Gyro-Free Inertial Navigation Systems Based on Linear Opto-Mechanical Accelerometers.

High-sensitivity uniaxial opto-mechanical accelerometers provide very accurate linear acceleration measurements. In addition, an array of at least six accelerometers allows the estimation of linear and angular accelerations and becomes a gyro-free inertial navigation system. In this paper, we analyze the performance of such systems considering opto-mechanical accelerometers with different sensitivities and bandwidths. In the six-accelerometer configuration adopted here, the angular acceleration is estimated using a linear combination of accelerometers' read-outs. The linear acceleration is estimated similarly but requires a correcting term that includes angular velocities. Accelerometers' colored noise from experimental data is used to derive, analytically and through simulations, the performance of the inertial sensor. Results for six accelerometers, separated by 0.5 m in a cube configuration show noise levels of 10-7 m s-2 and 10-5 m s-2 (in Allan deviation) for time scales of one second for the low-frequency (Hz) and high-frequency (kHz) opto-mechanical accelerometers, respectively. The Allan deviation for the angular velocity at one second is 10-5 rad s-1 and 5×10-4 rad s-1. Compared to other technologies such as MEMS-based inertial sensors and optical gyroscopes, the high-frequency opto-mechanical accelerometer exhibits better performance than tactical-grade MEMS for time scales shorter than 10 s. For angular velocity, it is only superior for time scales less than a few seconds. The linear acceleration of the low-frequency accelerometer outperforms the MEMS for time scales up to 300 s and for angular velocity only for a few seconds. Fiber optical gyroscopes are orders of magnitude better than the high- and low-frequency accelerometers in gyro-free configurations. However, when considering the theoretical thermal noise limit of the low-frequency opto-mechanical accelerometer, 5×10-11 m s-2, linear acceleration noise is orders of magnitude lower than MEMS navigation systems. Angular velocity precision is around 10-10 rad s-1 at one second and 5×10-7 rad s-1 at one hour, which is comparable to fiber optical gyroscopes. While experimental validation is yet not available, the results shown here indicate the potential of opto-mechanical accelerometers as gyro-free inertial navigation sensors, provided the fundamental noise limit of the accelerometer is reached, and technical limitations such as misalignments and initial conditions errors are well controlled.