A precise quaternion-based navigation algorithm for simulating signals of accelerometers and gyroscopes with low sample frequencies

Abstract

Accelerometers and gyroscopes based on MEMS technology are promising for tracing motion in medicine, sport activities, human-machine interaction, robotics and many other areas due to the fact that they are self-containing and have a range of other advantages. Three orthogonally placed accelerometers and gyroscopes are combined into a single module fitted with a controller for processing the signals from inertial sensors. However, the same module may be suitable for one application and inapplicable for another, since the accuracy of tracking a motion trajectory depends not only on the error characteristics of the inertial sensors but also on the trajectory itself. Simulation may help decide whether an inertial measurement unit is a reasonable choice for a specific application or not. The idea is to allow the user to preset a desirable motion trajectory and error characteristics of the inertial sensors specified by their manufacturer. Then software simulates signals of real accelerometers and gyroscopes and computes a set of potential trajectories upon these signals. Upon the discrepancies between the prescribed and synthesized trajectories one can judge on applicability of the inertial sensors with the preset error characteristics for a specific task, without implementing a real device. The software should be based on well-known navigation equations, expressed via direction cosine matrices or quaternions. However, the equations are only valid for infinitesimal rotation angles. Their usage leads to cumulating errors in computation of some trajectories due to the fact that low-cost accelerometers and gyroscopes available on the market offer limited sample frequencies. The work reveals the problem related to usage of the above-mentioned equations, both analytically and by numerical experiments. Examples of trajectories irreproducible at low frequencies are shown. The work analyzes the reasons why some trajectories are irreproducible and shows that the reasons can scarcely be eliminated in case of rotation matrices. We have proposed amended equations universal for any trajectory and any sample frequency.

Keywords

• navigation equation
• mems accelerometer
• mems gyroscope
• poisson equation
• quaternion
• signal synthesis
• trajectory