The random zero offset of accelerometer and

The random zero offset of accelerometer and gyroscope estimated by two-step observation update Kalman filter are shown in Table 2, one group of estimated results is shown in Fig. 3. Contrast with the data from Eq. (23) and the ones from Fig. 3 and Table 2, it can be seen that the random zero offset error of accelerometer and gyroscope estimated by the proposed Kalman filter can achieve orders of magnitude. In order to further verify the two-step observation update Kalman filter will not affect the pitch and roll estimation under the condition of magnetic distortion, the magnetic disturbances are artificially added into the output of magnetometers. We choose one group disturbances of 50 groups from the 300th Clotrimazole to 1751th to show in Fig. 4(left). Fig. 4(right) is the results of detection algorithm based on the magnetic dip angle. It is precise and sensitive to the presence of disturbance. The attitude error estimated from standard Kalman filter and two-step observation updates Kalman filter are shown in Table 3. One of the 50 results is shown in Fig. 5. Seen from Table 1, Table 3, it can be found that in the epoch of adding magnetic disturbance, the heading estimation peak-to-peak error from two-step observation updates Kalman filter increase from 0.35 degrees to 10.3 degrees which is smaller than the standard Kalman filter. The estimation error of pitch and roll are not affected by the abnormal observations, the variations of peak-to-peak error degree. Thus we introduce the equivalent weight matrix to construct Robust Kalman filter to reduce the influence of the magnetic disturbances. The Robust Kalman filter has the same prediction and measurement equation as two-step observations updates Kalman, but the gain matrix of robust Kalman is based on the equivalent weight matrix of observations, which reduce the weight of the observation during magnetic disturbance occurring. After 50 times experiment, the heading estimation error from the Robust Kalman and two-step observations updates Kalman are shown in Table 4. The comparison of heading estimation from one time experiment is shown in Fig. 6. During the magnetic disturbance occurring, in conjunction with the equivalent matrix, the robust Kalman filter can get less affection of the magnetic distortion. The peak-to-peak error maintain<5 degrees less than 10 degrees of two-step observations updates Kalman filter.
Conclusions and future work
Acknowledgements This project is supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2016YFB0502102), the National Natural Science Foundation of China (Grants Nos. 41274038, 41574024), the Beijing Natural Science Foundation (Grant No. 4162035), and the Aeronautical Science Foundation of China.
Introduction Aryl hydrocarbon receptor (AhR) was initially recognized as a mediator of toxicological actions of halogenated aromatic hydrocarbons (HAHs), polycyclic aromatic hydrocarbons (PAHs) and PAH-like chemicals (for review see Refs. [1,2]). AhR is a ligand-activated transcription factor belonging, together with AhR nuclear translocator (ARNT) and hypoxia-inducible factor 2α (Hif-2α), to the big basic-helix-loop-helix (bHLH) Per-Arnt-Sim (PAS) family [2,21]. Among many exogenous AhR agonists, 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) is the most potent. TCDD and other dioxins are present in air, soil, fresh and salt water sediments as well as in plants and animals. Because of their high lipid solubility and chemical stability, dioxins show an extremely high potential for retention in human and animal tissues. The half-life of TCDD in humans was estimated to be 7–10 years [23,26]. The unliganded AhR is located in cytosol and bound to chaperone proteins (e.g., hsp90, p23, and AhR-interacting protein 1) [6,19,32]. Upon ligand binding, the ligand/AhR complex is translocated to the nucleus, where it combines with ARNT [7,35]. The ligand-AhR-ARNT complex binds to a cognate dioxin-responsive element (DRE) present in regulatory regions of target genes, inducing their transcription [17].