PurposeThis paper aims to develop an adaptive unscented Kalman filter (AUKF) formulation for orientation estimation of aircraft and UAV utilizing low‐cost attitude and heading reference systems (AHRS).Design/methodology/approachA recursive least‐square algorithm with exponential age weighting in time is utilized for estimation of the unknown inputs. The proposed AUKF tunes its measurement covariance to yield optimal performance. Owing to nonlinear nature of the dynamic model as well as the measurement equations, an unscented Kalman filter (UKF) is chosen against the extended Kalman filter, due to its better performance characteristics. The unscented transformation of the UKF is shown to equivalently capture the effect of nonlinearities up to second order without the need for explicit calculations of the Jacobians.FindingsIn most conventional AHRS filters, severe problems can occur once the system suddenly experiences additional acceleration, resulting in erroneous orientation angles. On the contrary in the high dynamic accelerative mode of the new proposed filter the errors would not suddenly increase, since the additional to cruise accelerations are being continuously estimated resulting in substantially more accurate orientation estimation. This feature causes the associated filter errors to gradually increase, in the event of continuous vehicle acceleration, up to a point of zero additional acceleration that subsequently causes a subsidence of the error back to zero.Practical implicationsThe proposed filtering methodology can be implemented for orientation estimation of aircraft and UAV that are equipped with low‐cost AHRSs.Originality/valueTraditional AHRS algorithms utilize the accelerometers output for the computation of roll and pitch angles and magnetometer output for the heading angle. Moreover, these angles are also calculated from the gyroscopes output as well, but with errors that increase with time. Of course for some applications of AHRS system, orientation errors can be damped out with a proportional‐integral controller. In such a case, the filter cut‐off frequency is usually selected experimentally. But, for high accelerating vehicles utilizing AHRS, the system errors can become very large. A possible remedy to this problem could be to use more advanced nonlinear filter algorithms such as the one proposed.
This article aims to compensate the velocity and position errors that exist when the star sensor starts to work in a strapdown inertial navigation system aided by celestial navigation. These systems are integrated via unscented Kalman filter to estimate the current attitude and the gyros fixed bias, precisely. Since an accurate integration is desired, the nonlinear attitude equations are utilized in filter and these equations are propagated through a precise discretization method. Then, implementing the back-propagation and smoothing techniques, the initial attitude and the accelerometers fixed bias are also estimated. Finally, carrying out a parallel navigation, the velocity and position errors are compensated. The validity of the proposed method is investigated through simulation of launch vehicle navigation. Simulation results show a great reduction in velocity and position errors.
A new algorithm for complete pre-flight calibration of triple magnetometers is developed. The traditional approach for calibrating these sensors are based on a cumbersome procedure called ‘swing’ that involves levelling and rotating the vehicle containing the magnetometers through a series of known headings. Application of such a procedure is difficult and costly. Recently, new approaches have been developed to calibrate magnetometers without the need of attitude information. Such methods are used mostly for the calibration of biases and scale factors. Additionally in situations where misalignment errors are also to be estimated, they are usually modelled as errors of a non-orthogonal frame relative to an orthogonal frame creating six additional unknown parameters to be estimated. The presented approach in this article utilizes a three-step algorithm to fully calibrate triple magnetometers without the need of attitude information through a batch least-square non-linear estimator. Since misalignment parameters are not all identifiable through attitude-independent techniques, the measurement equation is initially factorized such that the non-observable parameters are removed. This would allow identification of three parameters through attitude-independent techniques, while identification of the other three that require horizon information is carried out using a secondary procedure. In step one of the proposed scheme, the non-linear observation equation is transformed, via two non-linear functions, to a linear space with respect to the unknown parameters and the new unknown parameters are estimated with batch least-square estimator. In the second step, the first non-linear function is solved for nine parameters that have non-linear relationships with respect to the desired biases, scale factors, and misalignments. Subsequently, the second non-linear function is solved giving the main unknown calibration parameters in a non-physical frame. Finally, in the third step, to find the required transformation matrix between the magnetometer platform frame, the magnetometer is rotated in a horizontal plane about x, y, and z platform axis, respectively. Assuming that the vertical component of the geomagnetic field is known, the calibration parameters are next determined with respect to the platform frame utilizing the rotation matrix. The proposed three-step algorithm does not need any initial condition or iterations for convergence and more importantly does not require any attitude information for the estimation of misalignments. The algorithm is simulated to validate the performance of the estimator using experimental data gathered from a magnetometer triad. Results show relative superiority when compared with those of the two-step algorithm with heading errors of the order of 0.5 to 1 degrees.
This paper introduces a new method for improving the inertial navigation system errors using information provided by the camera. An unscented Kalman filter is used for integrating the inertial measurement unit data with the features’ constraints extracted from the camera’s image. The constraints, in our approach, comprise epipolar geometry of two consecutive images with more than 65% coverage. Tracking down a known feature in two consecutive images results in emergence of stochastic epipolar constraint. It emerges in the form of an implicit measurement equation of the Kalman filter. Correctly matching features of the two images is necessary for reducing the navigation system errors because they act as external information for the inertial navigation system. A new method has been presented in this study based on the covariance analysis of the matched feature rays’ intersection points on the ground, which sieves the false matched features. Then, the inertial navigation system and matched feature information is integrated through the unscented Kalman filter filter and the states of the vehicle (attitude, position, and velocity) are corrected according to the last image. In this paper, the relative navigation parameters against the absolute one have been corrected. To avoid increasing dimensions of the covariance matrix, sequential updating procedure is used in the measurement equation. The simulation results show good performance of the proposed algorithm, which can be easily utilized for real flights.
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