Abstract: A vision-aided inertial navigation system (VINS) implements a square-root multi- state constraint Kalman filter (SR-MSCKF) for navigation. In one example, a processor of a VINS receives image data and motion data for a plurality of poses of a frame of reference along a trajectory. The processor executes an Extended Kalman Filter (EKF)- based estimator to compute estimates for a position and orientation for each of the plurality of poses of the frame of reference along the trajectory. For features observed from multiple poses along the trajectory, the estimator computes constraints that geometrically relate the multiple poses of the respective feature. Using the motion data and the computed constraints, the estimator computes state estimates for the position and orientation of the frame of reference. Further, the estimator determines uncertainty data for the state estimates and maintains the uncertainty data as a square root factor of a covariance matrix.