deletions | additions       diff --git a/Waveform optimization.tex b/Waveform optimization.tex  index f4a9870..e48b53a 100644  --- a/Waveform optimization.tex  +++ b/Waveform optimization.tex 
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$ = \sum_i^N \sum_t^{T_i} \iint dx_t^i (d_t^i - m(x_t^i))^2 P(x_t^i|D,\Theta)$  Where $P(x_t^i|D,\Theta)$ is the known posterior distribution of our hidden states at time $t$ for a trace $i$. $i$, and is a discrete talbe indexed by integer $l$ and $m$: $P_t^i[l,m]$ .  Since we work in discretized space we rewrite the above integral as: $ \sum_i^N \sum_t^{T_i} \sum_l \sum_m (d_t^i - \exp(\lambda[l])w[\phi[m]])^2 P_t^i[l,m]$