Recursive Implementations of the Schmidt-Kalman 'Consider' Filter

One method to account for parameters errors in the Kalman filter is to 'consider' their effect in the so-called Schmidt-Kalman filter. This paper addresses issues that arise when implementing a consider Kalman filter as a real-time, recursive algorithm. A favorite implementation of the Kalman filter as an onboard navigation subsystem is the UDU formulation. A new way to implement a UDU Schmidt Kalman filter is proposed. The non-optimality of the recursive Schmidt-Kalman filter is also analyzed, and a modified algorithm is proposed to overcome this limitation.