Track fusion of distributed EFRLS state estimators

We present two track fusion methods for distributed recursive state estimators of dynamic systems without knowledge of noise covariances. This estimator at every local sensor is to embed the dynamic matrix and the forgetting factor into the Recursive Least Squares (RLS) method to remedy the lack of knowledge of noises, which was developed in Zhu, 1999 and called the Extended Forgetting Factor Recursive Least Squares (EFRLS) estimator. We prove that the aforementioned fusion methods are exactly equivalent to the corresponding centralized EFRLS that uses all measurements from local sensors directly. Therefore, the two track fusion methods have the same advantages as the corresponding centralized EFRLS does. For example, they can perform almost as well as the precisely specified Kalman filter and still well even if there exists unknown cross-correlation between sensors and/or cross-correlation between the process and measurement noise sequences in time or space.