Vertical channel stabilization of barometer‐aided inertial navigation systems by optimal control

Abstract

This study investigates the problem of inertial navigation system's (INS's) vertical channel instability, which primarily results from the positive gravity feedback that takes place in the numerical integration step of the accelerometer measurements. Traditional solutions to the problem include using information from auxiliary sensors, typically barometers and global navigation satellite systems (GNSSs), integrated into INSs through feedback control loops (referred to as mechanizations) and/or Kalman filters (KFs). Most studies on this subject lack clarity regarding the methodology used for the mechanization tuning (by showing excessive empiricism) and/or disregard the benefits of using optimal control techniques for the purpose of the latter. This study, therefore, reviews the main mechanization used for vertical channel stabilization of baro‐inertial integrations and presents, as its main contribution, the performance analysis of new tuning techniques based on optimal control theory, namely, by linear quadratic regulator (LQR) and by minimization of performance indices such as the integral absolute error (IAE), integral squared error (ISE), integral of time multiplied absolute error (ITAE), and integral of time multiplied squared error (ITSE). To validate the proposed tunings, the integrated altitude and vertical velocity mean errors (MEs) and standard deviations (SDs) are used as metrics, which are compared with the corresponding MEs/SDs of the empirical tuning with highest performance/acceptance in the literature. We also evaluate the ability of the mechanizations to fulfill their ultimate goal, namely, to track the reference barometer input, by also attenuating its noise. Based on simulated and experimental results, the present study demonstrates and validates the effectiveness/robustness of the proposed optimal tunings, particularly those based on LQR and ITAE minimization.