How to smooth out a very inconsistent reading

Peter Nachtwey said:

It isn't clear how you calculated alpha and beta also I don't agree with your checks.

Click to expand...

The code is lifted basically 1-to-1 from the C sample code on the wikipedia page (https://en.wikipedia.org/wiki/Alpha_beta_filter).
The checks are also lifted directly from that page.

I will take a look into making an alpha-beta-gamma filter based on your notes and the mathcad sample. it will take some effort on my part since it has been a long time since I dabbled with matrix equations.

Excellent.

JesperMP said:

The code is lifted basically 1-to-1 from the C sample code on the wikipedia page (https://en.wikipedia.org/wiki/Alpha_beta_filter).
The checks are also lifted directly from that page.

Click to expand...

It isn't the code that I have a problem with. It how the gains get initialized that are the problem. First, it looks like that were picked by trial and error and that alpha and beta are totally independent when they shouldn't be.

I will take a look into making an alpha-beta-gamma filter based on your notes and the mathcad sample. it will take some effort on my part since it has been a long time since I dabbled with matrix equations.

Click to expand...

Very good.
I have this example too. It is written using wxMaxima.
https://deltamotion.com/peter/wxMaxima/ABG.html
Notice that below
(%o6)
I have a few different variations on how to calculate the K gains or alpha, beta and gamma. They are based on where the poles should be for the filter. There are different method if calculating where the poles should be.
The 3 real pole gains are safe and the Butterworth ones should be too. I tried them all. It didn't make much difference because the poles are in pretty good spots using tried and proven methods.

There should be only one parameter the user needs to changed and that is omega or the bandwidth. I usually place the bandwidth at the sqrt(sample_frequency*system_frequency) for starters. This frequency is low enough to filter out the sampling and quantizing noise but high enough not to affect the response too much. In my ABz.pdf I set the frequency to about 70.0 radians per second which is a little over 10 Hz. In the example the system frequency ( sine wave ) is 1 Hz and the sample frequency is 100 HZ so the sqrt( 1*100) = 10 Hz.

danilericardo said:

Some papers I found seemed to discuss kalman filter and alpha-beta-gamma filter in the same context as if they were the same thing.

Click to expand...

That is because the alpha-beta-gamma filter, or something very similar to it, is part of the Kalman filter. The difference is that the Kalman filter adjusts the filter gains by adding the Kalman Gain, Covariance Update, and Covariance Extrapolation equations.


See here: https://www.kalmanfilter.net/default.aspx

drbitboy is right. The A or F matrix that predicts or estimates the next state based on the current state are the same for alpha-beta-gamma, Luenberg observers and Kalman filters.
An alpha-beta-gamma will get you 98% of the benefit with only 5% of the hassle.

Full Kalman filters with update the Kalman gains every iteration. This requires a lot of processing power. It also requires knowing the measurement and system covariance which is something most people don't know so the fudge it. Static Kalman filter calculate the Kalman gains once but still use the covariance of the system and measurement. Alpha-beta-gamma filters make no pretense of being optimal but with care choices of the values for the K gains, one can get very good results with little effort. In any case, calculating the gains for the A or F matrix that estimate the next state is most important because then there is little to correct.