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) verti-cal channel instability, which primarily results from the positive gravity feedbackthat takes place in the numerical integration step of the accelerometer mea-surements. Traditional solutions to the problem include using information fromauxiliary sensors, typically barometers and global navigation satellite systems(GNSSs), integrated into INSs through feedback control loops (referred to asmechanizations) and/or Kalman filters (KFs). Most studies on this subject lackclarity regarding the methodology used for the mechanization tuning (by show-ing excessive empiricism) and/or disregard the benefits of using optimal controltechniques for the purpose of the latter. This study, therefore, reviews the mainmechanization used for vertical channel stabilization of baro-inertial integra-tions and presents, as its main contribution, the performance analysis of newtuning techniques based on optimal control theory, namely, by linear quadraticregulator (LQR) and by minimization of performance indices such as the inte-gral absolute error (IAE), integral squared error (ISE), integral of time multipliedabsolute error (ITAE), and integral of time multiplied squared error (ITSE).To validate the proposed tunings, the integrated altitude and vertical velocitymean errors (MEs) and standard deviations (SDs) are used as metrics, whichare compared with the corresponding MEs/SDs of the empirical tuning withhighest performance/acceptance in the literature. We also evaluate the abilityof the mechanizations to fulfill their ultimate goal, namely, to track the refer-ence barometer input, by also attenuating its noise. Based on simulated andexperimental results, the present study demonstrates and validates the effective-ness/robustness of the proposed optimal tunings, particularly those based onLQR and ITAE minimization.