STEP 1 - Build a Model

It's the most important step. 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 k (our signal values) may be evaluated by using a linear stochastic equation (the first one). Any x k is a linear combination of its previous value plus a control signal k and a process noise (which may be hard to conceptualize). Remember that, most of the time, there's no control signal u k .

The second equation tells that any measurement value (which we are not sure its accuracy) is a linear combination of the signal value and the measurement noise. They are both considered to be Gaussian.

The process noise and measurement noise are statistically independent.

The entities A, B and H are in general form matrices. But in most of our signal processing problems, we use models such that these entities are just numeric values. 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 k-1 and v k . We know that, in real life, no signal is pure Gaussian, but we may assume it with some approximation.

This is not a big problem, because we'll see that the Kalman Filtering Algorithm tries to converge into correct estimations, even if the Gaussian noise parameters are poorly estimated.

The only thing to keep in mind is : "The better you estimate the noise parameters, the better estimates you get."