Multi-sensor estimation fusion for linear equality constrained dynamic systems

The state of many dynamic systems evolve subject to some linear equality constraints. Using different techniques, different state estimators for linear equality constrained dynamic systems have been developed in the literature, including the pseudo measurement method, the projection method, the null space method, and the direct elimination method. However, their extension to the multi-sensor case has not been addressed. In this paper, using the measurement augmentation technique, we first extend all the above four types of estimators to multi-sensor constrained centralized fusion problems. Then the properties of these centralized fusers are analyzed. For multi-sensor constrained distributed fusion, direct application of standard distributed fusion is involved due to the singularity of local estimation mean square error (MSE) matrices. We suggest to use nonstandard distributed fusion by fully considering the difference between constrained and unconstrained state estimation. For multi-sensor constrained distributed fusion, we propose to send in dimension reduced local state estimates which are directly available in both the null space method and the direct elimination method. In this way, the singularity issue of the MSE matrices can be circumvented with saved communication from local sensors to the fusion center. Numerical examples further illustrate the similarities and differences among different estimation fusers.