Adaptive bias and attitude observer on the special orthogonal group for true-north gyrocompass systems: Theory and preliminary results

Abstract

This article reports an adaptive sensor bias observer and attitude observer operating directly on [Formula: see text] for true-north gyrocompass systems that utilize six-degree-of-freedom inertial measurement units (IMUs) with three-axis accelerometers and three-axis angular rate gyroscopes (without magnetometers). Most present-day low-cost robotic vehicles employ attitude estimation systems that employ microelectromechanical system (MEMS) magnetometers, angular rate gyros, and accelerometers to estimate magnetic attitude (roll, pitch, and magnetic heading) with limited heading accuracy. Present-day MEMS gyros are not sensitive enough to dynamically detect the Earth’s rotation, and thus cannot be used to estimate true-north geodetic heading. Relying on magnetic compasses can be problematic for vehicles that operate in environments with magnetic anomalies and those requiring high-accuracy navigation as the limited accuracy ([Formula: see text] error) of magnetic compasses is typically the largest error source in underwater vehicle navigation systems. Moreover, magnetic compasses need to undergo time-consuming recalibration for hard-iron and soft-iron errors every time a vehicle is reconfigured with a new instrument or other payload, as very frequently occurs on oceanographic marine vehicles. In contrast, the gyrocompass system reported herein utilizes fiber optic gyroscope (FOG) IMU angular rate gyro and MEMS accelerometer measurements (without magnetometers) to dynamically estimate the instrument’s time-varying true-north attitude (roll, pitch, and geodetic heading) in real-time while the instrument is subject to a priori unknown rotations. This gyrocompass system is immune to magnetic anomalies and does not require recalibration every time a new payload is added to or removed from the vehicle. Stability proofs for the reported bias and attitude observers, preliminary simulations, and a full-scale vehicle trial are reported that suggest the viability of the true-north gyrocompass system to provide dynamic real-time true-north heading, pitch, and roll utilizing a comparatively low-cost FOG IMU.

Uniform Complete Observability of Mass and Rotational Inertial Parameters in Adaptive Identification of Rigid-Body Plant Dynamics

“…There is an equivalence between persistant excitation (PE) and UCO. The relationship has been shown analytically for scalar plant models [9], for a class of nonlinear plants and associated parameter observers [5], and experimentally verified in the problem arising in sensor bias and attitude estimation in gyrocompass systems [24]. In the case of rigid body dynamic systems (1), the error system for ∆v (4) and ∆m (6) can be algebraically rearranged to be written as…”

“…In these approaches, the dynamical system of the error coordinates is needed and, in the case of rigid body dynamics, this system will be time-varying, and thus the observability condition is uniform for a given sliding time window [t 0 , t 0 + δ] t 0 , δ ∈ IR + . A practical application of this technique was employed by Spielvogel and Whitcomb in [24] to show asymptotic convergence of the sensor bias and observer to the true values. Spielvogel and Whitcomb show the equivalence between the signals having the property of persistent excitation and UCO of the error system ( [24] Lemma 1, proof in Appendix 1).…”

“…A practical application of this technique was employed by Spielvogel and Whitcomb in [24] to show asymptotic convergence of the sensor bias and observer to the true values. Spielvogel and Whitcomb show the equivalence between the signals having the property of persistent excitation and UCO of the error system ( [24] Lemma 1, proof in Appendix 1). This equivalence is shown in [9] for scalar adaptive plants.…”

“…If the pair [A e (t), C e ] is UCO then lim t→∞ ||∆m(t)|| = 0 as desired. (Proof is Lemma 1 in Appendix 1 of [24]). Thus, under this condition, parameter error will asymptotically converge to zero.…”

Online 3-Axis Magnetometer Hard-Iron and Soft-Iron Bias and Angular Velocity Sensor Bias Estimation Using Angular Velocity Sensors for Improved Dynamic Heading Accuracy

“…• Two papers by Spielvogel and Whitcomb (Spielvogel and Whitcomb, 2018b;Spielvogel and Whitcomb, 2019) do not address magnetometer calibration and instead focus on the calibration of high-end 6-axis IMUs (IMUs with a 3-axis accelerometer and a 3-axis optical angular rate sensor) used in gyrocompass systems. • Spielvogel and Whitcomb (Spielvogel and Whitcomb, 2018a) extends the work by Troni and Whitcomb (Troni and Whitcomb, 2019) to 9-axis IMUs.…”