Constrained non-linear fitting for stochastic modeling of inertial sensors

Nowadays with the development of inertial sensors based on Micro-Electromechanical Systems (MEMS), embedded accelerometers and gyroscopes can be found in several devices and platforms ranging from watches, smart phones, video game consoles up to terrestrial navigation and unmanned aerial vehicles (UAVs), etc. Despite the wide range of applications where such sensors are being used, it is well known that low-cost inertial sensors (MEMS grade) are affected by stochastic and deterministic errors that degrade the systems performance in a short period of time, which compromise the integrity and reliability, specially in navigation systems. Although different researches have been achieved to model the stochastic error of the MEMS sensors, it should be mentioned that the estimation of the stochastic noise component is still a non-trivial task. Therefore in this paper we evaluate an approach to obtain the stochastic error parameters by using a constrained non-linear fitting. We also implemented some of the most relevant works reported in the literature for estimating the stochastic error parameters of MEMS sensors. In order to evaluate the performance, a simulation analysis is achieved by generating a noise sources that typically influence the inertial sensors. The simulation shows that the non-linear fitting provides better results than traditional and some recent techniques in terms of the estimation of noise sources parameters. Eventually, we applied it to estimate the stochastic error model parameters from two MEMS-based Inertial Measurement Units (IMUs), specifically, the low-cost Microstrain 3DM-GX3-IMU and the ultra-low-cost Sparkfun Atomic IMU 6 dof. The stochastic error model parameters obtained from the analysis can be easily adapted into a GPS/INS integrated system.