The correction is essential because the transmitter and the receiver are not at the same position at the same time. Assuming reception time is $t$, transmission time is $t - \tau_{ltd}$.

The geometric range $\rho=|r_{tran} (t - \tau_{ltd}) - r_{rec} (t)|$, or equivalently:

${\tau_{ltd}}{i+1} = \frac{1}{c}|r{tran} (t - {\tau_{ltd}}i) - r{rec} (t)|$

Usually it will need several such iterations to converge. The effect of 400 km altitude is about 0.0013s.