Acceleration random walk, from its name, is widely modeled as an error from random processes. Contrarily, we hypothesize that acceleration random walk at the averaging time up to several hours can be treated as a deterministic error. In this work, we present initial results toward understanding the physics underlying acceleration random walk and development of deterministic models and associated compensation techniques. Simultaneous scanning through an array of on-chip stress and temperature sensors while recording data from the accelerometer enables compensation of the acceleration random walk using a trained neural network estimator over a four-hour test run.