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Both equation sets are applied at each k We made the modeling in STEP1, so we know the matrices A, B and H. (if you're lazy enough not to do it, I'll do it for you in the Example below).

The most remaining painful thing is to determine R and Q.

Also as an additional ease, while these values may change between states, most of the time, we can assume that they're constant.

If we are pretty sure that our system fits into this model (most of the systems do by the way), the only thing left is to estimate the mean and standard deviation of the noise functions W.

Keep in mind that the previous estimates will be the input for the current state.

Here, is the prior estimate which in a way, means the rough estimate before the measurement update correction. We use these prior values in our Measurement Update equations.

R is rather simple to find out, because, in general, we're quite sure about the noise in the environment. And at this stage, I can't give you a specific method.

To start the process, we need to know the estimate of x After we gathered all the information we need and started the process, now we can iterate through the estimates.

Kalman's ideas on filtering were initially met with skepticism, so much so that he was forced to first publish his results in a mechanical (rather than electrical) engineering journal.When I started doing my homework for Optimal Filtering for Signal Processing class, I said to myself :"How hard can it be? If you're humble enough to admit that you don't understand this stuff completely, you'll find this material very enlightening. As I mentioned earlier, it's nearly impossible to grasp the full meaning of Kalman Filter by starting from definitions and complicated equations (at least for us mere mortals). This article is the result of my couple of day's work and reflects the slow learning curves of a "mathematically challenged" person.This is not easy of course, but we have all the tools to do it.On the other hand, let's assume be 0.5, what do we get? In other words, we should find smarter coefficients at each state. First of all, you must be sure that, Kalman filtering conditions fit to your problem.

As we remember the two equations of Kalman Filter is as follows: It means that each x.