An adaptive unscented Kalman filter for quaternion‐based orientation estimation in low‐cost AHRS

Abstract

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.

INS/GNSS Tightly-Coupled Integration Using Quaternion-Based AUPF for USV

“…Different from [ 2 ], which proposed an adaptive EKF algorithm, for the UKF, modified measurement noise error covariance matrices are adaptively updated as: where is calculated as: where . The denotes the sigma-points drawn from the UKF a posterior estimates.…”

“…The integration of Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) is widely used for positioning and attitude determination for vehicles. The development of micro-electromechanical system (MEMS) technology has brought low-cost INS/GNSS integration approaches into practice [ 2 , 3 ]. A growing number of research groups are developing integrated navigation systems utilizing INS and GNSS due to the complementary nature of INS and GNSS principles.…”

Inexpensive CubeSat attitude estimation using COTS components and Unscented Kalman Filtering

“…[4], [5], [6], [7], [8]. This approach is characterized by a set of sample (sigma) points, which are used to approximate a Gaussian probability distribution; whereas, the well known Extended Kalman Filter (EKF) is distinguished by the fact that it uses a linearization of the nonlinear model equations around the current estimate.…”

Unscented Kalman Filtering for Single Camera Based Motion and Shape Estimation

“…Similar to the EKF, the unscented Kalman filter (UKF) [ 10 – 17 ] focuses on approximating the prediction probability characteristics and use the standard minimum mean square error estimator. The UKF has been developed in the context of state estimation of dynamic systems as a nonlinear distribution (or densities in the continuous case) approximation method.…”