Inertial measurement units (IMUs) are fundamental for attitude control of drones. With the advancements in micro-electro-mechanical systems (MEMS) fabrication processes, size, power consumption, and price of these sensors have reduced significantly and attracted many new applications. However, this came at the expense of sensors requiring frequent recalibration, as they are highly contaminated with systematic errors. This paper presents a novel method to jointly calibrate the accelerometer, gyroscope, and magnetometer triad in a MEMS IMU without additional equipment. Opportunistic zero change in velocity and position updates, and inclination updates were used in conjunction with relative orientation updates from magnetometers in a robust batch least-squares adjustment. Solutions from the proposed self-calibration were compared to existing calibration methods. Empirical results suggest that the new method is robust against magnetic distortions and can achieve performance similar to a specialized calibration that uses a more accurate (and expensive) IMU as reference. The jointly estimated accelerometer and gyroscope calibration parameters can deliver a more accurate dead-reckoning solution than the popular multi-position calibration method (i.e., 54% improvement in orientation accuracy) by recovering the gyroscope scale error and other systematic errors. In addition, it can improve parameter observability as well as reduce calibration time by incorporating dynamic data with static orientations. The proposed calibration was also applied on-site pre-mission by simply waving the sensor by hand and was able to improve the orientation tracking accuracy by 73%.

The handling of 3D orientations is a common element in many problems that arise in the estimation and control of dynamic systems. Over-parametrizations such as unit quaternions are commonly used to avoid singularities but come with the property of an invariant which needs to be preserved. By using numerical optimization methods, these invariants are subject to numeric errors and require stabilization. In this work, we adopt methods known from optimal control for the problem of state estimation. We present an optimization-based attitude estimator using the measurements of an inertial measurement unit and evaluate the performance of a first-order stabilization of the invariant by modifying the dynamics. The uncertainties of the estimator are analyzed for different configurations of the proposed stabilization. Finally, we show how the stabilization affects the estimation of parameters and justify the use of an additional equality constraint for the invariant to yield more robust and consistent results.

In recent years, microelectromechanical system (MEMS) inertial sensors (3D accelerometers and 3D gyroscopes) have become widely available due to their small size and low cost.Inertial sensor measurements are obtained at high sampling rates and can be integrated to obtain position and orientation information.These estimates are accurate on a short time scale, but suffer from integration drift over longer time scales.To overcome this issue, inertial sensors are typically combined with additional sensors and models.In this tutorial we focus on the signal processing aspects of position and orientation estimation using inertial sensors.We discuss different modeling choices and a selected number of important algorithms.The algorithms include optimization-based smoothing and filtering as well as computationally cheaper extended Kalman filter and complementary filter implementations.The quality of their estimates is illustrated using both experimental and simulated data.

Precise estimation of position, velocity, and orientation is crucial for robust control in airborne applications such as the fast maneuvering power kites for airborne wind energy generators. In this paper we present a sensor fusion approach for the measurements of a global navigation satellite system receiver and an inertial measurement unit, using methods from direct optimal control. The resulting optimization problem is based on the minimization of the weighted squared residuals between model predictions and measurements and solved using a direct collocation discretization strategy. The framework allows the formulation of a batch and filter estimator which include beside the estimation of the navigational states the identification of sensor parameters such as biases of the inertial measurement unit. The results of the algorithms are evaluated against a reference trajectory of a maneuvering single propeller aircraft and achieve root mean squared errors below 1 m in position, 0.4 ms-1 in velocity, and 0.5 deg in orientation for the batch estimator. The contribution in this paper is a first step towards the required robustness of state estimation for airborne applications.

The rise of autonomous systems operating close to humans imposes new challenges in terms of robustness and precision on the estimation and control algorithms. Approaches based on nonlinear optimization, such as moving horizon estimation, have been shown to improve the accuracy of the estimated solution compared to traditional filter techniques. This paper introduces an optimization-based framework for multi-sensor fusion following a moving horizon scheme. The framework is applied to the often occurring estimation problem of motion tracking by fusing measurements of a global navigation satellite system receiver and an inertial measurement unit. The resulting algorithm is used to estimate position, velocity, and orientation of a maneuvering airplane and is evaluated against an accurate reference trajectory. A detailed study of the influence of the horizon length on the quality of the solution is presented and evaluated against filter-like and batch solutions of the problem. The versatile configuration possibilities of the framework are finally used to analyze the estimated solutions at different evaluation times exposing a nearly linear behavior of the sensor fusion problem.

In inertial motion capture, a multitude of body segments are equipped with inertial sensors, consisting of 3D accelerometers and 3D gyroscopes. Using an optimization-based approach to solve the motion capture problem allows for natural inclusion of biomechanical constraints, modeling the connection of the body segments at the joint locations. The computational complexity of solving this problem grows cubically both with the length of the data set and with the number of sensors and body segments considered. In this work, we present a scalable solution to this problem using message passing, exploiting the structure that is inherent in the problem. As a proof-of-concept we apply our algorithm to data from a lower body configuration.

In inertial motion capture, a multitude of body segments are equipped with inertial sensors, consisting of 3D accelerometers and 3D gyroscopes. Using an optimization-based approach to solve the motion capture problem allows for natural inclusion of biomechanical constraints and for modeling the connection of the body segments at the joint locations. The computational complexity of solving this problem grows both with the length of the data set and with the number of sensors and body segments considered. In this work, we present a scalable and distributed solution to this problem using tailored message passing, capable of exploiting the structure that is inherent in the problem. As a proof-of-concept we apply our algorithm to data from a lower body configuration.

