Exploiting the quantum nature of atoms through the use of matter-wave interferometry has lead to the development of devices sensitive to, among other things, the local gravitational acceleration. Measurements of the gravitational acceleration have applications ranging from detection of subterranean density di erences to observation of general relativistic e ects. Light-pulse atom interferometers provide an absolute measurement of the gravitational acceleration with a sensitivity competitive and even surpassing the performance of classical sensors. The advantages of atom interferometers as inertial measurement devices have lead to e orts in increasing sensitivity and decreasing the physical dimensions of the measurement head, allowing them to be more transportable for eld use applications. With increasing sensitivity, it becomes more critical to address the noise source limitations a ecting the measurement, speci cally the in uence of ground motion on measurements. Vibrations coupling into the inertial reference add a time varying phase shift uncommon to the paths of the interferometer. This limitation is especially pertinent to transportable atom gravimeters measuring in the eld where inertial noise is typically far higher than in relatively quiet laboratory environments. Within this work, implementation and demonstration of inertial noise post-correction in an atom interferometer is shown within low inertial noise environments and simulated strong motion environments. For a high pulse separation time atom interferometer (T = 78 ms) post-correction yielded an increase in the short term stability from 4.4 x 10 ̄6 m/s2/√Hz to 9.2 x 10 ̄7 m/s2/√Hz. This method was reproduced with a di erent motion sensor to perform post-correction in a high motion environment, generated by introducing additional movement onto the inertial reference. By performing post-correction in the high motion environment, we were able to show an increase of short term stability of γ = 73.8. Current limitations to the post-correction resulted from self noise resolution limitations and spectral resolutions limitations. Beyond corrections with commercially available sensors, this work demonstrates the rst post-correction with a next generation compact optomechanical sensor. This optomechanical sensor is formed from monolithic fused silica capable of sensitively measuring accelerations of a harmonic oscillator test mass, which can be read-out optically. This novel motion sensor has the advantage to any previously shown sensor used for post-correction in the capacity that it is vacuum compatible, insensitive to magnetic elds and has the potential to be implemented directly into the inertial reference. In this work, inertial noise post-correction in a simulated high motion environment is shown, correcting from a short term stability of 8 x 10 ̄3 m/s2/√Hz to 5 x 10 ̄4 m/s2/√Hz. Post-correction was limited by the parasitic cavities within the ber required for optical read-out of the harmonic oscillator displacement and intensity noise uctuations of the source laser. The results shown within this work are congruent with previous works on atom chip gravimeters, both of which help move towards portable hand-held gravimeter measurement heads capable of sensitive inertial measurement.