Observability conditions for biased linear time invariant systems

Abstract

This paper addresses the existence of bias estimators in linear time invariant (LTI) systems. One approach to bias estimation is state augmentation, in which a new state corresponding to each unknown bias term is appended to the state vector. The Kalman filter is then applied to the augmented system and the biases are identified as part of the filtering process. A simplified observability rank test for the existence of bias estimators for a LTI system with unknown, constant state and measurement biases has been recently derived. A reduced row observability test matrix is used to show a necessary and sufficient condition for complete bias observability. This paper investigates the use of additional measurements in the system and their ability to alter the bias observability conditions of the system. Examples are presented.