# Predicting with a Kalman filter

Hi everybody,
I am not very acquainted with the ideas of the Kalman filter, but I have been searching about it in the Internet. As far as I understand,
the Kalman filter can be used to predict future values (outputs) of a system, by considering that the prediction error is a noise. However, to apply a Kalman filter we need (apart from an expected model of behaviour of the system) to know some statistics about the noise (mean and variance). So... in this, case, as the noise is the prediction error and the prediction error is what we want to minimize with the Kalman filter, it seems that we can't know those statistics a priori (they depend on how well the Kalman filter performs!).
To sum up, can the Kalman filter be used for predictions? (for example, to predict future values of the temperature of a room based on past values, or to predict future locations of a vehicle). If so, what is wrong in my previous reasoning?
I hope you can help me to clarify this doubt!
Sergio
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Sergio wrote:

The basic formulation of the Kalman filter calls out knowing the characteristics of the system you're modeling plus the characteristics of the noise that's driving it. Once you know this the performance of the filter and the statistics of the measurement (or prediction) error can be easily found.
So the Kalman filter can be used for predictions, and within the limits of its formulation will be the optimal filter -- but it still may not be good enough, and the limits you need to put on its formulation may mean that there are much better ways to do your prediction.
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Tim Wescott
Wescott Design Services
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Nothing can predict the future precisely. A statistical prediction has some value but is limited to averages and probabilities. Using derivatives to calculate trends yields helpful results for short term projections and increasing noise as we project further. Ultimately all is chaos. If the Kalman filter provided accurate predictions, Mr. Kalman would be a lottery billionaire.
Walter.

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If you have low-noise data and well-behaved (i.e. predictable) system dynamics then a predictor can be handy -- this is, after all, what you are doing when you go duck hunting and apply windage and lead.
The nice thing about a Kalman predictor is that if you're honest about your noise levels you may find that your "ideal predictor" is a low-pass filter, or a pass-through.
Walter Driedger wrote:

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Tim Wescott
Wescott Design Services