# Probability theory and statistics for Robotics and ME

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1. Jul 17, 2017

### debelino

I study control theory and robotics. Recently I figured out that I have a much deeper understanding of probability and statistics compared to my colleagues. Is this 'talent' valuable in my field and if so, where? We used this theory to define white noise, but nothing more...as of now.

Also I am generally good in math and physics and I have a high IQ. I am lazy to do repetitive work and because of all this I think a good strategy for me would be to specialise in a field full of hardcore theory to reduce competition by taking advantage of my scientifically oriented mind. It is easy for me to make connections between theory and practice and fulfils me to see that something I theorized about is working in the real world.

I need advices for my career. What should I concentrate on? Any book recommendation is also welcome. Sorry for my English, it is not my first language.

Last edited by a moderator: Jul 18, 2017
2. Jul 17, 2017

### FactChecker

Probability and statistics is very important in control theory. In every human effort, there is feedback, random behavior, and optimization. Regarding random behavior in control theory, your input sensors are not perfect and have a random component. Kalman filters are used to combine information, taking into account the reliability of each of the inputs. Also, there are usually random influences that can not be measured at all.
For a simple example that doesn't require Kalman filters, suppose an airplane flight control needs to estimate lateral velocities. It can integrate accelerometer inputs to get very fast reactions that, unfortunately, will drift and accumulate an error. It can also get GPS information at a much lower rate which does not react fast but does not drift. A complementary filter can be used to combine the high frequency input from the accelerometer with the low frequency input from the GPS and get the best of both in a single lateral velocity signal.

3. Jul 18, 2017

### debelino

Thank you for your fast replay.
Can you recommend me good books on this topic? What professional direction is good in my case?

4. Jul 18, 2017

### FactChecker

Unfortunately I am not up to date on current textbooks. I also do not know what your background is. Kalman filters are in many books on optimal control, but it is probably after a lot of preceding material. To get the background material, you can look at your university texts on control laws, multivariate statistics, and optimization.

Just to get an idea of what is involved, you may be interested in https://www.utdallas.edu/~sethi/Prosper/Control-Tex-Chapte13.pdf . It is advanced and I don't know what your background is, so don't worry if it looks intimidating. I am just mentioning it to show you how central statistics is in a field like stochastic optimal control.