Largest Ellipsoid Estimation for Unknown Measurement Error Dynamics

Author(s):

James Maley and Ryan Zurakowski

Abstract:

Largest ellipsoid estimation has promise for being able to handle measurement errors with known covariance but unknown dynamics. However, there is no proof that it will be consistent for a given system. The algorithm is converted into a covariance-form estimator, and the gain is clearly shown to be different from the Kalman gain. This formulation was used to examine the difference between the estimator covariance and the true covariance for the special case in which the measurement errors are constant. A counter-example shows that the estimator is not always consistent, but a consistency metric based on the steady-state covariance error is provided. Two simple simulation examples are used to demonstrate situations where the estimator works well and where it does not, while demonstrating the usefulness of the consistency metric.