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The geomagnetic field vector is a function of the satellite’s position. The position and speed of the satellite can be determined by comparing the geomagnetic field vector measured by on board three-axis magnetometer with the standard value of the international geomagnetic field. The geomagnetic model has the disadvantages of uncertainty, low precision and long-term variability. Therefore, accuracy of autonomous navigation using the magnetometer is low. The purpose of this paper is to use the geomagnetic and sunlight information fusion algorithm to improve the orbit accuracy.

In this paper, an autonomous navigation method for low earth orbit satellite is studied by fusing geomagnetic and solar energy information. The algorithm selects the cosine value of the angle between the solar light vector and the geomagnetic vector, and the geomagnetic field intensity as observation. The Adaptive Unscented Kalman Filter (AUKF) filter is used to estimate the speed and position of the satellite, and the simulation research is carried out. This paper also made the same study using the UKF filter for comparison with the AUKF filter.

The algorithm of adding the sun direction vector information improves the positioning accuracy compared with the simple geomagnetic navigation, and the convergence and stability of the filter are better. The navigation error does not accumulate with time and has engineering application value. It also can be seen that AUKF filtering accuracy is better than UKF filtering accuracy.

Geomagnetic navigation is greatly affected by the accuracy of magnetometer. This paper does not consider the spacecraft’s environmental interference with magnetic sensors.

Magnetometers and solar sensors are common sensors for micro-satellites. Near-Earth satellite orbit has abundant geomagnetic field resources. Therefore, the algorithm will have higher engineering significance in the practical application of low orbit micro-satellites orbit determination.

This paper introduces a satellite autonomous navigation algorithm. The AUKF geomagnetic filter algorithm using sunlight information can obviously improve the navigation accuracy and meet the basic requirements of low orbit small satellite orbit determination.

The main reason for the low accuracy of magnetometer-based autonomous orbit determination is the coarse accuracy of the geomagnetic field model. Furthermore, the geomagnetic field model error increases obviously during geomagnetic storms, which can still further reduce the navigation accuracy. The purpose of this paper is to improve the accuracy of magnetometer-based autonomous orbit determination during geomagnetic storms.

In this paper, magnetometer-based autonomous orbit determination via a measurement differencing extended Kalman filter (MDEKF) is studied. The MDEKF algorithm can effectively remove the time-correlated portion of the measurement error and thus can evidently improve the accuracy of magnetometer-based autonomous orbit determination during geomagnetic storms. Real flight data from Swarm A are used to evaluate the performance of the MDEKF algorithm presented in this study. A performance comparison between the MDEKF algorithm and an extended Kalman filter (EKF) algorithm is investigated for different geomagnetic storms and sampling intervals.

The simulation results show that the MDEKF algorithm is superior to the EKF algorithm in terms of estimation accuracy and stability with a short sampling interval during geomagnetic storms. In addition, as the size of the geomagnetic storm increases, the advantages of the MDEKF algorithm over the EKF algorithm become more obvious.

The algorithm in this paper can improve the real-time accuracy of magnetometer-based autonomous orbit determination during geomagnetic storms with a low computational burden and is very suitable for low-orbit micro- and nano-satellites.

In spite of the vehicle, magnetic field interference can be reduced by some measures and techniques in ammunition design and manufacturing stage, the corruption of the vehicle magnetic field can still reach hundreds to thousands of nanoteslas. Besides, the magnetic field that the ferromagnetic materials generate in response to the strong magnetic field in the vicinity of the body. So, a real-time and accurate vehicle magnetic field calibration method is needed to improve the real-time measurement accuracy of the geomagnetic field for spinning projectiles.

Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time. In the method, the elliptical model of magnetometer measurement is established to convert the coefficients of hard and soft iron errors into the parameters of the elliptic equation. Then, the parameters are estimated by recursive least square estimator in real-time. Finally, the initial conditions for the estimator are established using prior knowledge method or static calibration method.

Studies show the proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real-time. A turntable experiments indicate that the post-calibration residuals approximate the measurement noise of the magnetometer and the roll accuracy is better than 1°. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers' calibration in real-time.

Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time and the calculation is small. Besides, it does not take up storage space. The proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real time. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers’ calibration in real-time.

This paper aims to present the development and performance evaluation of an attitude and rate estimation algorithm using an extended Kalman filter structure based on a body‐referenced representation of the state.

The algorithm requires only geomagnetic field data and can be used as a low‐cost alternative or as a back‐up estimator in the case of attitude sensor failures. The satellite rate is estimated as a part of the filter state and thus no gyroscope is necessary. The assessment of the algorithm performance is realized through a Monte Carlo simulation using a low‐Earth orbit, nadir‐pointing satellite.

Given some attitude and rate error requirements, the range of admissible initial errors on the filter state and the effect of un‐modelled disturbance torque are determined, along with the achievable attitude and rate accuracies.

Because the simulation set‐up is clearly stated, the results of this evaluation can be used as a benchmark for other estimation algorithms.

