Gyro Bias Research Articles

Compensation method for temperature error of fiber optical gyroscope based on relevance vector machine.

Aiming to improve the bias stability of the fiber optical gyroscope (FOG) in an ambient temperature-change environment, a temperature-compensation method based on the relevance vector machine (RVM) under Bayesian framework is proposed and applied. Compared with other temperature models such as quadratic polynomial regression, neural network, and the support vector machine, the proposed RVM method possesses higher accuracy to explain the temperature dependence of the FOG gyro bias. Experimental results indicate that, with the proposed RVM method, the bias stability of an FOG can be apparently reduced in the whole temperature ranging from -40°C to 60°C. Therefore, the proposed method can effectively improve the adaptability of the FOG in a changing temperature environment.

A Simple Attitude Unscented Kalman Filter: Theory and Evaluation in a Magnetometer-Only Spacecraft Scenario

A quaternion-based attitude unscented Kalman filter is formulated with quaternion errors parameterized by small angle approximations and is applied to a filter with a state vector consisting of the attitude quaternion and the gyro bias vector. The filter is evaluated using extensive Monte Carlo data in a simulated lost-in-space scenario of a low-Earth orbiting spacecraft processing only three-axis magnetometer and gyro measurements. The filter is found to be robust, accurate, and rapidly convergent in this scenario for small true gyro biases and small initial uncertainties in their values, often converging in only one half of an orbit period to an attitude accuracy of 0.1 degrees. The filter convergence is found to depend significantly on the value of the true gyro biases as well as the initial gyro bias covariances. Monte Carlo results also indicate that this unscented Kalman filter is significantly less robust than an extended Kalman filter with the same attitude approach, but performs slightly better than another unscented Kalman filter with a generalized Rodrigues parameter approach to quaternion errors.

Pose Tracking and Sensor Self-Calibration for an All-terrain Autonomous Vehicle

In this work we address the simultaneous pose tracking and sensor self-calibration problem by applying a pose-graph optimization approach. A factor-graph is employed to store robot pose estimates at different time instants and calibration parameters such as magnetometer hard and soft iron distortion and gyroscope bias. Specific factors are developed in this paper to handle Ackermann kinematic readings, inertial measurement units, magnetometers and global positioning systems. An experimental evaluation supports the viability of the approach considering an autonomous all-terrain vehicle, for which we perform calibration and real-time pose tracking during navigation.

Quadrotor attitude estimation with gyroscope bias reconstruction capabilities

This paper addresses the problem of quadrotor attitude estimation when only IMU sensor data are available. First, a Smooth Sliding Mode (SSM) algorithm is considered to provide an estimation of roll/pitch angles. In a second step, the estimates provided by SSM algorithm are used to reformulate the innovation term of the complementary filter in order to enhance the estimation of attitude angles. In addition, it is shown how the proposed solution can be able to reconstruct a bias in the gyroscope measurements. Simulation results obtained on the nonlinear model of quadrotor illustrate the benefits of the proposed scheme.

Maximum Likelihood Identification of Inertial Sensor Noise Model Parameters

Accurate visual-inertial localization and mapping systems require accurate calibration and good sensor error models. To this end, we present a simple offline method to automatically determine the parameters of inertial sensor noise models. The proposed methodology identifies noise processes across a large range of strength and time-scales, for example, weak gyroscope bias fluctuations buried in broadband noise. This is accomplished with a classical maximum likelihood estimator, based on the integrated process (i.e., the angle, velocity, or position), rather than on the angular rate or acceleration as is standard in the literature. This trivial modification allows us to capture noise processes according to their effect on the integrated process, irrespective of their contribution to rate or acceleration noise. The cause of the noise is not discussed in this article. The method is tested on different classes of sensors by automatically identifying the parameters of a standard inertial sensor noise model. The results are analyzed qualitatively by comparing the model’s Allan variance to the Allan variance computed directly from sensor data. A simulation that resembles one of the devices under test facilitates a quantitative analysis of the proposed estimator. Comparison with a competing, state-of-the-art method shows the advantages of the algorithm.

Analysis of dead zone sources in a closed-loop fiber optic gyroscope.

Analysis of the dead zone is among the intensive studies in a closed-loop fiber optic gyroscope. In a dead zone, a gyroscope cannot detect any rotation and produces a zero bias. In this study, an analysis of dead zone sources is performed in simulation and experiments. In general, the problem is mainly due to electrical cross coupling and phase modulation drift. Electrical cross coupling is caused by interference between modulation voltage and the photodetector. The cross-coupled signal produces spurious gyro bias and leads to a dead zone if it is larger than the input rate. Phase modulation drift as another dead zone source is due to the electrode contamination, the piezoelectric effect of the LiNbO3 substrate, or to organic fouling. This modulation drift lasts for a short or long period of time like a lead-lag filter response and produces gyro bias error, noise spikes, or dead zone. For a more detailed analysis, the cross-coupling effect and modulation phase drift are modeled as a filter and are simulated in both the open-loop and closed-loop modes. The sources of dead zone are more clearly analyzed in the simulation and experimental results.

