How did we get the update equations? The original $u_{kl}$ equation has a $I_y^2 u_{kl}$ term but it looks like its a $I_x^2 u_{kl}$ term in the update equation.

Is the question how we go from the equations at the top of this page, to the ones on the bottom?

$(1 + \lambda(I_x^2 + I_y^2))u_{kl} = (1 + \lambda I_y^2) \bar{u}{kl} - \lambda I_x I_y \bar{v}{kl} - \lambda I_x I_t$

$(1 + \lambda(I_x^2 + I_y^2))u_{kl} = (1 + \lambda I_x^2 + \lambda I_y^2) \bar{u}{kl} - \lambda I_x^2 \bar{u}{kl} - \lambda I_x I_y \bar{v}_{kl} - \lambda I_x I_t$

$u_{kl} = \frac{1 + \lambda I_x^2 + \lambda I_y^2}{1 + \lambda(I_x^2 + I_y^2)} \bar{u}{kl} - \frac{\lambda I_x^2 \bar{u}{kl} + \lambda I_x I_y \bar{v}_{kl} + \lambda I_x I_t}{1 + \lambda(I_x^2 + I_y^2)}$

$u_{kl} = \bar{u}{kl} - \frac{I_x^2 \bar{u}{kl} + I_x I_y \bar{v}_{kl} + I_x I_t}{\lambda^{-1} + (I_x^2 + I_y^2)}$