Kalman Filters

[nickmagus]

hey thanks for the help and the book recommendation i got a couple of copies (cheep thanks to amazon) no chance you wanna explain a little of the math thats mostly what i was having trouble with.

[EricH]

Originally Posted by nickmagus

hey thanks for the help and the book recommendation i got a couple of copies (cheep thanks to amazon) no chance you wanna explain a little of the math thats mostly what i was having trouble with.

I'm a second-year college student, and I haven't had differential equations yet. If you don't have Calculus 2 (advanced integrals (including exponential and logarithmic) and series) under your belt, you probably aren't ready for what's known as "Difficult" Equations. That's next semester for me. (After Calc 3 this semester...) So if Calc BC is equivalent to Calc 2, you have a half-chance of undersanding the math. If not, you'll have to learn on the side.

[Manoel]

Truth is, you probably won't see Kalman filters even in college - only in grad school.

jee7s already gave you a pretty good basic explanation on what a Kalman filter does, so let me tell you about your options. It's great that you're interested in an advanced topic, and I don't mean to disencourage you, but if you're taking Calculus now, there's a LONG way ahead, and you're probably better off going to college to receive a formal training.

Here's the most likely course route, after Calculus:

Linear Algebra (basic course, I wish someone told me back then how important it would be)
Differential Equations
An Applied Math course (Laplace and Fourier transforms)
Signals and Systems
Classical Control
Linear System Theory
(So-called) Modern Control - state space approach
Intro to Stochastic Processes
Optimal Control (finally you're gonna hear about the Kalman filter)

The last four courses are probably graduate level, depending on where you go to school. As you can see, you're looking at four to six years of college education. It won't be easy, but as a FIRST student you already have a competitive advantage over your future peers: to be curious as hell (and I say that from experience - not too long ago I was in your position).

Let us know if you have further questions.

[nickmagus]

thanks for the help everyone.

[mluckham]

The first I heard of Kalman Filters was in articles related to the Darpa challenge ... it was my impression it was a means to process signal inputs AND combine inputs from multiple sensors (like wheel encoders plus gyro plus accelerometer) into some sort of matrix which would evaluate the most correct decision data.

From reading this thread I now understand that the Kalman Filter is a means to extract a good signal (opinion/estimate) from a noisy one - usually from ONE sensor.

Since it seems that the Kalman Filter is a very advanced topic, in First we can use simpler filtering techniques such as moving averages, throwing out "obviously bad" minimum and maximum sensor readings, and more advanced filters such as FIR and FFT. Some more discussion about filtering sensor inputs, and combining multiple sensors into decision-making software, can be found at http://www.servomagazine.com/search.php and searching for filter.

Searching for sensor fusion on the same site produces some interesting articles about combining multiple sensors to make decisions, particularly the July and August 2006 articles entitled "Autonomous Robots and Multiple Sensors".

[Samuel H.]

Originally Posted by mluckham

The first I heard of Kalman Filters was in articles related to the Darpa challenge ... it was my impression it was a means to process signal inputs AND combine inputs from multiple sensors (like wheel encoders plus gyro plus accelerometer) into some sort of matrix which would evaluate the most correct decision data.

From reading this thread I now understand that the Kalman Filter is a means to extract a good signal (opinion/estimate) from a noisy one - usually from ONE sensor.

Actually, because the Kalman filter is based on matrix operations, it is very flexible and can be used for varying numbers of sensors and state variables. For a comprehensive set of links see http://www.cs.unc.edu/~welch/kalman/

[Richard Wallace]

Several summers ago, a college mentor from FRC 931 built a low cost self-balancing scooter as a demonstration project while working as an intern in my lab at Emerson. His creation looked very much like one built earlier by Trevor Blackwell. Both versions employ Kalman filters to correct for drift in the tilt angle estimated by integrating a gyro's output.

While that student has gone on to pursue PhD level work since then, he had never heard of a Kalman filter before starting the project. Full comprehension of the Kalman filter's mathematical beauty requires the kind of study that previous posters in this thread have described -- and that study is rewarding for its own sake. However, you can apply what others have done without getting to that depth.

Yes, the mathematical basis for balancing an inverted pendulum really is rocket science. Be encouraged by the evidence that the math works, not intimidated by its beautiful details.

[nickmagus]

its true i can utilize someone else's implementation but i don't like to do that unless i at least understand their implementation myself. and typically apart from basic framework code (which is a pain) i like to implement code myself (or use code implemented by my teammates) its just hard to properly use code that you don't understand. for example i was looking at the code for an old robot fixing it up and i found the PID loop was adding the D term to the output which is exactly the opposite of what you want so i like to at least understand the basics (including the basic math) behind the code i write. Anyone can use someone else's algorithms but if they don't try to understand them they get nothing from it. so when i wrote a auto tune loop for a PID earlier this year based on zigler-nicoles it was only after reading an entire text book from a cal tech course (which was fascinating and free btw i recommend it http://www.cds.caltech.edu/~murray/a...itle=Main_Page)

[Richard Wallace]

Originally Posted by nickmagus

its true i can utilize someone else's implementation but i don't like to do that unless i at least understand their implementation myself. ...

OK, so you like the beautiful details. I do too.

BTW, the former FRC 931 college mentor that I mentioned above is Brandon Heller. He is a PhD student at Stanford now. I think he also was one of the mentors for FRC 8 (your team) last year.

As Sam mentioned a couple of posts up, Kalman filters are good for much more than just figuring out which way is up (whatever your frame of reference). Your exploration of the details might lead to applications beyond balancing an inverted pendulum, and one of those might find its way onto your team's next robot. Have fun with it.

[nickmagus]

ya he was a mentor of ours last year. Im not sure of his status this year but thanks i'll ask him about it. but first for research into the beautiful details and some other concepts in control theory, beyond what i already know. thanks all for your help and support.