Multiple-Point Temperature Gradient Algorithm for Ring Laser Gyroscope Bias Compensation.

To further improve ring laser gyroscope (RLG) bias stability, a multiple-point temperature gradient algorithm is proposed for RLG bias compensation in this paper. Based on the multiple-point temperature measurement system, a complete thermo-image of the RLG block is developed. Combined with the multiple-point temperature gradients between different points of the RLG block, the particle swarm optimization algorithm is used to tune the support vector machine (SVM) parameters, and an optimized design for selecting the thermometer locations is also discussed. The experimental results validate the superiority of the introduced method and enhance the precision and generalizability in the RLG bias compensation model.

A DCM Based Attitude Estimation Algorithm for Low-Cost MEMS IMUs

An attitude estimation algorithm is developed using an adaptive extended Kalman filter for low-cost microelectromechanical-system (MEMS) triaxial accelerometers and gyroscopes, that is, inertial measurement units (IMUs). Although these MEMS sensors are relatively cheap, they give more inaccurate measurements than conventional high-quality gyroscopes and accelerometers. To be able to use these low-cost MEMS sensors with precision in all situations, a novel attitude estimation algorithm is proposed for fusing triaxial gyroscope and accelerometer measurements. An extended Kalman filter is implemented to estimate attitude in direction cosine matrix (DCM) formation and to calibrate gyroscope biases online. We use a variable measurement covariance for acceleration measurements to ensure robustness against temporary nongravitational accelerations, which usually induce errors when estimating attitude with ordinary algorithms. The proposed algorithm enables accurate gyroscope online calibration by using only a triaxial gyroscope and accelerometer. It outperforms comparable state-of-the-art algorithms in those cases when there are either biases in the gyroscope measurements or large temporary nongravitational accelerations present. A low-cost, temperature-based calibration method is also discussed for initially calibrating gyroscope and acceleration sensors. An open source implementation of the algorithm is also available.

Inertial/celestial-based fuzzy adaptive unscented Kalman filter with Covariance Intersection algorithm for satellite attitude determination

This paper deals with the attitude determination algorithm for the satellite with an attitude measurement unit that is comprised of one gyroscope and two star trackers installed perpendicularly. Since the data updating rate of star trackers is typically lower than that of the gyro and filter, appropriate compensation is made for star sensors, but this results in more difficulties of determining the performed noise level. A fuzzy adaptive tuning method is used to help tuning, and with modified Rodrigues parameters and rotation vector to represent attitude error, a fuzzy adaptive unscented Kalman filter with minimal skew sampling method is realized, which works as a sub-system and estimates sub-optimal attitude states and gyro bias. Two such sub-systems are federated into the framework of Covariance Intersection algorithm to achieve data fusion for an optimal attitude and gyro bias estimation in system level. Simulation is performed to verify the attitude determination algorithm presented in this paper.

An iterative method for the accurate determination of airborne gravity horizontal components using strapdown inertial navigation system/global navigation satellite system

In strapdown inertial navigation system and global navigation satellite system-based airborne gravimetry, there is a circular problem between the navigation solution and the gravity vector estimation. On one hand, the gravity vector estimation depends on the navigation solution. On the other hand, the navigation solution requires a predetermined gravity model. The normal gravity, which differs from the actual gravity by an amount known as the gravity disturbance, is commonly used for the navigation solution, and this will result in errors of gravimetry. We reviewed this problem and found that an iterative method can be effective if there were no gyroscope biases in the inertial navigation system measurements. Iteratively, the differences between the estimated gravity vector and actual gravity vector can converge to constant values in this specific condition. If we know the gravity values at the endpoints of each survey line, these constant values can be compensated for by matching these endpoints. After such compensations, the repeatability of the estimated horizontal gravity components can be improved significantly. An application to real airborne data was performed to test the validity of the new method. The results yielded an internal accuracy in the horizontal component of approximately 3 mGal with a spatial resolution of 4.8 km.

