A theoretical analysis of the round-off propagation in different Kalman filter implementations

A theoretical analysis is made of the error propagation due to numerical round-off for four different Kalman filter implementations: the conventional Kalman filter, the square root covariance filter, the square root information filter and the Chandrasekhar square root filter. From these error models, new insights about the applicability of the different filters and their sensitivity to round-off, is obtained. It is shown that the CKF may become completely unreliable when the original plant is unstable, and that this is easily circumvented by a number of techniques. The square root filters, often quoted to possess a conditioning or sensitivity that is the square root of that of the CKF, are shown to possess this property only for the computation of the covariance of the filtered signal and not for the computation of the Kalman gain or the filtered estimate. Finally, the Chandrasekhar filter is shown to be numerically unstable.