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The three-axis magnetic sensors are mostly calibrated by scalar method such as ellipsoid fitting and so on, but these methods cannot completely determine the 12 parameters of the error model. A two-stage calibration method based on particle swarm optimization (TSC-PSO) is proposed, which makes full use of the amplitude invariance and direction invariance of Earth’s magnetic field vector.

The TSC-PSO designs two-stage fitness function. Stage 1: design a fitness function of the particle swarm by the amplitude invariance of the Earth’s magnetic field to obtain a preliminary error matrix G and the bias error B. Stage 2: further design the fitness function of the particle swarm by the invariance of the Earth’s magnetic field to obtain a rotation matrix R, thereby determining the error matrix uniquely.

The proposed TSC-PSO can completely determine 12 unknown parameters in error model and further decrease the maximum fluctuation error of the Earth’s magnetic field amplitude and the absolute error of heading.

The proposed TSC-PSO provides an effective solution for three-axis magnetic sensor error compensation, which can greatly reduce the price of magnetic sensors and be used in the fields of Earth’s magnetic survey, drilling and Earth’s magnetic integrated navigation.

The proposed TSC-PSO has significantly improved the magnetic field amplitude and heading accuracy and does not require additional heading reference. In addition, the method is insensitive to noise and initialization conditions, has good robustness and can converge to a global optimum.

The differential magnetic gradient tensor system is usually constructed from the three-axis magnetic sensor array. While the effects of measurement error, sensor performance and baseline distance on localization performance of such systems have been widely reported, the research about the effect of spatial design of sensor array is less presented. This paper aims to provide a spatial design method of sensor array and corresponding optimization strategy to localization based on magnetic tensor gradient to get the optimum design of the sensor array. Based on the results of simulation, magnetic localization systems constructed from the proposed array and the traditional array have been built to carry out a localization experiment. The results of experiment have verified the effectiveness of magnetic localization based on the proposed array.

The authors focus on the localization of the magnetic target based on magnetic gradient by using three-axis magnetic sensor array and combine a design method with corresponding optimization strategy to get the optimum design of the sensor array.

This paper provides an array design and optimization method for magnetic target localization based on magnetic gradient to improve the localization performance.

In this paper, the authors focus on the magnetic localization based on magnetic gradient by using three-axis magnetic sensors and study the effect of the spatial design of sensor array on localization performance.

Continuum manipulators are often used in complex and narrow space in recent years because of their flexibility and safety. Vision is considered to be one of the most direct methods to obtain its spatial shape. However, with the improvement of the cooperation requirements of multiple continuum manipulators and the increase of space limitation, it is impossible to obtain the complete spatial shape information of multiple continuum manipulators only by several cameras.

This paper proposes a fusion method using inertial navigation sensors and cameras to reconstruct the shape of continuum manipulators in the whole workspace. The camera is used to obtain the position information, and the inertial navigation sensor is used to obtain the attitude information. Based on the above two information, the shape of the continuum manipulator is reconstructed by fitting Bézier curve.

The experiment result of single continuum manipulator shows that the cubic Bézier curves is applicable to curve fitting of variable curvature, the maximum fitting error is about 2 mm. Meanwhile, the experiment result shows that this method is not affected by obstacles and can still reconstruct the shape of the continuum manipulators in 3-D space by detecting the position and attitude information of the end.

According to the authors’ knowledge, this is the first study on spatial shape reconstruction of multiple continuum manipulators and the first study to introduce inertial navigation sensors and cameras into the field of shape reconstruction of multiple continuum manipulators in narrow space. This method is suitable for shape reconstruction of manipulator with variable curvature continuum manipulator. When the vision of multiple continuum manipulators is blocked by obstacles, the spatial shape can still be reconstructed only by exposing the end point. The structure is simple, but it has certain accuracy within a certain range.

Three-axis accelerometers play a vital role in monitoring the vibrations in aircraft machinery, especially in variable flight temperature environments. The sensitivity of a three-axis accelerometer under different temperature conditions needs to be calibrated before the flight test. Hence, the authors investigated the efficiency and sensitivity calibration of three-axis accelerometers under different conditions. This paper aims to propose the novel calibration algorithm for the three-axis accelerometers or the similar accelerometers.

