Log-linearization of an intertemporal budget constraint

I’m trying to recreate the paper "Learning about Monetary Policy Rules when
Long-Horizon Expectations Matter" by Preston.

At one point he says that he log linearizes the intertemporal budget constraint

$$W_{t}^{i}=sum_{j=0}^{infty} R_{t, t+j}left[P_{t+j} C_{t+j}^{i}-P_{t+j} Y_{t+j}^{i}right]$$

where $W_{t}^{i} equivleft(1+i_{t-1}right) B_{t-1}$, $bar{imath}_{t}=beta^{-1}-1$ (denoting the steady state of $i$), $hat{i}=log [(1+i) /(1+bar{i})]= log frac{R_{t,t+1}}{R}$ in order to obtain
$$hat{E}_{t}^{i} sum_{T=t}^{infty} beta^{T-t} hat{C}_{T}^{i}=varpi_{t}^{i}+hat{E}_{t}^{i} sum_{T=t}^{infty} beta^{T-t} hat{Y}_{T}^{i}$$

with $varpi_{t}^{i} equiv W_{t}^{i} /left(P_{t} bar{Y}right)$.

I tried a houndred times to linearize the budget constraint but i can’t really figure out what he did.

Since $ln x_t = ln x – hat x_t rightarrow x_t = x e^{hat x_t}$ i wrote the the intertemporal budget constraint as

begin{align}
W_t^i =&sum_j^{infty} R e^{hat R_{t,t+1}} P e^{hat P_{t+j}} left[ ( C e^{hat C_t+j}) – (Y e^{hat Y_t})right]\
W_t^i=& sum_j^{infty} RP e^{hat R_{t,t+1} + hat P_{t+j}} left[ ( C e^{hat C_t+j}) – (Y e^{hat Y_t})right] \
W_t^i approx & sum_j^{infty} RP (1+ hat R_{t,t+1}+ hat P_{t+j}) left[ (C(1+hat C_{t+j})(Y(1+ hat Y_{t+j})right]
end{align}
ANd then i don’t know how to procede. Where do the steady state values of $R$ and $C$ disappear?