However there are a lot of external magnetic field

However, there are a lot of external magnetic field disturbances in urban environments, for example when the AHRS is close to a ferrous or magnetic object, which will disturb the output of magnetometer, then the observational errors cannot satisfy the assumption of Kalman filtering, and so, the attitude estimates will be biased (Armstrong et al., 2010, Koo et al., 2009, De Vries et al., 2009). It is noted that the magnetic SR1078 output provides not only yaw information but also some information on pitch and roll angles. Once there is a large magnetic disturbance, the pitch and roll are also affected (Sabatini, 2006). Thus, we propose a quaternion-based indirect Kalman filter with two-step observations update so that the magnetic sensor output is only used for yaw estimation error compensation (Suh, 2010). In addition, the proposed system uses the magnetic dip angle to detect magnetic field distortion, which has more sensitivity than only depend on magnetic field strength. And then the robust Kalman filter will be used to weaken the influence of the disturbances in magnetic observations. The robust filter utilizes the equivalent weight matrix to reduce the weight of the magnetic observations with disturbance (Yang et al., 2001, Pourtakdoust and Asl, 2007). The paper is organized as follows. The magnetic distortion detection algorithm is presented in Section 2. Section 3 focuses on the indirect robust Kalman filter with 2 step observations update. Section 4 is the experiment validation of the proposed system. Finally, we draw some conclusions and shed light on future work in Section 5.
Magnetic distortion detection The magnetic dip angle is the angle between the lines of flux of the Earth’s magnetic field and the surface of the Earth (Roetenberg et al., 2005). We designed an experiment, in which a three-axis magnetometer was kept static and a ferrous object was linearly moved gradually towards the magnetometer in the same horizontal plane. Fig. 1 shows the variations of magnetic strength, dip angle and heading. From Fig. 1, we noted that the dip angle changes faster than the magnetic strength as the systems enters areas with magnetic distortions (the head and the dip angle firstly change on epoch 1300th, while magnetic strength on epoch 1750th). Thus, the presence of disturbance would be undetected or detected late solely with the change of magnetic field strength (Yadav and Bleakley, 2014). According to the analysis above, the detection criterion of the presence of magnetic disturbance can read:where , and denote the direction vectors of the accelerometer and the magnetometer output in body frame, respectively. is the calculated dip angle and the expected dip angle comes from the world magnetic model (WMM) (Yadav and Bleakley, 2014). The threshold refers to the noise floor. It is noted that the East component of the Earth’s magnetic field in WMM is not zero and the declination can be computed via the East and North component of the Earth’s magnetic field in absence of magnetic distortion.
Robust Kalman filter
Experimental validation We design an experiment to verify the performance of the proposed algorithm. The simulation data is generated by Matlab. The attitude maneuver and bias parameters used in the simulation data are as follows: We randomly generate 50 groups of simulation data without magnetic disturbances。The attitude estimation error statistic results based on two-step observation updates Kalman filter are shown in Table 1. The attitude tracking result and estimation error from one group of simulation data are shown in Fig. 2. Gyroscope and accelerometer bias estimation results are given in Fig. 3. From Fig. 2 and Table 1, it can be seen that if there is no magnetic distortion, the filter with 2 step observations updates can guaranty the accuracy of the heading maintain<0.3 degree peak-to-peak error and pitch and roll maintain degree.