The authors propose a hybrid genetic algorithm–particle swarm optimisation–back-propagation neural network (GA–PSO–BPNN) algorithm. This method has high global search ability, fast convergence speed and strong non-linear fitting capability; it follows the rules of natural selection and survival of the fittest. The authors describe the experimental setup for the calibration of the three-axis accelerometer using a three-comprehensive electrodynamic vibration test box, which provides different temperatures. Furthermore, to evaluate the performance of the hybrid GA–PSO–BPNN algorithm for sensitivity calibration, the authors performed a detailed comparative experimental analysis of the BPNN, GA–BPNN, PSO–BPNN and GA–PSO–BPNN algorithms under different temperatures (−55, 0 , 25 and 70 °C).

It has been showed that the prediction error of three-axis accelerometer under the hybrid GA–PSO–BPNN algorithm is the least (approximately ±0.1), which proved that the proposed GA–PSO–BPNN algorithm performed well on the sensitivity calibration of the three-axis accelerometer under different temperatures conditions.

The designed GA–PSO–BPNN algorithm with high global search ability, fast convergence speed and strong non-linear fitting capability has been proposed to decrease the sensitivity calibration error of three-axis accelerometer, and the hybrid algorithm could reach the global optimal solution rapidly and accurately.

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.

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.

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.

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.

The purpose of this paper is to propose a high-precision attitude solution to solve the attitude drift problem caused by the dispersion of low-cost micro-electro-mechanical system devices in strap-down inertial navigation attitude solution of micro-quadrotor.

In this study, a three-stage attitude estimation scheme that combines data preprocessing, gyro drifts prediction and enhanced unscented Kalman filtering (UKF) is proposed. By introducing a preprocessing model, the quaternion orientation is calculated as the composition of two algebraic quaternions, and the decoupling feature of the two quaternions makes the roll and pitch components independent of magnetic interference. A novel real-time based on differential value (DV) estimation algorithm is proposed for gyro drift. This novel solution prevents the impact of quartic characteristics and uses the iterative method to meet the requirement of real-time applications. A novel attitude determination algorithm, the pre-process DV-UKF algorithm, is proposed in combination with UKF based on the above solution and its characteristics.

Compared to UKF, both simulation and experimental results demonstrate that the pre-process DV-UKF algorithm has higher reliability in attitude determination. The dynamic errors in the three directions of the attitude are below 2.0°, the static errors are all less than 0.2° and the absolute attitude errors tailored by average are about 47.98% compared to the UKF.

This paper fulfils an identified need to achieve high-precision attitude estimation when using low-cost inertial devices in micro-quadrotor. The accuracy of the pre-process DV-UKF algorithm is superior to other products in the market.

The paper aims to describe the sensors used for interfacing with consumer electronic devices.

The paper describes the types of sensors employed in user‐interface devices such as trackballs, mice, touch pads, touch screens and gesture‐based systems. It concludes with a brief consideration of brain‐computer interface technology.

It is shown that a diverse range of sensors is used to interface with consumer electronics. They are based on optical, electrical, acoustic and solid‐state (MEMS) technologies. In the longer term, many may ultimately be replaced by sensors that interpret thought by detecting brain waves.

The paper provides a timely review of the sensors used to interface with consumer electronics. These constitute a very large and rapidly growing market.

The magnetometer measurement update plays a key role in correcting yaw estimation in fusion algorithms, and hence, the yaw estimation is vulnerable to magnetic disturbances. The purpose of this study is to improve the ability of the fusion algorithm to deal with magnetic disturbances.

In this paper, an adaptive measurement equation based on vehicle status is derived, which can constrain the yaw estimation from drifting when vehicle is running straight. Using this new measurement, a Kalman filter-based fusion algorithm is constructed, and its performance is evaluated experimentally.

The experiments results demonstrate that the new measurement update works as an effective supplement to the magnetometer measurement update in the present of magnetic disturbances, and the proposed fusion algorithm has better yaw estimation accuracy than the conventional algorithm.

