Orientation estimation using low cost sensors is an important task for Micro Aerial Vehicles (MAVs) in order to obtain a good feedback for the attitude controller. The challenges come from the low accuracy and noisy data of the MicroElectroMechanical System (MEMS) technology, which is the basis of modern, miniaturized inertial sensors. In this article, we describe a novel approach to obtain an estimation of the orientation in quaternion form from the observations of gravity and magnetic field. Our approach provides a quaternion estimation as the algebraic solution of a system from inertial/magnetic observations. We separate the problems of finding the "tilt" quaternion and the heading quaternion in two sub-parts of our system. This procedure is the key for avoiding the impact of the magnetic disturbances on the roll and pitch components of the orientation when the sensor is surrounded by unwanted magnetic flux. We demonstrate the validity of our method first analytically and then empirically using simulated data. We propose a novel complementary filter for MAVs that fuses together gyroscope data with accelerometer and magnetic field readings. The correction part of the filter is based on the method described above and works for both IMU (Inertial Measurement Unit) and MARG (Magnetic, Angular Rate, and Gravity) sensors. We evaluate the effectiveness of the filter and show that it significantly outperforms other common methods, using publicly available datasets with ground-truth data recorded during a real flight experiment of a micro quadrotor helicopter.

/pdf/keeping-a-good-attitude-a-quaternion-based-orientation-2uoi13loy2.pdf

Keeping a Good Attitude: A Quaternion-Based Orientation Filter for IMUs and MARGs

This paper proposes a novel quaternion-based attitude estimator with magnetic, angular rate, and gravity (MARG) sensor arrays. A new structure of a fixed-gain complementary filter is designed fusing related sensors. To avoid using iterative algorithms, the accelerometer-based attitude determination is transformed into a linear system. Stable solution to this system is obtained via control theory. With only one matrix multiplication, the solution can be computed. Using the increment of the solution, we design a complementary filter that fuses gyroscope and accelerometer together. The proposed filter is fast, since it is free of iteration. We name the proposed filter the fast complementary filter (FCF). To decrease significant effects of unknown magnetic distortion imposing on the magnetometer, a stepwise filtering architecture is designed. The magnetic output is fused with the estimated gravity from gyroscope and accelerometer using a second complementary filter when there is no significant magnetic distortion. Several experiments are carried out on real hardware to show the performance and some comparisons. Results show that the proposed FCF can reach the accuracy of Kalman filter. It successfully finds a balance between estimation accuracy and time consumption. Compared with iterative methods, the proposed FCF has much less convergence speed. Besides, it is shown that the magnetic distortion would not affect the estimated Euler angles.

Fast Complementary Filter for Attitude Estimation Using Low-Cost MARG Sensors

Focusing on generalized sensor combinations, this paper deals with the attitude estimation problem using a linear complementary filter (CF). The quaternion observation model is obtained via a gradient descent algorithm. An additive measurement model is then established according to derived results. The filter is named as the generalized CF where the observation model is simplified as a linear one that is quite different from previous-reported brute-force nonlinear results. Moreover, we prove that representative derivative-based optimization algorithms are essentially equivalent to each other. Derivations are given to establish the state model based on the quaternion kinematic equation. The proposed algorithm is validated under several experimental conditions involving the free-living environment, harsh external field disturbances, and aerial flight test aided by robotic vision. Using the specially designed experimental devices, data acquisition and algorithm computations are performed to give comparisons on accuracy, robustness, time-consumption, and so on with representative methods. The results show that not only the proposed filter can give fast, accurate, and stable estimates in terms of various sensor combinations but also produces robust attitude estimation in the scenario of harsh situations, e.g., irregular magnetic distortion. Note to Practitioners —Multisensor attitude estimation is a crucial technique in robotic devices. Many existing methods focus on the orientation fusion of specific sensor combinations. In this paper, we make the problem more concise. The results given in this paper are very general and can significantly decrease the space consumption and computation burden without losing the original estimation accuracy. Such performance will be of benefit to robotic platforms requiring flexible and easy-to-tune attitude estimation in the future.

https://hal.archives-ouvertes.fr/hal-01958652/document

Generalized Linear Quaternion Complementary Filter for Attitude Estimation From Multisensor Observations: An Optimization Approach

40 years of sensor fusion for orientation tracking via magnetic and inertial measurement units: Methods, lessons learned, and future challenges

This paper presents a quaternion-based Kalman filter for real-time estimation of the orientation of a quadrotor. Quaternions are used to represent rotation relationship between navigation frame and body frame. Processing of a 3-axis accelerometer using Adaptive-Step Gradient Descent (ASGD) produces a computed quaternion input to the Kalman filter. The step-size in GD is set in direct proportion to the physical orientation rate. Kalman filter combines 3-axis gyroscope and computed quaternion to determine pitch and roll angles. This combination overcomes linearization error of the measurement equations and reduces the calculation cost. 3-axis magnetometer is separated from ASGD to independently calculate yaw angle for Attitude Heading Reference System (AHRS). This AHRS algorithm is able to remove the magnetic distortion impact. Experiments are carried out in the small-size flight controller and the real world flying test shows the proposed AHRS algorithm is adequate for the real-time estimation of the orien...

