Bayesian Estimation and Tracking: A Practical Guide

6.1 Linear Dynamic Models

For a linear dynamic model, (5.1) can be written as

(6.1)

where F is a deterministic transition matrix that is independent of time. For most cases, the control factor u_n is not needed but we will include it in what follows for the sake of completion.

Putting (6.1) into (5.37) we obtain

(6.2)

which reduces to

(6.3)

Similarly, putting (6.1) into (5.38), yields

(6.4)

But, since

(6.5)

for a linear dynamic model it follows immediately that

(6.6)

where is the dynamic noise covariance matrix.