A theoretical study about H∞Filter based SLAM is proposed to propose a sufficient condition for estimation purposes. Two different cases of initial state covariance are given and analyzed to obtain a best solution for SLAM problem with consideration of process and measurement noises statistical behavior. If the proposed conditions are not satisfied during estimation, then the estimation will exhibit unbounded uncertainties and consequently result in erroneous inference. Simulation results demonstrates the performance as what this paper suggested on the theoretical analysis. These results consistently supports and guarantees our previous findings.