A computer-implemented method is provided for generating the estimation of current position, velocity and acceleration state vectors and associated uncertainty estimation (covariance) of a boosting ballistic missile. The method includes constructing a state tensor of the projectile from a plurality of sensor measurements in Earth-Centered, Earth-Fixed (ECEF) coordinates; translating the state tensor to Cartesian coordinates as a transform state; determining a covariance matrix from the transform state; updating the transformed state as an updated transform state; and updating the covariance matrix as an updated covariance. The process can further include adjusting the covariance matrix by an approximate transition matrix and a process noise matrix. The noise matrix can be translated from a local noise matrix based on a propagation time-step, a scaling parameter, and a bias process noise level. A time-of-flight in the state tensor can be updated by smoothing from a launch event.