Pure-Inertial AHRS with Adaptive Elimination of Non-Gravitational Vehicle Acceleration
Pavol Malinak, Milos Sotak, Zdenek Kana, Honeywell International, Czech Republic; Jindrich Dunik, Honeywell International and University of West Bohemia, Czech Republic; Radek Baranek, Honeywell International, Czech Republic
Attitude and heading reference system (AHRS) is a system providing an estimate of the vehicle attitude (i.e., difference of vehicle orientation from a tangential plane) and heading (i.e., difference of vehicle heading from a direction to geographic north) , , . There are two conceptually different approaches to the AHRS design, namely the global positioning system (GPS) aided AHRS and the pure inertial AHRS. The former approach is based on the processing of the inertial measurements (including accelerometer, gyroscope, and magnetometer measurements) and GPS aiding. Although such an approach allows to design a cost-effective AHRS providing accurate attitude and heading estimate in nominal conditions, it suffers from the common mode errors/faults of the aiding sources affecting the AHRS solution. The common mode failure significantly reduces the usability of the AHRS in high-integrity complex navigation architectures (i.e., in architectures with probability of hazardous misleading information less or equal to 1e-9) appearing in air traffic and regional grade aircrafts. The latter approach, based solely on the processing of the inertial measurement, is not affected by any GPS common mode failure and thus it is a natural choice for high-integrity navigation architectures. The pure AHRS is further developed in the paper.
Considering the low-cost microelectromechanical systems (MEMS) inertial sensors with no capability of gyrocompasing, the pure inertial AHRS computes the vehicle orientation on the basis of two pairs of non-collinear vectors, where each pair is expressed in different coordinate system (typically in the body and tangential frame) . The pair is composed by the magnetic field vector, measured by the magnetometer, and the gravity field vector, measured by the accelerometer. The pure inertial AHRS can be realized using a complementary filter or a statistical estimator. The complementary filter combines the outputs of the accelerometer passed through a low-pass filter, gyroscope through a high-pass filter, and magnetometer to get the attitude and heading estimate. The statistical filter combines prior information including the state-space model and posterior information coming from the measurement. The statistical filter is predominantly realized by a Kalman filter based state estimator such as the extended Kalman filter (EKF). The complementary filter based AHRS is more computationally effective whereas the EKF-based AHRS allows straightforward utilization of the detailed models of the errors affecting the measurements which in turn results in better estimation performance.
Irrespective of the design, the pure inertial AHRS is, however, sensitive to any uncompensated non-gravitational vehicle acceleration which is an inherent part of the accelerometer measurement. An undetected, ignored, or, uncompensated non-gravitational acceleration may significantly worsen quality of the estimated vehicle orientation provided by the pure inertial AHRS. In literature, two approaches dealing with the non-gravitational acceleration compensation can be identified. A simple approach is to detect a vehicle (non-gravitational) acceleration and to compute the orientation estimate only if non-gravitational acceleration is not detected . Such an approach has a clear limitation in the necessity to specify a threshold, below which the orientation estimate is not provided, and in limited continuity and availability of the estimated attitude and heading navigation information. Another approach, suitable for the EKF based AHRS, takes advantage of adaptation of the measurement noise covariance matrix ; the larger non-gravitational acceleration is detected, the higher measurement noise covariance matrix is applied for the AHRS navigation solution computation. As a consequence, in highly dynamic trajectories, the measurements are almost ignored by the EKF and the filter is prone to diverge as it is mostly governed by a process model (state equation of the state-space model).
The goal of the paper is to propose and illustrate a design of a new computationally efficient and high-integrity EKF-based pure inertial AHRS with non-gravitational vehicle acceleration elimination. The proposed design is based on the simultaneous estimation of the vehicle orientation and non-gravitational vehicle acceleration. Estimation of the non-gravitational acceleration is allowed by a design of the vehicle non-gravitational acceleration (time-correlated) model of which parameters (e.g., the steady state variance and the time constant) are adaptively and on-line tuned reflecting the actual dynamics of the vehicle. The model of the non-gravitational vehicle acceleration is used within the process model, thus, not directly affecting any part of the measurement equation, which improves utilization of information coming from all measurements. Known and sufficiently accurate model of the non-gravitational acceleration allows estimation and subsequent mitigation of the non-gravitational acceleration in the proposed EKF-based AHRS even in highly dynamic scenarios.
To adapt parameters of the proposed non-gravitational acceleration model, the concept of the so called synthetic acceleration has been developed. The synthetic acceleration is a stochastic variable designed to approximate the true non-gravitational vehicle acceleration. The first two statistical moments of the synthetic acceleration are recursively computed on the basis of estimated and pre-processed measured variables and, then, used for adaptive calculation of the parameters of the process describing the estimated non-gravitational vehicle acceleration.
In particular, two methods for synthetic acceleration characteristics computation are proposed in the paper; the effective and conservative method. The former method computes the synthetic acceleration characteristics of the basis of the best available attitude and heading estimate. The method is computationally efficient, however, it is shown that it provides a quality estimate of the synthetic acceleration characteristics only under assumption of relatively small uncertainty of the available vehicle orientation estimate. Such an assumption may be violated especially during the AHRS initialization phase. To mitigate the assumption of the relatively exact orientation estimate, the latter method is proposed which computes the synthetic acceleration characteristics in a grid of acceptable orientation solutions.
The novel EKF-based AHRS is illustrated in a numerical study using real and synthetic data in two scenarios with low and high acceleration trajectory of aircraft. The performance of the proposed AHRS is compared with the performance of a complementary filter based AHRS, which reveals significant improvement in the estimation performance.
It should be noted that the paper provides additional information and details regarding the mathematical background and derivation, and performance evaluation with respect to the recent US patent  and US patent application .
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