We now describe a simple problem that we will
analyze using the HMM tools.
Consider the HMM with the following parameters:
The output of the HMM is a time series with a
16-sample step size (i.e. the state is allowed to change
every 16 output samples). The output is Gaussian with
mean and variance depending on the state as follows:
| State |
Mean |
Var |
| 1 |
0 |
1 |
| 2 |
0 |
4 |
| 3 |
2 |
1 |
For each 16-sample segment, the sample mean and standard deviation
are computed. This constitutes a 2-dimensional feature vector
that is the observation space of the HMM.
![$\displaystyle A=\left[\begin{array}{ccc}
.8 & .1 & .1 \\
.1 & .8 & .1 \\
....
...ight]
\;\;\;\;
\pi=\left[\begin{array}{c}
1 \\
0 \\
0 \end{array}\right]
$](img1651.png)