Minimizing Euclidian State Estimation Error for Linear Uncertain Dynamic Systems Based on Multisensor and Multi-Algorithm 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.