An inertial sensing system comprises a first multi-axis atomic inertial sensor, a second multi-axis atomic inertial sensor, and an optical multiplexer optically coupled to the first and second multi-axis atomic inertial sensors. The optical multiplexer is configured to sequentially direct light along different axes of the first and second multi-axis atomic inertial sensors. A plurality of micro-electrical-mechanical systems (MEMS) inertial sensors is in operative communication with the first and second multi-axis atomic inertial sensors. Output signals from the first and second multi-axis atomic inertial sensors aid in correcting errors produced by the MEMS inertial sensors by sequentially updating output signals from the MEMS inertial sensors.