4.1. Position of the problem

We are examining two discrete time processes:

images

–of the 2nd order;

–not necessarily wide sense stationary (WSS) (thus they do not necessarily have a spectral density).

images is called the state process and is the process (physical for example) that we are seeking to estimate, but it is not accessible directly.

images is called the observation process, which is the process we observe (we observe a trajectory images which allows us to estimate the corresponding trajectory images.

A traditional example is the following:

images

where images is also a random process.

We thus say that the state of the process is perturbed by a parasite noise images (perturbation due to its measurement, transmission, etc.).

In what ...

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