# Kalman Filter for Beginners: with MATLAB Examples

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It depends what you have in mind by "understand". If you want to understand how to derive a filter, tweak it and apply to a complex task you need a good matrix algebra and algorithms' grip on top of a very good understanding of mathematical modeling which means differential equations.

If you want to understand how already written Kalman algorithm works, and that, it is only a more "flexible/adaptive" version of low pass filter, you need only some good book and do not go deep into equations. One of the best books I can recommend is by Kim Phil

If you want to have more specific answer, you probably need to ask more specific question as @hd1 already suggested.

Kalman Filter is often thought of as a linear filter where you have all model matrices but the idea of filter and its first applications come from non-linear models. In that case you use functions instead of matrices.

If the functions for prediction and update are highly non-linear you can use statistical methods to estimate your parameters on-line. The first look what you can take is unscented kalman filter which recovers mean and covariance from deterministic sampling technique - unscented transformation. I think in your case this could be the best to start with.

There are other variants of Kalman Filter. You can start from wikipedia but if you google "adaptive kalman filter" you can see the variety of the subject.

If you want to get deeper into the subject but not necessary start with all maths I recommend very good book: Kalman Filter for Beginners to start with by Phil Kim . There are also other possibility as sensor fusion, but it is another broad subject.

This is a very nice breakdown of Kalman Filtering. One slight correction - Kalman Filtering is one approach to solving the SLAM problem, but SLAM doesn’t require a KF. A particle filter, for example, can be used to solve the SLAM problem.

For anyone interested in further resources to better understand the intuition behind KFs, I’ve found this resource incredibly valuable (although a little pricey): https://www.amazon.com/Kalman-Filter-Beginners-MATLAB-Exampl...