Minimizing Euclidian state estimation error for uncertain dynamic systems based on multisensor and multi-algorithm Fusion

In this paper, a dynamic system with model uncertainty and bounded noises is considered. We propose several efficient methods of centralized fusion, distributed fusion and fusion of multiple parallel algorithms for minimizing Euclidian estimation error of the state vector. To make Euclidian estimation error as small as possible, the classic measure of “size” of an ellipsoid-trace of the shape matrix of the ellipsoid is extended to a class of weighted measure which can emphasize the importance of the interested entry of the state vector and make its confidence interval smaller. Moreover, it can be proved that both the centralized fusion and the distributed fusion are better than the estimation of single sensor in the class of the weighted measures. These results are illustrated by a numerical example. Most importantly, sufficiently taking advantages of the two facts that minimizing a scalar objective cannot guarantee to derive an optimal multi-dimensional confidence ellipsoid solution, as well as, multiple sensors and multiple algorithms have the feature of advantage complementary, we will construct various estimation fusion methods at both the fusion center and local sensors to yield as significantly as possible interlaced estimate intervals of every entry of the state vector for minimizing Euclidian estimation error.