Survey of nonlinear attitude estimation methods
01 Jan 2007-Journal of Guidance Control and Dynamics (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 30, Iss: 1, pp 12-28
TL;DR: A survey of modern nonlinear filtering methods for attitude estimation based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance is provided.
Abstract: This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST and the backwards-smoothing extended Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A twostep approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, Associate Professor, Department of Mechanical & Aerospace Engineering. Email: johnc@eng.buffalo.edu. Associate Fellow AIAA. Aerospace Engineer, Guidance, Navigation and Control Systems Engineering Branch. Email: Landis.Markley@nasa.gov. Fellow AIAA. Postdoctoral Research Fellow, Department of Mechanical & Aerospace Engineering. Email: cheng3@eng.buffalo.edu. Member AIAA.
Citations
More filters
TL;DR: An observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online.
Abstract: This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.
1,581Â citations
Book•
03 Sep 2016
TL;DR: In this article, the authors present a static method for determining the attitude of an individual in relation to an object, using a combination of static and dynamic methods. But they do not specify the parameters of the static method.
Abstract: Attitude Determination and Estimation.- Matrices, Vectors, Frames, Transforms.- Rotational Kinematics and Dynamics.- Sensors and Actuators.- Static Attitude Determination Methods.- Filtering for Attitude Determination.- Attitude Control.
654Â citations
14 Oct 2008
TL;DR: A nonlinear complementary filter is proposed that combines accelerometer output for low frequency attitude estimation with integrated gyrometer output for high frequency estimation that is evaluated against the output from a full GPS/INS that was available for the data set.
Abstract: This paper considers the question of using a nonlinear complementary filter for attitude estimation of fixed-wing unmanned aerial vehicle (UAV) given only measurements from a low-cost inertial measurement unit. A nonlinear complementary filter is proposed that combines accelerometer output for low frequency attitude estimation with integrated gyrometer output for high frequency estimation. The raw accelerometer output includes a component corresponding to airframe acceleration, occurring primarily when the aircraft turns, as well as the gravitational acceleration that is required for the filter. The airframe acceleration is estimated using a simple centripetal force model (based on additional airspeed measurements), augmented by a first order dynamic model for angle-of-attack, and used to obtain estimates of the gravitational direction independent of the airplane manoeuvres. Experimental results are provided on a real-world data set and the performance of the filter is evaluated against the output from a full GPS/INS that was available for the data set.
488Â citations
TL;DR: In this paper, a robust iterated extended Kalman filter (EKF) based on the generalized maximum likelihood approach (termed GM-IEKF), is proposed for estimating power system state dynamics when subjected to disturbances.
Abstract: This paper develops a robust iterated extended Kalman filter (EKF) based on the generalized maximum likelihood approach (termed GM-IEKF) for estimating power system state dynamics when subjected to disturbances. The proposed GM-IEKF dynamic state estimator is able to track system transients in a faster and more reliable way than the conventional EKF and the unscented Kalman filter (UKF) thanks to its batch-mode regression form and its robustness to innovation and observation outliers, even in position of leverage. Innovation outliers may be caused by impulsive noise in the dynamic state model while observation outliers may be due to large biases, cyber attacks, or temporary loss of communication links of PMUs. Good robustness and high statistical efficiency under Gaussian noise are achieved via the minimization of the Huber convex cost function of the standardized residuals. The latter is weighted via a function of robust distances of the two-time sequence of the predicted state and innovation vectors and calculated by means of the projection statistics. The state estimation error covariance matrix is derived using the total influence function, resulting in a robust state prediction in the next time step. Simulation results carried out on the IEEE 39-bus test system demonstrate the good performance of the GM-IEKF under Gaussian and non-Gaussian process and observation noise.
335Â citations
Cites methods from "Survey of nonlinear attitude estima..."
...Specifically, the IEKF linearizes the system nonlinear equations iteratively to compensate for the higherorder terms, whereas the UKF leverages the unscented transformation by deterministically providing sigma points to approximate the mean and covariance matrix of a random state vector, thus achieving better accuracy than the EKF [7], [8]....
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References
More filters
Journal Article•
1,682Â citations
TL;DR: An observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online.
Abstract: This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.
1,581Â citations
1,544Â citations
TL;DR: Two computationally efficient algorithms are presented for determining three-axis attitude from two or more vector observations that are useful to the mission analyst or spacecraft engineer for the evaluation of launch-window constraints or of attitude accuracies for different attitude sensor configurations.
Abstract: Two computationally efficient algorithms are presented for determining three-axis attitude from two or more vector observations. The first of these, the TRIAD algorithm, provides a deterministic (i.e., nonoptimal) solution for the attitude based on two vector observations. The second, the QUEST algorithm, is an optimal algorithm which determines the attitude that achieves the best weighted overlap of an arbitrary number of reference and observation vectors. Analytical expressions are given for the covariance matrices for the two algorithms using a fairly realistic model for the measurement errors. The mathematical relationship of the two algorithms and their relative merits are discussed and numerical examples are given. The advantage of computing the covariance matrix in the body frame rather than in the inertial frame (e.g., in terms of Euler angles) is emphasized. These results are valuable when a single-frame attitude must be computed frequently. They will also be useful to the mission analyst or spacecraft engineer for the evaluation of launch-window constraints or of attitude accuracies for different attitude sensor configurations.
1,394Â citations