Positioning and navigation are important tasks for autonomous mobile robots. Different sensors, including video cameras, can be used for this purpose. One approach to estimating the movement between two camera positions is based on solving the problem of minimizing the reprojection error. The numerical solution of this problem for a large number of observed points can be time-consuming for on-board systems of autonomous robots. In the paper, the approach to calculate the reprojection error is proposed. This approach allows reducing the complexity of the calculation of the reprojection error to a constant time independent of the number of observed points. Experimental tests were carried out. It is shown that this approach demonstrates similar accuracy in comparison with the standard one.