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I have a flying robot with magnetic coil as a sensor. An output from the coil is measured every second in different position. I know the position of the coil and its angles. I need to estimate the unknown position of magnetic source.

As the output is with noise I assume I need to use Kalman filter, but not sure how to start in this case. Do you know if i can implement Kalman to estimate the position of the source? Do not really know how to start. Did anyone know similar example described somewhere?

Thanks for all advice.

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  • $\begingroup$ For the start, I would learn state-space representation and from there you can pick up pieces to reach Kalman filter. $\endgroup$
    – jomegaA
    Mar 10, 2020 at 8:48
  • $\begingroup$ youtube.com/… Lecture 32, 33 and 33 but there are other good stuff too $\endgroup$
    – jomegaA
    Mar 10, 2020 at 8:50

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To start, you have to write a probabilistic model of your system. Let us denote, your outputs (observations) as $\bf{y}_t$'s and the true positions as $\bf{x}_t$'s. To use Kalman filter, you have to be sure that underlying noise is Gaussian and your observation and transition models (I will explain in the sequel) are linear.

First, write a reasonable observation model such that, $$ \mathbf{y}_t = H_t \mathbf{x}_t + \mathbf{w}_t $$

In this model, you aim to model how your true positions are corrupted and become observations. Thus you have to determine $H_t$. For example, if you are using a camera and want to know 3D positions, then observation model is a camera matrix which projects the real world points to 2D points. In your case, you have to know sensor characteristics (or model it).

Second, you have to write a transition model, this requires to use physical knowledge of the underlying system. For instance, if we model a ball and try to model its evolution in time, certainly we have to write a motion model. Transition model can be written as,

$$ \mathbf{x}_t = F_t \mathbf{x}_{t-1} + \mathbf{\eta}_t $$

Notice that, in both models, the noise terms are Gaussian and $H$ and $F$ are linear. To use Kalman filter, you have to know these models, i.e., you should have a probabilistic model which explains the underlying physical structure. Then you can use the Kalman filtering recursions, which are straightforward from this point.

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