A linear state space model is of two equations, one of state space and the other of measurement. Estimation methods for the parameters of the model have been developed from the historic Kalman filter method. The Bayes estimation has also been used under a variety of conditions on the parameter space. We explored the availability of the Bayes method for parameter estimation with no constraints on the parameter space and found that the estimation for the state space is acceptable as long as the priors are not vague on both the state and the parameter space. We also investigated the model where the measurement matrix is contaminated with noise and found that the estimates for the state space were more accurate than those by the methods in literature. We made remarks on extended applications of the Bayes method for the linear state space model where a variety of constraints are imposed on the parameter space.