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This paper presents a statistically consistent SLAM algorithm where the environment is represented using a collection of B-Splines. The use of B-Splines allow environment to be represented without having to extract specific geometric features such as lines or points. Our previous work proposed a new observation model that enables raw measurements taken from a laser range finder to be transferred into relative position information between the control points of a B-Spline and the robot pose where the observation is made. One of the unresolved issues in the work was the estimation of the observation covariance, which is addressed through an analytical approach in this paper. As the uncertainty associated with the observation model is accurately defined and an optimization approach is used in the estimation process, the proposed SLAM algorithm can produce consistent estimates. Both simulation and experimental data are used for evaluation of the results.