Using geo-mapping data and only at least one inertial sensor, a Bayesian estimator uses at least one element of an uncorrected inertial navigation vector, of a moveable object on a surface, to estimate inertial navigation error information including corresponding statistical information. The estimated inertial navigation error information is used to error correct the uncorrected inertial navigation vector. The Bayesian filter also predicts inertial navigation error information, including corresponding statistical information, for a future time instance when a next uncorrected inertial navigation vector will be obtained.