Covariance Debiasing for the Distributed Kalman Filter

A solution to exact Track-to-Track Fusion (T2TF) at arbitrary communication rates has been found under the assumption that all measurement error covariances are known to each of the sensors. The scheme, which is referred to as the "Distributed Kalman Filter" (DKF), produces a fused estimate that is equivalent to a central Kalman filter that processes all measurements. However, there is degradation in the estimation quality of the DKF, if the actual measurement error covariances do not match the assumed model. This degradation manifests itself as a bias in the state estimate and an inconsistent covariance. It has been shown that this bias in the state estimate can be removed by transmitting a correction matrix. The contribution of this paper is the introduction of an additional correction matrix that enables a consistent covariance matrix to be reconstructed. The resulting Double Debiased Distributed Kalman Filter (D3KF) is evaluated by simulation in a scenario where measurement origin uncertainty is encountered.