The necessary assumptions and approximations used to derive the filter equations are explicitly pointed out for the benefit of the readers. Well‐defined filter initial conditions are used in an extensive series of tests resulting into a unique set of findings.

This study aims to address the problem of the divergence of traditional inertial navigation system (INS)/celestial navigation system (CNS)-integrated navigation for ballistic missiles. The authors introduce Doppler navigation system (DNS) and X-ray pulsar navigation (XNAV) to the traditional INS/CNS-integrated navigation system and then propose an INS/CNS/DNS/XNAV deep integrated navigation system.

DNS and XNAV can provide velocity and position information, respectively. In addition to providing velocity information directly, DNS suppresses the impact of the Doppler effect on pulsar time of arrival (TOA). A pulsar TOA with drift bias is observed during the short navigation process. To solve this problem, the pulsar TOA drift bias model is established. And the parameters of the navigation filter are optimised based on this model.

The experimental results show that the INS/CNS/DNS/XNAV deep integrated navigation can suppress the drift of the accelerometer to a certain extent to improve the precision of position and velocity determination. In addition, this integrated navigation method can reduce the required accuracy of inertial navigation, thereby reducing the cost of missile manufacturing and realising low-cost and high-precision navigation.

The velocity information provided by the DNS can suppress the pulsar TOA drift, thereby improving the positioning accuracy of the XNAV. This reflects the “deep” integration of these two navigation methods.

Autonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion.

This paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model.

While EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination.

The intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models.

The results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation.

With the development of integrated circuit and communication technology, digital secure communication has become a research hotspot. This paper aims to design a five-dimensional fractional-order chaotic secure communication circuit with sliding mode synchronous based on microcontroller (MCU).

First, a five-dimensional fractional-order chaotic system for encryption is constructed. The approximate numerical solution of fractional-order chaotic system is calculated by Adomian decomposition method, and the phase diagram is obtained. Then, combined with the complexity and 0–1 test algorithm, the parameters of fractional-order chaotic system for encryption are selected. In addition, a sliding mode controller based on the new reaching law is constructed, and its stability is proved. The chaotic system can be synchronized in a short time by using sliding mode control synchronization.

The electronic circuit is implemented to verify the feasibility and effectiveness of the designed scheme.

It is feasible to realize fractional-order chaotic secure communication using MCU, and further reducing the synchronization error is the focus of future work.

The purpose of this paper is to examine the localisation of ferromagnetic objects buried in the underground. More specifically, it deals with the reconstruction of the XY‐positions, the depths (Z‐positions), the number, and the extension of the objects based on geomagnetic measurements. This paper introduces a minimum‐norm reconstruction approach and evaluates its performance in a simulation study.

A minimum‐L2‐norm estimation based on the truncated singular value decomposition method with lead field weighting is proposed in order to localise geomagnetic sources. The sensor setup and positions are taken from real measurements. The source space is formed by an automatically generated grid. At each grid point, a magneto‐static dipole is assumed.

Sources with different depths and XY‐positions could be successfully reconstructed. The proposed approach is not overly sensitive to errors/noise in measurement values and sensor positions.

The approach described in this paper can be used for applications like geoprospection, archaeology, mine clearing, and the clean‐up of former waste deposits.

This paper's purpose was to examine the impact of geomagnetic activity (GMA) on the timing and valuation of earnings information disclosed by firms every quarter.

The authors start the analyses with a sample of 112,669 client firms from 1989 to 2018. To analyze the impact of GMA on the earnings response coefficient (ERC), the authors use the three-day cumulative abnormal returns and cumulative abnormal returns for the extended post-earnings announcement window [2, 75] as the dependent variables. The authors interact unexpected earnings (UE) with the C9 Index, an index commonly used to measure GMA and study how GMA affects the pricing of new public information. To examine the effect of GMA on the timing of disclosure of earnings news, the authors regress a variant of the GMA index on the propensity to disclose bad earnings news.

The authors find significantly lower earnings response coefficients during periods of high GMA. This effect is permanent and stock prices do not correctly incorporate the implications of earnings information over time. The authors also show that managerial behavior is affected by GMA as well and the managers are more (less) likely to release bad (good) news during periods of higher activity. Finally, the authors also find that in situations where stakeholders are likely to rely on modern technology that depends minimally on humans, the adverse impact of GMA on the pricing of earnings information is mitigated.

The literature on the effect of GMA on the capital market is very limited and focuses primarily on stock returns, while the behavioral finance literature focuses on circumstances like weather, temperature and sporting outcome to study how the investors' mood affects their capital market behavior. The authors add to both the literature by investigating how GMA influences investors' and managers' behaviors in the capital market.

The work presented here is based on the assumption that all non‐linear properties, appearing in the evolution of magnetic fluids, are a complex system. Then, the establishment of a relationship between the structural changes in the geomagnetic field and the occurrence of earthquakes by employing the so‐called infrastructural informational analysis is undertaken. From the authors’ previously published serial work, it was found that the “zero isotropic zone” is a “discernible characteristic indication” which can be applied to the predictions of earthquakes with great practical effect.