Attitude and gyro bias estimation by the rotation of an inertial measurement unit

In navigation applications, the presence of an unknown bias in the measurement of rate gyros is a key performance-limiting factor. In order to estimate the gyro bias and improve the accuracy of attitude measurement, we proposed a new method which uses the rotation of an inertial measurement unit, which is independent from rigid body motion. By actively changing the orientation of the inertial measurement unit (IMU), the proposed method generates sufficient relations between the gyro bias and tilt angle (roll and pitch) error via ridge body dynamics, and the gyro bias, including the bias that causes the heading error, can be estimated and compensated. The rotation inertial measurement unit method makes the gravity vector measured from the IMU continuously change in a body-fixed frame. By theoretically analyzing the mathematic model, the convergence of the attitude and gyro bias to the true values is proven. The proposed method provides a good attitude estimation using only measurements from an IMU, when other sensors such as magnetometers and GPS are unreliable. The performance of the proposed method is illustrated under realistic robotic motions and the results demonstrate an improvement in the accuracy of the attitude estimation.

Analytical Observability Analysis of INS with Vehicle Constraints

This paper was first published online on 17 September 2014 (DOI: 10.1002/navi.63) and appears in the Fall 2014 issue of the journal (Volume 61, Issue 3, pp. 227 - 236). Subsequent to its publication online and in print, the authors would like to address two points in the paper which were erroneous: 1. In Fig. 5e, which depicts the degree of observability (DOO) for the heading error state, there are two points in which the graph converges. This was concluded to be due to observability at those points in time. In fact, the momentary convergence was due to an error in the implementation of the transfer between the dynamics (i.e., the change from acceleration to no acceleration and vice versa) at those time points. The reader's sole attention should be on the behavior of the graph in general, i.e., divergent, thus showing that the heading error state is unobservable in the discussed scenario. 2. On page 5 (after Eq. (32) and before the Analysis section) the following was stated: "… if the vehicle is turning ( ), the unobservable subspace cannot be found, since Eq. (29) is unsolvable due to rank defect. This means that the 12 error states are observable in this case. Thus, an accelerating and turning vehicle, with the aiding of the body velocity constraint, is observable in the velocity and orientation error states and the accelerometer and gyroscope bias residual states, meaning the drift and covariance of these states are reduced during the time of acceleration and maneuvers. The only error state that is unobservable, in this case, is the position error state." Clearly this paragraph is incorrect, as there are unobservable states for vehicles that are accelerating, including accelerations induced by turning with constant velocity (namely, heading, accelerometer biases in the x and y axes, and gyroscope bias in the z-axis).

Error analysis of a new planar electrostatic gravity gradiometer for airborne surveys

Moving-base gravity gradiometry has proven to be a convenient method to determine the Earth’s gravity field. The ESA mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has enabled to map the Earth gravity field and its gradients with a resolution of 80 km, leading to significant advances in physical oceanography and solid Earth physics. At smaller scales, airborne gravity gradiometry has been increasingly used during the past decade in mineral and hydrocarbon exploration. In both cases the sensitivity of gradiometers to the short wavelengths of the gravity field is of crucial interest. Here, we quantify and characterize the error on the gravity gradients estimated from measurements performed with a new instrument concept, called GREMLIT, for typical airborne conditions. GREMLIT is an ultra-sensitive planar gravitational gradiometer which consists in a planar acceleration gradiometer together with 3 gyroscopes. To conduct this error analysis, a simulation of a realistic airborne survey with GREMLIT is carried out. We first simulate realistic GREMLIT synthetic data, taking into account the acceleration gradiometer and gyroscope noises and biases and the variation of orientation of the measurement reference frame. Then, we estimate the gravity gradients from these data. Special attention is paid to the processing of the gyroscopes measurements whose accuracy is not commensurate with the ultra-sensitive gradiometer. We propose a method to calibrate the gyroscopes biases with a precision of the order $$10^{-8}$$ rad/s. In order to transform the tensor from the measurement frame to the local geodetic frame, we estimate the error induced when replacing the non-measured elements of the gravity gradient tensor by an a priori model. With the appropriate smoothing, we show that it is possible to achieve a precision better than 2E for an along-track spatial resolution of 2 km.

An interval Kalman filter–based fuzzy multi-sensor fusion approach for fault-tolerant heading estimation of an autonomous surface vehicle

This article presents a novel fuzzy–logic based multi-sensor data fusion algorithm for combining heading estimates from three separate weighted interval Kalman filters to construct a robust, fault-tolerant heading estimator for the navigation of the Springer autonomous surface vehicle. A single, low-cost gyroscopic unit and three independent compasses are used to acquire data onboard the vehicle. The gyroscope data, prone to sporadic bias drifts, are fused individually with readings from each of the compasses via a weighted interval Kalman filter. Unlike the standard Kalman filter, the weighted interval Kalman filter is able to provide a robust heading estimate even when subject to such gyroscope bias drifts. The three ensuing weighted interval Kalman filter estimates of the vehicle’s heading are then fused via a fuzzy logic algorithm designed to provide an accurate heading estimate even when two of the three compasses develop a fault at any time. Simulations and real-time trials demonstrate the effectiveness of the proposed method.

