This page contains the LDM e_step with RTS smoother States Estimation results under matlab.

In this experiment, we use 2-dimensional X[] and 3 dimensional Y[].

RTS algorithm adds an additional backward estimation after the regular forward states estimation. Then, it provides the optimal linear combination for these two estimations. Here we give the experiments results with analysis.

Plot 1

The backward estimation gives resonable estimation for the hidden states. However, comparing to forward estimation it is a little bit worse for this specified LDM.

Plot 2

The linear combination of forward and backward estimations gives a good curve.

Plot 3

In this plot, estimation with RTS didn't enhance the performance. But it's reasonable and still promising.

For this experiment, we gave exactly correct parameters to do the hidden states estimations. However, the EM step will first initialize the parameters (which is far way from the real parameters) and then do the E step and M step recursively. The forward estimation and backward estimation are supposed to be quite different and RTS smoother is promising to get closer to the real hidden states.

The EM experiments will provide the answer.