PhilipW, I thought your link is good for starters so are Ron's. At least you get an example with numbers. The example provides only a simple value like a position or speed. The F array in your example would normally be derived from a model of the system so you must be able to find that first. The idea is that the new value is a waited average of the old value and the new measure value kind of like the low pass filter that has been covered so many times on the forum. The trick is finding the optimal weights.
In a more complicated example x could be an array of position, velocity and acceleration and F would be a 3 by 3 array. This quickly gets outside the realm of PLC math.
I find that working through an example like the one you have is the only way to learn. I can provide .csv files that have time, target position, actual position, target velocity, actual velocity and control output. You can use this data for practicing and working through examples.
It is good to get a math package like Matlab, Mathcad or the free Scilab. I know Scilab has a Kalman function.
Just curious, what are you going to do with it? I use a related algorithm to provide more accurate velocities and accelerations. Maybe you can convince Rockwell to let you design a Kalman filter module so others can accurately their conveyor speeds from low resolution encoders.
I think you have good examples. If you want more info then you should ask this question on sci.engr.control.
There was also an article in Embedded Systems by Jack Crenshaw that I recommend. It has code and works through a simple position and velocity example.