Observability Analysis and Filter Design for the Orion Earth–Moon Attitude Filter

The Orion attitude navigation design is presented, together with justification of the choice of states in the filter and an analysis of the observability of its states while processing star tracker measurements. The analysis shows that when the gyroscope biases and scale factors drift at different rates and are modeled as first-order Gauss–Markov processes, the states are observable so long as the time constants are not the same for both sets of states. In addition, the inertial-measurement-unit-to-star-tracker misalignments are modeled as first-order Gauss–Markov processes and these states are estimated. These results are used to finalize the design of the attitude estimation algorithm and the attitude calibration maneuvers.

Effect of external and internal magnetic fields on the bias stability in a Zeeman laser gyroscope

With the specific features of electronic systems of a Zeeman laser gyroscope taken into account, the basic physical mechanisms of the magnetic field effect on the bias stability and the factors giving rise to the internal magnetic fields are revealed. The hardware-based methods of reducing the effect of external and internal magnetic fields are considered, as well as the algorithmic methods for increasing the stability of the bias magnetic component by taking into account its reproducible temperature and time dependences. Typical experimental temperature and time dependences of the magnetic component of the Zeeman laser gyro bias are presented, and by their example the efficiency of the proposed methods for reducing the effect of magnetic fields is shown.

Temperature compensation method using readout signals of ring laser gyroscope.

Traditional compensation methods using temperature-related parameters have little effect when the ring laser gyroscope (RLG) bias changes rapidly. To solve this problem, a novel RLG bias temperature compensation method using readout signals is proposed in this paper. Combined with the least squares support vector machine (LS-SVM) algorithm, the novel method can improve the precision of the RLG bias. Experiments show that by utilizing the readout signals in the LS-SVM model, the RLG bias stability can be significantly raised compared to the original data. The novel method proposed in this paper is shown to be feasible, even when the RLG bias changes rapidly.

Initial Alignment by Attitude Estimation for Strapdown Inertial Navigation Systems

This paper derives a novel initial alignment method for the strapdown inertial navigation system (SINS), which transforms the attitude alignment into an attitude estimation problem. The process model of the proposed initial alignment method by attitude estimation is established by decomposition of the attitude matrix. The measurement model is constructed based on a generalized velocity integration formula that can integrate the inertial measurements over certain fixed time intervals. The contributions of the work presented here are twofold. First, the attitude estimation-based structure enables the proposed method to estimate the gyroscope biases other than the attitude quaternion, which is celebrated for the low-cost SINS. The second is the application of the proposed generalized velocity integration formula to attenuate the accumulated errors in vector observations caused by the traditional velocity integration formula. Experimental road tests are performed with a low-cost SINS, which validate the efficacy of the proposed method.

A Simple Observer for Gyro and Accelerometer Biases in Land Navigation Systems

In various applications of land vehicle navigation and automatic guidance systems, Global Navigation Satellite System/Inertial Measurement Unit (GNSS/IMU) positioning performance crucially depends on the attitude determination accuracy affected by gyro and accelerometer bias instabilities. Traditional bias estimation approaches based on the Kalman filter suffer from implementation complexity and require non-intuitive tuning procedures. In this paper we propose, as an alternative, a simple observer that estimates inertial sensor biases exclusively in terms of quantities with obvious geometrical meaning. By this, any multidimensional vector-matrix operations are avoided and observer tuning is substantially simplified. The observer has been successfully tested in a farming vehicle navigation system.

Relative attitude and position estimation for a tumbling spacecraft

This paper presents a novel relative attitude and position estimation approach for a tumbling spacecraft. It is assumed that the tumbling chief spacecraft is in failure or out of control and there is no a priori rotation rate information. The Euler's rotational dynamics is used to propagate the chief angular velocity, and the unknown inertia parameter circumstance is also considered. The integrated sensor suit comprises a rate-integrating gyro and a vision-based navigation system on the deputy spacecraft. Two relative quaternions that map the chief Local Vertical Local Horizontal (LVLH) frame to the deputy and chief body frames are involved to construct the line-of-sight observations. Therefore, the assumption that the chief body frame coincides with its LVLH frame in the traditional algorithm can be released. The general relative equations of motion for eccentric orbits are used to describe the positional dynamics. An extended Kalman filter is derived to estimate the relative quaternions, relative position and velocity, deputy gyro bias, as well as chief angular velocity and inertia ratios. Simulation results verify the validity and feasibility of the proposed algorithm.