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by krick
2599 days ago
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You could, kind of. Basically, Kalman filter is this: you have 2 noisy data sources with a known real-life connection (like, vehicle position and velocity), so instead of an accurate measurement for each you have 2 "wide" gaussians. When you multiply them, you still get a gaussian, but a much narrower one, meaning: you still don't know the exact position for sure, but (kind of surprisingly) now you know it with a much greater precision than you had with the direct measurement. In fact, I agree that this one is not really good explanation. I cannot remember, where I saw my favourite one, but there are really plenty of them in the internet, many are well illustrated and pretty clear overall, so if you are actually interested, I think you won't have much trouble understanding it after a few links from the first page of your favorite search-engine. |
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Trying to simplify even further: you don't need 2 sources, just one, for which the distribution of noise is gaussian. And a model of how the data should evolve over time. Straight-line constant-speed for example, but also, static, turning, accelerating/decelerating... You need to be able to predict the next measurement from the previous one. The Kalman filter then uses the difference between the prediction from the model and the measurement, the incertitude on the measurement, and gives you: a smoothed estimation of the 'real' position of the object, an estimation of the 'noisyness' of your input data (i.e. How much does the data fit the model), and the ability to predict next positions accurately...
Well, not sure this word-soup simplifies anything...
Kalman filters are a bit counter intuitive if you don't have a strong background in probabilities... They clicked for me when 1- shown in comparison with other simpler filters 2- I played with each dimension of the formula on a toy example...
They're also very fun because they can be used in so many ways (sensor data fusion, non gaussian noise models, incredibly complex trajectory models...).