Optimal distributed estimation fusion with transformed data

Most of the existing distributed estimation fusion algorithms rely on the existence of the inverses of the corresponding error covariance matrices, e.g., distributed estimation fusion algorithms based on the information form of the Kalman filter and the optimal weighted least-square (WLS) estimator. Theoretically speaking, the error covariance matrices are only at least positive semi-definite and not necessarily invertible. To overcome this, by taking a linear transformation of the raw measurements received by each local sensor, an optimal distributed estimation fusion scheme is proposed in this paper. Compared with the existing distributed estimation fusion schemes, the new algorithm is not only optimal in the sense that it is equivalent to the centralized fusion, the communication requirements from each sensor to the fusion center are equal to or less than most of the existing distributed fusion algorithms. One possible way to relieve the computational complexity of the new algorithm is also discussed.