Quiet down out there!
Understand how to cut down on the noise in your system, using the math behind the Kalman filter. If you know something about the dynamics of the system, you can make a better estimate of what it's doing now and what it's going to do next.
The universe is a noisy place. More so in Manhattan, Detroit, or the galactic core; less so in the Swiss Alps or interstellar space, but noisy everywhere. No matter how hard you try, you can't escape the noise.
Few people understand this better than scientists and engineers, especially those of us who work with embedded real-time systems. Chances are, the first time you hooked up some measuring sensor to an analog-to-digital converter, you learned this lesson well.
Most likely, you decided to insert a low-pass filter into the signal path. That will remove a lot of the noise, all right, but also the fine structure of the system behavior. And it necessarily adds a time delay to the system--a delay that will affect the stability of a control system.
Filters have their place, for sure. But in the end, the use of a low-pass filter is a tacit admission that we don't have a clue what the system is really doing. We filter it because it's the only recourse we have. We treat the input signal as pseudo-static, and hope that our sample rate is fast enough to make the signal look like a constant.
On the other hand, there can be times when we do know--or think we know--how the system should behave. A real physical system obeys the laws of physics. A reactor in a chemical plant is going to follow the laws governing its particular chemical reaction. An airplane in flight is going to obey Newton's laws of motion.
In such cases, we can do a little better than simply relying on brute force low-pass filters. If we know something about the dynamics of the system, we can make a better estimate of what it's doing now and what it's going to do next. That concept has been the focus of my last few columns and will remain our focus for the near future. This is the third installment of the series.