The present invention provides a new set of algorithmic solutions to accommodate track inaccuracy information in track databases. Navigation and measurement aiding processes are defined by a stochastic mode relative to a moving rail frame defined so that it is aligned with the heading of the compensated track database at the current along track-position. Filtering generates long and short wavelength track alignment disturbances commensurate with track grade to compensate for track database errors; a stochastic error model is defined as the difference between the deterministic implementation and the actual stochastic processes Bayesian estimation of the error variables is implemented via a digital Kalman filter with the navigation, database, and measurement errors removed by subtracting the filter estimates.