Rigid motion computation or estimation is a cornerstone in numerous fields. Attitude computation can be achieved by integrating the angular velocity measured by gyroscopes, the accuracy of which is crucially important for the dead-reckoning inertial navigation. The state-of-the-art attitude algorithms have unexceptionally relied on the simplified differential equation of the rotation vector to obtain the attitude. This paper proposes a Functional Iteration technique with the Rodrigues vector (named the RodFIter method) to analytically reconstruct the attitude from gyroscope measurements. The RodFIter method is provably exact in reconstructing the incremental attitude as long as the angular velocity is exact. Notably, the Rodrigues vector is analytically obtained and can be used to update the attitude over the considered time interval. The proposed method gives birth to an ultimate attitude algorithm scheme that can be naturally extended to the general rigid motion computation. It is extensively evaluated under the attitude coning motion and compares favorably in accuracy with the mainstream attitude algorithms. This work is believed having eliminated the long-standing theoretical barrier in exact motion integration from inertial measurements.
Magnetometers, gyroscopes and accelerometers are commonly used sensors in a variety of applications. The paper proposes a novel gyroscope calibration method in the homogeneous magnetic field by the help of magnetometer. It is shown that, with sufficient rotation excitation, the homogeneous magnetic field vector can be exploited to serve as a good reference for calibrating low-cost gyroscopes. The calibration parameters include the gyroscope scale factor, non-orthogonal coefficient and bias for three axes, as well as its misalignment to the magnetometer frame. Simulation and field test results demonstrate the method's effectiveness.
Magnetometer and inertial sensors are widely used for orientation estimation. Magnetometer usage is often troublesome, as it is prone to be interfered by onboard or ambient magnetic disturbance. The onboard soft-iron material distorts not only the magnetic field, but the magnetometer sensor frame coordinate and the cross-sensor misalignment relative to inertial sensors. It is desirable to conveniently put magnetic and inertial sensors information in a common frame. Existing methods either split the problem into successive intrinsic and cross-sensor calibrations, or rely on stationary accelerometer measurements which is infeasible in dynamic conditions. This paper formulates the magnetometer calibration and alignment to inertial sensors as a state estimation problem, and collectively solves the magnetometer intrinsic and cross-sensor calibrations, as well as the gyroscope bias estimation. Sufficient conditions are derived for the problem to be globally observable, even when no accelerometer information is used at all. An extended Kalman filter is designed to implement the state estimation and comprehensive test data results show the superior performance of the proposed approach. It is immune to acceleration disturbance and applicable potentially in any dynamic conditions.
Precise autonomous navigation remains a substantial challenge to all underwater platforms. Inertial Measurement Units (IMU) and Doppler Velocity Logs (DVL) have complementary characteristics and are promising sensors that could enable fully autonomous underwater navigation in unexplored areas without relying on additional external Global Positioning System (GPS) or acoustic beacons. This paper addresses the combined IMU/DVL navigation system from the viewpoint of observability. We show by analysis that under moderate conditions the combined system is observable. Specifically, the DVL parameters, including the scale factor and misalignment angles, can be calibrated in-situ without using external GPS or acoustic beacon sensors. Simulation results using a practical estimator validate the analytic conclusions.
Magnetometer has received wide applications in attitude determination and scientific measurements. Calibration is an important step for any practical magnetometer use. The most popular three-axis magnetometer calibration methods are attitude-independent and have been founded on an approximate maximum likelihood (ML) estimation with a quartic subjective function, derived from the fact that the magnitude of the calibrated measurements should be constant in a homogeneous magnetic field. This paper highlights the shortcomings of those popular methods and proposes to use the quadratic optimal ML estimation instead for magnetometer calibration. Simulation and test results show that the optimal ML calibration is superior to the approximate ML methods for magnetometer calibration in both accuracy and stability, especially for those situations without sufficient attitude excitation. The significant benefits deserve the moderately increased computation burden. The main conclusion obtained in the context of magnetometer in this paper is potentially applicable to various kinds of three-axis sensors.
Inertial measurement unit (IMU) and odometer have been commonly-used sensors for autonomous land navigation in the global positioning system (GPS)-denied scenarios. This paper systematically proposes a versatile strategy for self-contained land vehicle navigation using the IMU and an odometer. Specifically, the paper proposes a self-calibration and refinement method for IMU/odometer integration that is able to overcome significant variation of the misalignment parameters, which are induced by many inevitable and adverse factors such as load changing, refueling and ambient temperature. An odometer-aided IMU in-motion alignment algorithm is also devised that enables the first-responsive functionality even when the vehicle is running freely. The versatile strategy is successfully demonstrated and verified via long-distance real tests.
Integration of inertial navigation system (INS) and global navigation satellite system (GNSS) is usually implemented in engineering applications by way of Kalman-like filtering. This form of INS/GNSS integration is prone to attitude initialization failure, especially when the host vehicle is moving freely. This paper proposes an online constrained-optimization method to simultaneously estimate the attitude and other related parameters including GNSS antenna's lever arm and inertial sensor biases. This new technique benefits from self-initialization in which no prior attitude or sensor measurement noise information is required. Numerical results are reported to validate its effectiveness and prospect in high accurate INS/GNSS applications.
The above-mentioned work [1] in IEEE-TR'08 presented an extended Kalman filter for calibrating the misalignment between a camera and an IMU. As one of the main contributions, the locally weakly observable analysis was carried out using Lie derivatives. The seminal paper [1] is undoubtedly the cornerstone of current observability work in SLAM and a number of real SLAM systems have been developed on the observability result of this paper, such as [2, 3]. However, the main observability result of this paper [1] is founded on an incorrect proof and actually cannot be acquired using the local observability technique therein, a fact that is apparently not noticed by the SLAM community over a number of years.
This note improves our above-mentioned recent work by effectively depressing the adverse effect of the lever arm on attitude estimation.
Inertial navigation applications are usually referenced to a rotating frame. Consideration of the navigation reference frame rotation in the inertial navigation algorithm design is an important but so far less seriously treated issue, especially for ultra-high-speed flying aircraft or the future ultra-precision navigation system of several meters per hour. This paper proposes a rigorous approach to tackle the issue of navigation frame rotation in velocity/position computation by use of the newly-devised velocity/position integration formulae in the Part I companion paper. The two integration formulae set a well-founded cornerstone for the velocity/position algorithms design that makes the comprehension of the inertial navigation computation principle more accessible to practitioners, and different approximations to the integrals involved will give birth to various velocity/position update algorithms. Two-sample velocity and position algorithms are derived to exemplify the design process. In the context of level-flight airplane examples, the derived algorithm is analytically and numerically compared to the typical algorithms existing in the literature. The results throw light on the problems in existing algorithms and the potential benefits of the derived algorithm.