Efficient calculation of gradient in state estimation

Nearly all the computational time required in digital calculation of the gradient of an error index with respect to initial state is taken up by integration of differential equations. By direct application of the variational calculus, it is shown that the gradient may be calculated by integration of the state equations and costate equations, namely 2n equations. Previously, it has been thought necessary to integrate the n state equations and n2 state-sensitivity equations, namely n2+n equations.