Suppose we have a Kalman filter. We have a position sensor, for example GPS. We use the filter to estimate position. However in all examples I see higher derivatives in the state vector: speed, acceleration and sometimes jerk. There is no sensor that calculates these values directly, so they must be somehow calculated from the GPS readings.(adsbygoogle = window.adsbygoogle || []).push({});

There is a prediction matrix butit only tells us how to integrate, not diffrerentiate. The sample matrix for my class of filters looks like that:

\begin{array}{ccc} 1 & dt & dt^2/2 \\ 0 & 1 & dt \\ 0 & 0 & 1 \end{array}

I know it can update a parameter given all higher derivatives, i.e. position from speed. But how can it compute speed from position?

The only place where the differentiation may happen is the correction step. The prediction matrix is used in the computation of Kalman gain so maybe that's how it's done?

Am I correct?

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# How does the Kalman filter calculate derivatives?

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