[TFortunato]

Hoping I can help you grok the problem a bit more. Typing on phone, so please excuse the lack of decent formatting.

A moving average is a good place to start thinking about it. Think about a case where you would use a moving average, and why. You are probably using it because you have some measurement (sensor) that you know is noisy, and so by averaging out the noise (taking the mean of a number of samples) you try to get a better estimate of the true value. If you know how noisy the sensor is, you can get an idea of how many samples you should average over to get a good measurement. You can also take the standard deviation and report both the mean and variance of your measurement over multiple samples if you wanted.

For purposes of this example moving forward -- we are going to estimate all of our sensed or inferred values as a gaussian, parameterized by mean and variance. It's a simple way to give a measurement with some uncertainty around it.

This can be a good start if you know nothing little about the system you are measuring, other then the sensor / measurement is noisy. However for many systems you may have multiple quantities you are interested in estimating, and you have some idea of how they relate to each other.

Take your example of a physical system with acceleration, velocity and position. Basic physics will tell you that if at time t, you are at position p, moving at velocity v, then at time t+dt, your position should be roughly p+(v*dt). Similarly, you can update your velocity estimate using your estimate of acceleration. If this is a system under your control, then you can also take things like a force you commanded to update your acceleration model. This is great, by using physics, without any measuring after time 0, we can just figure everything out forward in time forever, by simply using our process model! However, because your initial estimates had some uncertainty, what you will find is that, if you just keep doing this, the uncertainty grows larger and larger with each time step, and eventually become so large as to be useless.

Enter tha kalman filter. What the kalman filter does is tries to combine the information given by your sensors and combine it with your process model to give you a better estimate of the quantities you are interested in than you could get from either technique alone.

Every time step the filter will make an state estimate using the process model based on your previous state estimate, and then use your current sensor measurements to update that state estimate, both in terms of the mean and uncertainty. In the basic kalman filter you assume your process model is linear, all of your estimates are simple gaussians, and then decide how much you want to weigh your model vs. your sensors via a simple multiplying factor, "the kalman gain"

Sorry again I couldn't write this out as a program, and the likely horrible run-on sentences that come from typing on a phone, but I hope that a quick overview of what the technique is trying to do will help make it a little easier to fill in the owl!

[meling]

Wow. Thanks. That was a wonderful explanation. I’ve been wondering if a Kalman filter could be used in a distributed system to estimate latencies between pairs of processes for the purpose of computing a near optimal dissemination tree.

[chubs]

Thanks a lot! That does explain some of the ideas behind it nicely. Sometimes when looking at equations it's easy to miss the forest for the trees so to speak, so this helps.