Article
A Global Interconnected Observer for Attitude and
Gyro Bias Estimation with Vector Measurements
Huijuan Guo * , Huiying Liu, Xiaoxiang Hu and Yan Zhou
School of Automation, Northwestern Polytechnical University, Xi’an 710072, China;
lhy2005@nwpu.edu.cn (H.L.); xxhu@nwpu.edu.cn (X.H.); lea@mail.nwpu.edu.cn (Y.Z.)
* Correspondence: guohuijuan@mail.nwpu.edu.cn
Received: 10 October 2020; Accepted: 12 November 2020; Published: 14 November 2020
Abstract:
This paper proposes a novel interconnected observer to get good estimates of attitude and
gyro bias from high-noise vector measurements. The observer is derived based on the theory of
nonlinear and linear cascade systems, and its error dynamics have the properties of global exponential
stability and robustness to bounded noise. These properties ensure the convergence and boundedness
of the attitude and gyro bias estimation errors. To obtain higher estimation accuracy, an approach to
calculate time-varying gains for the proposed auxiliary observer is designed under the premise of
considering noise terms in the rate gyro and vector sensors. The simulation results show that when
the vector sensors’ outputs contain high-level noise, the proposed observer with time-varying gains
yields better performance in both the transient and steady-state phases.
Keywords:
attitude estimation; nonlinear observer; global exponential stability; robustness;
navigation; low-cost sensor
1. Introduction
Attitude estimation of a rigid body is an indispensable part of navigation. Questions of estimating
attitude have been a field of concern for decades due to its numerous applications in various systems,
such as unmanned underwater vehicles (UUVs) [
1
], unmanned aerial vehicles (UAVs) [
2
], and others [
3
].
A rigid body’s attitude can be resolved by integrating the angular velocity from a rate gyro output.
However, even with high-precision gyros, the accumulated drift over time can affect the accuracy of
the attitude estimation, not to mention the low-cost ones. A typical approach to estimate attitude is to
utilize algebraic methods of vector measurements only by comparing vectors measured in either the
body-fixed coordinate frame or the reference frame with vectors measured in the other. Triad and Quest
in [
4
] used two or more nonparallel vector measurements to determine the attitude. Unfortunately,
bias and noise can easily corrupt the vector measurements. Therefore, combining angular velocity
sensors with vector sensors (e.g., accelerometers, magnetometers, star trackers, or sun sensors) has
been developed for improving the estimation accuracy.
The current approaches for estimating attitude and gyro bias from vector sensors and rate gyros
can be summarized into two classes, stochastic filtering algorithms (such as EKF, UKF, and their
variants; see [
5
–
7
]) and nonlinear observers (e.g., [
8
,
9
]). Although EKFs and UKFs have been widely
used, they cannot guarantee convergence in strongly nonlinear systems, and UKFs may increase
the computational cost. In recent years, more efforts have been made in constructing nonlinear
observers. In [
10
,
11
], nonlinear complementary filters designed on the special orthogonal group
SO(
3
)
for low-cost measurement units became the foundation of other observers. On this basis,
Grip et al.
[
12
]
developed semi-globally stable observers with gyro bias and time-varying reference vectors. After that,
they came up with an alternative semi-global attitude observer in the unit quaternion space [
13
] by
employing the theory of cascaded linear and nonlinear system observers, which appeared in [
14
,
15
].
Sensors 2020, 20, 6514; doi:10.3390/s20226514 www.mdpi.com/journal/sensors
