Evolution of forecast error covariances

eb(t) = (Xb(t) - Xt(t)) : forecast error

eo(t) = (yo(t) - HXt(t)) : observation error

ea(t) = (Xa(t) - Xt(t)) : analysis error

• Evolution equation

• At t = t0, e(t0) = ea(t0).For a linear differential equation, the solution at time t can be related to the initial conditions by its propagator R(t,t0) such that

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