This paper explores a novel model to describe linear dynamic system with random delays. Compared with the existing research, the probabilities of random delays in the novel model are calculated by conditional probabilities. Therefore, the process noises and measurements noises in the new model for random delay problems are infinitely correlated. By treating the model as random parameter matrices Kalman filtering with one-step correlated noises approximately, the new state estimators are presented. Numerical examples show that the new estimators work better than the existing algorithm in many cases.

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.

In this paper, a multisensor linear dynamic system with model uncertainty and bounded noises is considered. Based on previously developed set-valued estimation methods in terms of convex optimization, we propose several efficient algorithms of centralized sensor fusion, distributed sensor fusion, and multi-algorithm fusion to minimize the Euclidian estimation error of the state vector. Obviously, an ellipsoid/box with a larger “size” cannot be in general guaranteed to contain another ellipsoid/box with a smaller “size” since centers and shapes of the two ellipsoids/boxes may be different from each other. This fact and the complementary advantages of multiple sensors and multiple algorithms motivate us to construct multiple estimation ellipsoids/boxes squashed along each entry of the state vector as much as possible respectively by using the technique of multiple differently weighted objectives. Then intersection fusion of these estimation ellipsoids/boxes yields a final Euclidian-error-minimized state estimate. Numerical examples show that the new method with multi-algorithm at both the sensors and the fusion center can significantly reduce the Euclidian estimation error of the state.