On optimal distributed Kalman filtering in non-ideal situations

The distributed processing of measurements and the subsequent data fusion is called Track-to-Track fusion. Although a solution for the Track-to-Track fusion that is equivalent to a central processing scheme has been proposed, this algorithm suffers from strict requirements regarding the local availability of knowledge about utilized models of the remote nodes. By means of simple examples, we investigate the effects of incorrectly assumed models and trace the errors back to a bias, which we derive in closed form. We propose an extension to the exact Track-to-Track fusion algorithm that corrects the bias after arbitrarily many time steps. This new approach yields optimal results when the assumptions about the measurement models are correct and otherwise still provides the exact value for the mean-squared-error matrix. The performance of this algorithm is demonstrated and applications are presented that, e.g., allow the employment of nonlinear filter methods.