In this paper, we present an approach to combine measurements from inertial sensors (accelerometers and gyroscopes) with time-of-arrival measurements from an ultrawideband (UWB) system for indoor positioning. Our algorithm uses a tightly coupled sensor fusion approach, where we formulate the problem as a maximum a posteriori (MAP) problem that is solved using an optimization approach. It is shown to lead to accurate 6-D position and orientation estimates when compared to reference data from an independent optical tracking system. To be able to obtain position information from the UWB measurements, it is imperative that accurate estimates of the UWB receivers' positions and their clock offsets are available. Hence, we also present an easy-to-use algorithm to calibrate the UWB system using a maximum-likelihood (ML) formulation. Throughout this work, the UWB measurements are modeled by a tailored heavy-tailed asymmetric distribution to account for measurement outliers. The heavy-tailed asymmetric distribution works well on experimental data, as shown by analyzing the position estimates obtained using the UWB measurements via a novel multilateration approach.

In inertial human motion capture, a multitude of body segments are equipped with inertial measurement units, consisting of 3D accelerometers, 3D gyroscopes and 3D magnetometers. Relative position and orientation estimates can be obtained using the inertial data together with a biomechanical model. In this work we present an optimization-based solution to magnetometer-free inertial motion capture. It allows for natural inclusion of biomechanical constraints, for handling of nonlinearities and for using all data in obtaining an estimate. As a proof-of-concept we apply our algorithm to a lower body configuration, illustrating that the estimates are drift-free and match the joint angles from an optical reference system.

Autonomous Simultaneous Localization and Mapping (SLAM) is an important topic in many engineering fields. Since stop-and-go systems are typically slow and full-kinematic systems may lack accuracy and integrity, this paper presents a novel hybrid “continuous stop-and-go” mobile mapping system called Scannect. A 3D terrestrial LiDAR system is integrated with a MEMS IMU and two Microsoft Kinect sensors to map indoor urban environments. The Kinects’ depth maps were processed using a new point-to-plane ICP that minimizes the reprojection error of the infrared camera and projector pair in an implicit iterative extended Kalman filter (IEKF). A new formulation of the 5-point visual odometry method is tightly coupled in the implicit IEKF without increasing the dimensions of the state space. The Scannect can map and navigate in areas with textureless walls and provides an effective means for mapping large areas with lots of occlusions. Mapping long corridors (total travel distance of 120 m) took approximately 30 minutes and achieved a Mean Radial Spherical Error of 17 cm before smoothing or global optimization.

Measurements from magnetometers and inertial sensors (accelerometers and gyroscopes) can be combined to give 3D orientation estimates. In order to obtain accurate orientation estimates it is imperative that the magnetometer and inertial sensor axes are aligned and that the magnetometer is properly calibrated for both sensor errors as well as presence of magnetic distortions. In this work we derive an easy-to-use calibration algorithm that can be used to calibrate a combination of a magnetometer and inertial sensors. The algorithm compensates for any static magnetic distortions created by the sensor platform, magnetometer sensor errors and determines the alignment between the magnetometer and the inertial sensor axes. The resulting calibration procedure does not require any additional hardware. We make use of probabilistic models and obtain the calibration algorithm as the solution to a maximum likelihood problem. The efficacy of the proposed algorithm is illustrated using experimental data collected from a sensor unit placed in a magnetically disturbed environment onboard a jet aircraft.

The usage of inertial sensors has traditionally been confined primarily to the aviation and marine industry due to their associated cost and bulkiness. During the last decade, however, inertial sen ...

This paper applies the second order Taylor approximation to model the nonlinear uncertainty of acceleration rotation for MEMS based strapdown integration. Filtering solutions for tracking comprising inertial sensors require a good statistical modeling of the inertial measurements. The nonlinearity results in an umbrella-shape probability density distribution, and causes net downward vertical acceleration bias, which can not be estimated by traditional methods using only the first order approximation. This in turn leads to increasing vertical velocity and position errors after double integration which is significant for MEMS grade inertial sensors. Moreover, the analytical second order nonlinear term is applied in an extended Kalman filter (EKF) framework and compared with a normal EKF. The benefits of the method are demonstrated using a 3D MEMS IMU.

This paper is concerned with the problem of estimating the relative translation and orientation of an inertial measurement unit and a camera, which are rigidly connected. The key is to realize that this problem is in fact an instance of a standard problem within the area of system identification, referred to as a gray-box problem. We propose a new algorithm for estimating the relative translation and orientation, which does not require any additional hardware, except a piece of paper with a checkerboard pattern on it. The method is based on a physical model which can also be used in solving, for example, sensor fusion problems. The experimental results show that the method works well in practice, both for perspective and spherical cameras.

Commercially available Ultra-Wideband (UWB) systems typically consist of a network of synchronized UWB receivers which track a large number of small, battery powered and inexpensive UWB transmitters. Reported indoor position accuracies lie in the order of decimetres, but suffer from multipath effects and non-line-of-sight (NLOS) conditions. These effects are most prominent while tracking moving objects or persons and give rise to distorted and bumpy trajectories. Although the obtained performance is often sufficient for the aforementioned applications, many potential application areas have higher performance requirements.