The minimum variance state estimation for unconstrained systems is equivalent to the error covariance optimal state estimation, but now the optimal criterion of error covariance in unconstrained systems is still used to solve the state estimation of constrained systems, ignoring the variance of state estimation. This paper introduces the concept of matrix-convex-combination and derives the minimum variance fusion estimation based on optimal matrix-convex-combination. Then it is extended to linear equality constrained dynamic systems, and the minimum variance estimate with equality constraints based on matrix-convex-combination (C-MCCV) is proposed, which will reduce the covariance of constraint state estimation. At the same time, the statistical properties of C-MCCV are compared with that of the error covariance optimal constrained Kalman estimation (C-KP), and it is verified that C-MCCV is equivalent to C-KP when the state estimation converges within the constrained region. In this case, the equality constrained state estimation can be approximately regarded as unconstrained state estimation. The use of this algorithm is demonstrated on a simple vehicle tracking problem.