that might be a good place to start.

alanbernstein 5y ago

IIRC, The kalman filter has a state-space formulation, in which it is clear that it is equivalent to an LTI filter (https://en.m.wikipedia.org/wiki/Linear_filter https://en.m.wikipedia.org/wiki/Linear_filter). However, I believe updating the statistics of the system in response to updated measurements breaks the "time invariant" part. This is precisely the classic concept of an audio filter, which is, I believe, the inspiration for the term "filter" in other contexts. Bloom filters and selfie filters don't have much in common in a technical sense, but if you squint you can see the connection.

billfruit 5y ago

Filter has very established definition in Signal Processing, and covers things which can do a lot of things, essentially something that can manipulate how energy or power is distributed over a set of frequencies. A common analogy is yo imagine it as an entity that can turn a block of stone to a sculpture, by removing material.