This paper shows that a general multisensor unbiased linearly weighted estimationfusion essentially is the linear minimum variance (LMV) estimation with linearequality constraint, and the general estimation fusion formula is developed by extendingthe Gauss-Markov estimation to the random parameter under estimation. First, we formulatethe problem of distributed estimation fusion in the LMV setting. In this setting, thefused estimator is a weighted sum of local estimates with a matrix weight. We show thatthe set of weights is optimal if and only if it is a solution of a matrix quadratic optimizationproblem subject to a convex linear equality constraint. Second, we present a uniquesolution to the above optimization problem, which depends only on the covariance matrixCk. Third, if a priori information, the expectation and covariance, of the estimated quantityis unknown, a necessary and suf[1] cient condition for the above LMV fusion becoming thebest unbiased LMV estimation with known prior information as the above is presented. Wealso discuss the generality and usefulness of the LMV fusion formulas developed. Finally,we provide an off-line recursion of Ck for a class of multisensor linear systems with coupledmeasurement noises.