Minimization of Roundoff Errors in Digital Realizations of Kalman Filters

A recently developed transfer function based roundoff error minimization method is applied on digital realizations of discrete-time Kalman filters. The resulting digital realization is compared to other existing realizations of Kalman filter. It is shown that the new realization is by far better than all other realizations from the estimation variance point of view. This variance can be further reduced if the proposed method is applied on the transfer function matrix of Williamson realization [14], rather than on that of the ideal Kalman filter.