https://journals.sagepub.com/doi/pdf/10.5772/61313

Quaternion-Based Kalman Filter for AHRS Using an Adaptive-Step Gradient Descent Algorithm:

In this paper, we consider the problem of a rigid body attitude estimation under external acceleration using a small inertial/magnetic sensors module containing a triad of gyroscope, accelerometer, and magnetometer. This paper is focused on two main challenges. The first one concerns the attitude estimation during dynamic cases, in which external acceleration occurs. In order to compensate for such external acceleration, we design a quaternion-based adaptive Kalman filter q-AKF. Precisely, a smart detector is designed to decide whether the body is in static or dynamic case. Then, the covariance matrix of the external acceleration is estimated to tune the filter gain. The second challenge is related to the energy consumption issue of gyroscope. In order to ensure a longer battery life for the inertial measurement units, we study the way to reduce the gyro measurements acquisition by switching on/off the sensor while maintaining an acceptable attitude estimation. The switching policy is based on the designed detector. The efficiency of the proposed scheme is evaluated by means of numerical simulations and experimental tests.

/pdf/energy-aware-adaptive-attitude-estimation-under-external-zouen5r7z5.pdf

Energy-Aware Adaptive Attitude Estimation Under External Acceleration for Pedestrian Navigation

This paper considers rigid body attitude estimation from a small inertial/magnetic sensor module containing triaxial gyroscopes, accelerometers, and magnetometers. Precisely, two challenges are addressed. The first one concerns attitude estimation during various dynamic conditions, in which external acceleration occurs. Although external acceleration is one of the main source of loss of performance in attitude estimation methods, this problem has not been sufficiently addressed in the literature. An adaptive algorithm compensating external acceleration from the residual in the accelerometer is proposed. At each step, the covariance matrix associated with the external acceleration is estimated to adaptively tune the filter gain. The second challenge is focused on the energy consumption issue of gyroscopes for long-term battery life of Inertial Measurement Units. We study the way to reduce the gyro measurement acquisition while maintaining acceptable attitude estimation. Through numerical simulations, under external acceleration and parsimonious gyroscope's use, the efficiency of the proposed q-AKF is illustrated.

/pdf/adaptive-kalman-filter-for-mems-imu-based-attitude-4dpyvpzjt6.pdf

Adaptive Kalman filter for MEMS-IMU based attitude estimation under external acceleration and parsimonious use of gyroscopes

This paper proposes the design of an attitude estimation algorithm for a rigid body subject to accelerated maneuvers. Unlike the current literature where the process model is usually driven by triaxial gyroscope measurements, we investigate a new formulation of the state-space model where the process model is given by triaxial accelerometer measurements. The observation model is given by triaxial gyroscope and magnetometer measurements. The proposed model is written as a descriptor system and takes the external acceleration sensed by the accelerometer into account. Based on this model, a Quaternion Descriptor Filter (QDF) is developped and its performance is evaluated through simulations and experimental tests in pedestrian navigation.

/pdf/data-fusion-based-descriptor-approach-for-attitude-2jv235ppgk.pdf

Data fusion-based descriptor approach for attitude estimation under accelerated maneuvers

In this paper, a new modeling and filtering approach for rigid body attitude estimation is investigated. In contrast to the current state-of-the art where the process model is driven by gyroscope measurements, we propose an alternative modeling formulation where the process model is fed by the magnetometer measurements. The resulting dynamic model takes the form of a descriptor system, also known as singular system. Based on this model and using the quaternion formalism we derive a recursive filter whose performance is validated through numerical and experimental tests.

Descriptor approach for attitude estimation

A trailer assist system is an Advanced Driver Assistance System. It enables a more effective maneuvering of a trailer towed by a vehicle. It is particularly useful in constraint scenarios such as parking, traffic jam, turns, etc. Traditionally, trailer assist systems are based on image processing methods or require specific sensors to measure the hitch angle. In this paper, we propose to estimate the hitch angle by making use of the existing rear camera of the vehicle and by using an image processing approach, thus avoiding the supplementary angle measurement sensor. To this extent, a dedicated database is collected and annotated. Two different methods are developed to predict this corresponding angle, the first method is based on a convolutional neural network and the second one is a deterministic image processing method. The two approaches are finally compared in terms of accuracy and execution time.

Aida Makni

Papers

Energy-Aware Adaptive Attitude Estimation Under External Acceleration for Pedestrian Navigation

Adaptive Kalman filter for MEMS-IMU based attitude estimation under external acceleration and parsimonious use of gyroscopes

Data fusion-based descriptor approach for attitude estimation under accelerated maneuvers

Descriptor approach for attitude estimation

Image Based Vehicle-Trailer Angle Estimation