I have been reading the paper "Bridging P-Q Modeling Divide with Factor HJM Modeling Framework" by Lyashenko and Goncharov (2022). On Equation 5 of page 4 of the paper, I came across the volatility process $\Sigma_{t}$ which is a K x N matrix where K is the dimension of basis vector and N is the dimension of Brownian motion. Assuming I have the data for spot rates at many maturities and at every time, how can I find this volatility process term?
I know that it can't be the same as volatility of spot rate or the forward rate. For example, given the screenshot below from page 18 of the paper, I have $R_{t}$ and can find out $B_{R}$. The issue is to find out the volatility processes $\Sigma_{t}$ or $\Sigma_{t}^{R}$.
