Globally exponentially stable attitude and gyro bias estimation with application to GNSS/INS integration (original) (raw)

A nonlinear observer for integration of GNSS and IMU measurements with gyro bias estimation

2012

We present an observer for estimating position, velocity, attitude, and gyro bias, by using inertial measurements of accelerations and angular velocities, magnetometer measurements, and satellite-based measurements of position and (optionally) velocity. The design proceeds in two stages: in Stage I, an attitude and gyro bias estimator is designed based on an unmeasured signal. In Stage II, that design is recovered using measured signals only, by combining it with a position and velocity estimator. We prove exponential convergence of the estimation error from all desired initial conditions and test the design using realistic flight simulation.

Nonlinear observer for GNSS-aided inertial navigation with quaternion-based attitude estimation

2013 American Control Conference, 2013

For applications with limited computational capacity, observers designed based on nonlinear stability theory offer an alternative to computationally demanding extended Kalman filters. In this paper, we present a semiglobally stable nonlinear observer for estimating position, velocity, attitude, and gyro bias by combining a GNSS receiver with an inertial measurement unit including a magnetometer. Previous work by the authors on this topic was based on local navigation equations that ignored the Earth's rotation and curvature. Moreover, the attitude was represented by an over-parameterized 9degrees-of-freedom matrix. The current paper improves on these aspects by using navigation equations that take the Earth's rotation and curvature into account, and by representing the attitude estimate as a unit quaternion. Furthermore, the observer is tested experimentally on data from a light fixedwing aircraft.

A GES attitude observer with single vector observations

Automatica, 2012

This paper proposes a globally exponentially stable (GES) observer for attitude estimation based on a single time-varying reference vector, in inertial coordinates, and corresponding vector, in body-fixed coordinates, in addition to angular velocity readings. The proposed solution is computationally efficient and, in spite of the fact that the observer does not evolve on the Special Orthogonal Group SO(3), an explicit solution on SO(3) is also provided, whose error is shown to converge exponentially fast to zero for all initial conditions. The distinct roles of the inertial and the corresponding body-fixed vectors on the observability of the system are also examined and simulation results are shown that illustrate the performance of the proposed attitude observer in the presence of low-grade sensor specifications.

A uniformly semiglobally exponentially stable nonlinear observer for GNSS- and camera-aided inertial navigation

22nd Mediterranean Conference on Control and Automation, 2014

In this paper a nonlinear observer for estimation of position, velocity, acceleration, attitude and gyro bias of an Unmanned Aerial Vehicle (UAV) is proposed. The sensor suite consists of an Inertial Measurement Unit (IMU), a Global Navigation Satellite System (GNSS) receiver, a video camera, an altimeter, and an inclinometer. The camera and machine vision systems can track features from the environment and calculate the optical flow. These data, together with those from the other sensors, are fed to the observer, that is proven to be uniformly semiglobally exponentially stable (USGES). The performance of the observer is tested on simulated data by assuming that the camera system can provide the necessary information.

Globally exponentially stable cascade observers for attitude estimation

Control Engineering Practice, 2012

This paper presents the design, analysis, and performance evaluation of a novel cascade observer for attitude estimation. A sensor-based observer, which resorts to rate gyro readings and a set of vector observations, estimates the rate gyro bias. Afterwards, a cascaded observer explicitly estimates the attitude in the form of a rotation matrix based on the rate gyro measurements, the vector observations, and the estimated gyro bias. The overall error dynamics are globally exponentially stable and the proposed system is computationally efficient. Finally, the resulting estimator is successfully evaluated, in simulation and experimentally, with ground truth data in both cases.

Attitude Estimation Based on Time-Varying Reference Vectors with Biased Gyro and Vector Measurements

IFAC Proceedings Volumes, 2011

We present two results on attitude estimation using vector and rate gyro measurements, when both sets of measurements are biased. The first result concerns an observer for attitude and gyro bias that has previously been presented by Hamel and Mahony, and by Mahony, Hamel, and Pflimlin, with proven almost-global stability results when either (i) the reference vectors in the inertial frame are stationary; or (ii) the reference vectors are time-varying but the gyro measurements are unbiased. We prove that the same observer with an added parameter projection is semiglobally exponentially stable when bias estimation is included and the reference vectors are time-varying. The second result concerns estimation of bias in the body-fixed vector measurements. We show how the bias can be estimated in a manner that is decoupled from the attitude and gyro bias estimation, provided the measurements are sufficiently excited relative to the level of measurement noise.

Nonlinear Attitude Observer Based on Range and Inertial Measurements

IEEE Transactions on Control Systems Technology, 2013

We address the problem of attitude and rate gyros bias estimation based on inertial and range data. Range measurements are obtained from beacons installed in an inertial frame and acoustic sensors fixed in the moving body reference frame. A nonlinear observer is proposed and its stability and performance properties are studied resorting to Lyapunov techniques. In the presence of constant bias on the rate gyro measurements, the attitude and bias estimates are shown to converge exponentially fast to the desired values inside an almost global region of attraction. For time-varying bias with bounded derivative, a local result of ultimate boundedness is provided. The performance of the proposed nonlinear observer is validated experimentally using a high accuracy calibration table, which provides ground truth signals for comparison with the resulting estimates.

Nonlinear Attitude Estimation Using Intermittent Linear Velocity and Vector Measurements

2021 60th IEEE Conference on Decision and Control (CDC), 2021

This paper investigates the problem of continuous attitude estimation on SO(3) using continuous angular velocity and linear acceleration measurements as well as intermittent linear velocity and inertial vector measurements. First, we propose a nonlinear observer for the case where all the measurements are continuous and almost global asymptotic stability (AGAS) is shown using the notion of almost global input-to-state stability (ISS) on manifolds. Thereafter, a hybrid attitude observer, with AGAS guarantees, is proposed in terms of intermittent linear velocity and vector measurements. Numerical simulation results are presented to illustrate the performance of the proposed hybrid observer.

A global exponential observer for velocity-aided attitude estimation

2016

We propose a simple nonlinear observer for estimating the attitude and velocity of a rigid body from the measurements of specific acceleration, angular velocity, magnetic field (in body axes), and linear velocity (in body axes). It is uniformly globally exponentially convergent, and also enjoys other nice properties: global decoupling of pitch and roll estimation from magnetic measurements, good local behavior, and easy tuning. The observer is "geometry-free", in the sense that it respects only asymptotically the rotational geometry. The good behavior of the observer, even when the measurements are noisy and biased is illustrated in simulation.

Nonlinear Observer on SO(3) for Attitude Estimation on Rotating Earth using Single Vector Measurements

IEEE Control Systems Letters

This letter presents a novel attitude estimation solution, built on SO(3), that resorts to single measurements of a constant inertial vector, in addition to angular velocity readings provided by a set of three high-grade fiber optic rate gyros, which are assumed to be sensitive to the angular motion of the Earth. This approach contrasts with typical attitude solutions that require either a single but time-varying inertial vector, or measurements of two non-collinear inertial vectors. The designed nonlinear observer features only one tuning scalar parameter that, in view of the region of convergence of the rotation matrix error, is shown to render the proposed solution almost globally asymptotically stable. Extensive simulation results with realistic noise, including Monte Carlo, are presented that allow to assess the achievable performance.