Abstract: Included are embodiments for determining an inertial quantity. One embodiment of a method includes combining readings from a plurality of inertial sensors to produce an estimate of the value of an inertial quantity in a manner that is fault-tolerant, more accurate than traditional sensor arrangements, and able to handle non-linear and non-Gaussian systems. Embodiments of a method also include utilizing a Monte Carlo estimation-based inference system to adaptively combine the inertial sensor outputs into a fault-tolerant highly-accurate inertial quantity estimate, an axis-reversed-paired physical arrangement of inertial sensors to minimize effects of environmental and process noise, and cross-associating sensors to ensure good sensor associations and reduce the effects of sample impoverishment.