# estimation of the position of the magnetic source

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.

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

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