4.1. Position of the problem
We are examining two discrete time processes:
– of the second order;
– not necessarily wide sense stationary (WSS) (thus they do not necessarily have a spectral density).
is called the state process and is the process (physical for example) that we are seeking to estimate, but it is not accessible directly.
is called the observation process, which is the process we observe (we observe a trajectory which allows us to estimate the corresponding trajectory .
A traditional example is the following:
where is also a random process.
We thus say that the state process is perturbed by a parasite noise (perturbation due to its measurement, transmission, ...