A new time update for the two-step optimal filter is presented. This time update eliminates the occurrence of low eigenvalues in the first-step covariance for certain systems. This event left the first-step covariance singular (or negative definite) and often resulted in an unstable implementation. The new time update is guaranteed positive definite and significantly improves the performance of the two-step estimator on all systems. The two-step filter is an alternative to the standard recursive estimators that are applied to nonlinear measurement problems, such as the extended and iterated extended Kalman filters. It improves the estimate error by splitting the cost function minimization into two steps (a linear first step and a nonlinear second step) by defining a set of first-step states that are nonlinear combinations of the desired states. A linear approximation is made in the time update of the first-step states rather than in the measurement update as in conventional methods.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics