# Good book or reference to learn Kalman Filter

I am totally new to the Kalman filter. I've had some basic courses on conditional probability and linear algebra. Can someone suggest a good book or any resource on the web which can help me can understand Kalman Filter operation?

Most websites start directly with the formula and what they mean, but I am more interested in its derivation, or if not detail derivation then at least the physical significance of each operation and parameter.

• take a look at this question: dsp.stackexchange.com/q/2066/1273 Sep 16, 2012 at 17:10
• Here there is a very helpful series of 55 short lectures, starting from scratch
– Usta
Jun 8, 2017 at 20:59
• A highly cited paper, it will give you a practical understanding on this topic click here Apr 26, 2018 at 17:28

Many years ago I wrote the tutorial N. A. Thacker, A. J. Lacey - The Likelihood Interpretation of the Kalman Filter (Also on CiteSeerX) on the Kalman filter. It derives the filter using both the conventional matrix approach as well as showing it's statistical assumptions as an 'optimal' least squares filter.

• It was you!!! = ) Fantastic tutorial, I really enjoyed reading it sometime last year. Welcome to DSP.SE!!! Sep 17, 2012 at 12:47
• This is a great tutorial. Do you think you could update it if you have any new thoughts about Kalman filter? Thank You.
– Royi
Apr 26, 2013 at 17:26

This seems to be a nice write-up of the Kalman filter: Bilgin Esm - Kalman Filter For Dummies

I was searching for a book as well, best to cover the basics required to learn and implement kalman filtering in real life situation. So far I finalized my choice to this:

Fundamentals of Kalman Filtering: A Practical Approach (Progress in Astronautics and Aeronautics) by Paul Zarchan

I think this should be the one and I'm ordering it now. :)

A Very good book to learn Kalman Theory and implementation using MATLAB is here

Recently, Mandic, Danilo P. and Kanna, Sithan and Constantinides, Anthony G. published "On the Intrinsic Relationship Between the Least Mean Square and Kalman Filters" in IEEE Signal processing magazine:

The Kalman filter and the least mean square (LMS) adaptive filter are two of the most popular adaptive estimation algorithms that are often used interchangeably in a number of statistical signal processing applications. They are typically treated as separate entities, with the former as a realization of the optimal Bayesian estimator and the latter as a recursive solution to the optimal Wiener filtering problem. In this lecture note, we consider a system identification framework within which we develop a joint perspective on Kalman filtering and LMS-type algorithms, achieved through analyzing the degrees of freedom necessary for optimal stochastic gradient descent adaptation. This approach permits the introduction of Kalman filters without any notion of Bayesian statistics, which may be beneficial for many communities that do not rely on Bayesian methods.

A good 3 part series of Youtube Videos (~10 mins each) provides an intuitive understanding of the Kalman Filter.

Student Dave - Tutorial: Kalman Filter with MATLAB (YouTube Video).

One thing to note is that there are various ways to derive the Kalman Filter equations and each method gives you a different perspective of how it works. So, I suggest that you look into 2 - 3 different derivations to help you internalize this algorithm.

A good book that I’ve personally used is Optimal Filtering by Brian D.O. Anderson and John B. Moore. The entire book is dedicated to a precise explanation of the discrete-time Kalman filter and its extensions.

The best resource is Wikipedia page in my opinion. Here is a minimal and simple implementation of Kalman Filter with same notations given in Wikipedia page: https://github.com/zziz/kalman-filter