Chapter 4

Estimation

4.1. Position of the problem

We are examining two discrete time processes:

image

– of the second order;

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

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

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

A traditional example is the following:

image

where image is also a random process.

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

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