deletions | additions       diff --git a/Waveform optimization.tex b/Waveform optimization.tex  index eaaf381..e74c1b6 100644  --- a/Waveform optimization.tex  +++ b/Waveform optimization.tex 
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We want to maximize the expected value of the log of the joint distribution of hidden states and data, $P(D,X|\Theta)$ with respect to the unknown states, conditioned on the data and the current parameters:  $\argmax_{\Theta_k} \begin{equation}  \argmax_{\Theta_k}  \int_X log( P(D,X|\Theta_k) ) P(X|D,\Theta_{k-1}) $ \label{eq:Qem}  \end{equation}  In the context of our HMM the joint distribution $P(D,X|\Theta)$ is given by $\prod_i^N P(d_t^i,x_i^t|\Theta) = \prod_i^N P(d_t^i|x_i^t,\Theta)P(x_i^t|\Theta)$.