Bias-Error Accumulation Analysis for Inertial Navigation Methods

Abstract

In theera of Internet of Things (IoT), sensor plays a more vital role and its quality has a great impact on final measurement. From the viewpoint of final measurement, there are two kinds of effects: bias-only measurement and error-growth measurement. The bias-only measurement can be directly read from a sensing device, and each measurement is only distorted by the inherited bias error of the sensor, e.g., measuring temperature by a thermometer sensor. On the other hand, the error-growth measurement cannot be read directly but be calculated by combining multiple former sampling data, therefore multiple bias errors are accumulated in the measurement. For instance, in inertial navigation, the raw data sampled from an inertial measurement unit (IMU) are converted into a trajectory by multiple integral operations, so the errors of new sampling data are continuously added into the trajectory, and the deviation of the traced trajectory will reach an unacceptable level over time. Clearly, a good IMU trajectory strategy is the one with a less error-accumulation effect. Unfortunately, the analysis of error-growth effect remains not well studied, which motivates this work. This letter first proposes a theoretical error-growth effect analysis framework. Next, we use it to analyze three typical inertial methods, namely single-IMU method, gyro-free-IMU (GF-IMU) method, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> -free accelerometer pair (OFAP) method. Finally, the theoretical derivations of the three inertial methods are proved by simulation results.