This paper presents a linear Kalman filter for yaw estimation of land vehicles using magnetic angular rate and gravity (MARG) sensors. A gyroscope measurement update depending on the vehicle status and constraining yaw estimation is introduced. To determine the vehicle status, the correlations between outputs from different sensors are analyzed based on the vehicle kinematic model and Coriolis theorem, and a vehicle status marker is constructed. In addition, a two-step measurement update method is designed. The method treats the magnetometer measurement update separately after the other updates and eliminates its impact on attitude estimation. The performances of the proposed algorithm are tested in experiments and the results show that: the introduced measurement update is an effective supplement to the magnetometer measurement update in magnetically disturbed environments; the two-step measurement update method makes attitude estimation immune to errors induced by magnetometer measurement update, and the proposed algorithm provides more reliable yaw estimation for land vehicles than the conventional algorithm.

Purpose: The sources of magnetic sensors errors are numerous, such as currents around, soft magnetic and hard magnetic materials and so on. The traditional methods mainly use explicit error models, and it is difficult to include all interference factors. This paper aims to present an implicit error model and studies its high-precision training method.Design/methodology/approach: A multi-level extreme learning machine based on reverse tuning (MR-ELM) is presented to compensate for magnetic compass measurement errors by increasing the depth of the network. To ensure the real-time performance of the algorithm, the network structure is fixed to two ELM levels, and the maximum number of levels and neurons will not be continuously increased. The parameters of MR-ELM are further modified by reverse tuning to ensure network accuracy. Because the parameters of the network have been basically determined by least squares, the number of iterations is far less than that in the traditional BP neural network, and the real-time can still be guaranteed.Findings: The results show that the training time of the MR-ELM is 19.65 s, which is about four times that of the fixed extreme learning algorithm, but training accuracy and generalization performance of the error model are better. The heading error is reduced from the pre-compensation ±2.5° to ±0.125°, and the root mean square error is 0.055°, which is about 0.46 times that of the fixed extreme learning algorithm.Originality/value: MR-ELM is presented to compensate for magnetic compass measurement errors by increasing the depth of the network. In this case, the multi-level ELM network parameters are further modified by reverse tuning to ensure network accuracy. Because the parameters of the network have been basically determined by least squares, the number of iterations is far less than that in the traditional BP neural network, and the real-time training can still be guaranteed. The revised manuscript improved the ELM algorithm itself (referred to as MR-ELM) and bring new ideas to the peers in the magnetic compass error compensation field.

This paper proposes methods for orientation information extraction using only three components of observations. In two vector situation, the norm equation and the dot production equation are used to estimate the unavailable components, and then the results are used to estimate the orientation; in one vector situation, all possible orientations are described by a function of one variable, from which the formulas for determining limited ranges of Euler angles are derived. The proposed methods are experimentally verified with real sensor data and simulation data in multiple orientations. It is found that, a combination of three vector observation components contains effective orientation information, but the information is incomplete and varies with the situation and orientation; in two vector situation, the method can get at most four orientation estimations in general and even an unique estimation in a special orientation, the RMS error of yaw, pitch, and roll estimations in experiments are respectively 2.7 degrees, 1.4 degrees and 2.2 degrees; in one vector situation, the method can always get two Euler angles with smaller ranges than their full ranges, and the spans of the ranges can even reduce to zero in some orientations.