Optimal Distributed Kalman Filtering Fusion Algorithm Without Invertibility of Estimation Error and Sensor Noise Covariances

Although the globally optimal distributed Kalman filtering fusion has been proposed and studied for more than twenty years, the invertibility of estimation error and measurement noise covariances has been always a restrictive assumption to derive a globally optimal distributed Kalman filtering fusion equivalent to the centralized Kalman filtering fusion. This letter proposes an optimal distributed Kalman filtering fusion algorithm for general dynamic systems without invertibility of estimation error and measurement noise covariances. The new algorithm uses the convex combination fusion, whose fusion weights are recursively given. Computer experiments show that the performance of this fusion algorithm is very likely to be equivalent to that of the centralized Kalman filtering fusion. In practice, the new fusion algorithm can be applied to any distributed Kalman filtering fusion, such as the equality constrained distributed Kalman filtering fusion.