ABSTRACT
Kalman filtering is one of the most popular recursive least mean square error (LMSE) algorithms to optimally estimate the unknown state or process of a dynamic system. This chapter describes the system model of Kalman filtering and presents the existing fusion formula. It presents a new distributed Kalman filtering fusion formula with singular estimation error covariance matrices. The chapter considers optimal Kalman filtering fusion with both singular covariances of filtering errors and measurement noises. It then provides several numerical examples that demonstrate that the globally optimal distributed Kalman filtering fusion (GODKF) not only provides theoretical support to the combination optimal distributed Kalman filtering fusion (CLDKF), but also uses less computation quantity than the CLDKF. The chapter also presents two types of dynamic systems modeled as two objects moving on a circle and a straight line with process noise and measurement noise, respectively.