The paper proposes a new adaptive measurement equation for yaw estimation based on vehicle status. And, using this measurement, the fusion algorithm can not only reduce the weight of disturbed sensor measurement but also utilize the character of vehicle running to deal with magnetic disturbances. This strategy can also be used in other orientation estimation fields.

The purpose of this paper is to present a hybrid manufacturing system that integrates stereolithography (SL) and direct print (DP) technologies to fabricate three‐dimensional (3D) structures with embedded electronic circuits. A detailed process was developed that enables fabrication of monolithic 3D packages with electronics without removal from the hybrid SL/DP machine during the process. Successful devices are demonstrated consisting of simple 555 timer circuits designed and fabricated in 2D (single layer of routing) and 3D (multiple layers of routing and component placement).

A hybrid SL/DP system was designed and developed using a 3D Systems SL 250/50 machine and an nScrypt micro‐dispensing pump integrated within the SL machine through orthogonally‐aligned linear translation stages. A corresponding manufacturing process was also developed using this system to fabricate 2D and 3D monolithic structures with embedded electronic circuits. The process involved part design, process planning, integrated manufacturing (including multiple starts and stops of both SL and DP and multiple intermediate processes), and post‐processing. SL provided substrate/mechanical structure manufacturing while interconnections were achieved using DP of conductive inks. Simple functional demonstrations involving 2D and 3D circuit designs were accomplished.

The 3D micro‐dispensing DP system provided control over conductive trace deposition and combined with the manufacturing flexibility of the SL machine enabled the fabrication of monolithic 3D electronic structures. To fabricate a 3D electronic device within the hybrid SL/DP machine, a process was developed that required multiple starts and stops of the SL process, removal of uncured resin from the SL substrate, insertion of active and passive electronic components, and DP and laser curing of the conductive traces. Using this process, the hybrid SL/DP technology was capable of successfully fabricating, without removal from the machine during fabrication, functional 2D and 3D 555 timer circuits packaged within SL substrates.

Results indicated that fabrication of 3D embedded electronic systems is possible using the hybrid SL/DP machine. A complete manufacturing process was developed to fabricate complex, monolithic 3D structures with electronics in a single set‐up, advancing the capabilities of additive manufacturing (AM) technologies. Although the process does not require removal of the structure from the machine during fabrication, many of the current sub‐processes are manual. As a result, further research and development on automation and optimization of many of the sub‐processes are required to enhance the overall manufacturing process.

A new methodology is presented for manufacturing non‐traditional electronic systems in arbitrary form, while achieving miniaturization and enabling rugged structure. Advanced applications are demonstrated using a semi‐automated approach to SL/DP integration. Opportunities exist to fully automate the hybrid SL/DP machine and optimize the manufacturing process for enhancing the commercial appeal for fabricating complex systems.

This work broadly demonstrates what can be achieved by integrating multiple AM technologies together for fabricating unique devices and more specifically demonstrates a hybrid SL/DP machine that can produce 3D monolithic structures with embedded electronics and printed interconnects.

This study aims to find a novel solution to the calibration of three-axis magnetometers to suppress errors of sensors. The nature of the calibration process is parameter estimation and hence the purpose of the paper is to calculate the error parameters and eliminate sensor errors and obtain the true value of the pure magnetic field.

The paper puts forward a calibration method using an alternative iteration looping optimization (AILO) to estimate the parameters. The proposed method divided the parameters to be estimated into two parts: a portion less than one and the other greater than one. Parameters with different orders of magnitude are calculated respectively, which let one part to be a known quantity and the other part is derived by the known quantity; the derived quantity is used to calculate the known quantity again, and looping iteration multiple times until the iteration termination condition is satisfied.

The simulation and experimental results indicate that the calibration accuracy is improved at least by two orders by the proposed method compared to the two-step method and the linear decreasing weight particle swarm optimization (LDW-PSO) algorithm which proves the validity of the proposed method.

The proposed method can improve the calibration accuracy of total magnetic field, which provides a reference to the calibration of three-axis magnetometers.

A calibration method based on the AILO is proposed in this paper, which is used to improve the calibration accuracy of the three-axis magnetometer.