We examine statistical models of noise, processing calculus, filtering and signal processing in MEMS-technology inertial measurement units (IMUs). Dynamic systems are controlled using the measured data which perturbed by the noise, drift, bias, etc. In aerospace, automotive, electronic, manufacturing, medical, naval and robotic systems, the linear (a(x),a(y),a(z)) and angular (alpha(theta)alpha(phi)alpha(psi)) accelerations are measured as ((a(x)) over cap,(a(y)) over cap,(a(z)) over cap) and ((alpha(theta)) over cap,(alpha(phi)) over cap,(alpha(psi)) over cap). The major objective is to enable physical and processing data integrity (conformity, consistency, completeness and validity) to assess system performance and capabilities by deriving adequate post-processed ((a(x)) over tilde,(a(y)) over tilde,(a(z)) over tilde) and ((alpha(theta)) over tilde,(alpha(phi)) over tilde,(alpha(Psi)) over tilde). Low-power multi-degree-of-freedom MEMS accelerometers and gyroscopes are studied. These IMUs include multi-axis accelerometer and gyroscope with processing integrated circuits (ICs). These ICs implement sensing, diagnostics, compensation, interfacing, conversions, signal conditioning, etc. The strategic-, navigation-, tactical- and consumer-grade IMUs may require post-processing. The data integrity enhancement is needed in the inertial navigation systems (aircraft, satellites, submarines and unmanned aerial vehicles), cell phones, gimbals, robots, etc. Noise attenuation, similar to arcsecond/sec and similar to mu g stability, similar to 500 Hz bandwidth, linearity, and adequate signal processing may be accomplished by the navigation-grade IMUs. This will reduce the dependence on global positioning systems, as well as ensure uncompromised navigation, guidance and control. The information quality is affected by the device physics, probabilistic characteristics, processing capabilities, etc. The data quality affects system's performance metrics, decision analysis, mission effectiveness, etc. The MEMS IMUs characteristics are of a particular importance for command, control and intelligence systems. With fundamental limits on sensing, microfabrication and microelectronics constraints, the advanced processing calculus and enabling signal processing may ensure beyond-state-of-the-art capabilities.