New, Guaranteed Positive Time Update for the Two-Step Optimal Estimator
N. Jeremy Kasdin · Journal of Guidance Control and Dynamics · 2000
A new time update for the two-step optimal e lter is presented. This time update eliminates the occurrence of low eigenvaluesin thee rst-step covariance for certain systems. This event left the e rst-step covariance singular (or negative dee nite ) and often resulted in an unstable implementation. The new time update is guaranteed positive dee nite and signie cantly improves the performance of the two-step estimator on all systems. The two-step e lter is an alternative to the standard recursive estimators that are applied to nonlinear measurement problems, such as the extended and iterated extended Kalman e lters. It improves the estimate error by splitting the cost function minimization into two steps (a linear e rst step and a nonlinear second step ) by dee ning a set of e rst-step states that are nonlinear combinations of the desired states. A linear approximation is made in the time update of the e rst-step states rather than in the measurement update as in conventional methods.