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An on-site and fast synchronous measurement of coil constant and nonorthogonal angle, using an all-optical atomic magnetometer, was reported in this article. Based on the spectrum analysis of electron paramagnetic resonance of spin-polarized potassium under different magnetic fields, the measurement models of coil constant and nonorthogonal angle were established, according to which we experimentally obtained the weighted average results with related estimated uncertainties: the coil constants in the $x$ -, $y$ -, and $z$ -axes were (145.9 ± 0.3) nT/mA, (149.5 ± 0.3) nT/mA, and (129.6 ± 0.1) nT/mA, respectively; the nonorthogonal angles existing in the $x z$ and $y z$ axes were (0.11 ± 0.02)° and (0.23 ± 0.02)°, respectively. The determination results of the residual magnetic field in the $z$ -axis, with two comparative experiments, demonstrated the validity of this on-site synchronous measurement method. The present method can be easily used in calibrating coil constant and nonorthogonal angle for all-optical atomic magnetometers, especially for miniaturized ones.

Deep space exploration missions continue to become more ambitious, driving the need to investigate autonomous navigation systems that are accurate and timely. The solar Doppler difference navigation is a newly developed and promising celestial autonomous navigation method for use, particularly, in the crucial capture period. In this paper, we present novel analyses for three error sources for the solar Doppler difference navigation from the perspective of geometry, motivated with a Mars deep space exploration example. The geometry error sources include the area overlap rate of the direct and the reflected solar light sources, the spread effects related to the time difference of arrival (TDOA) of light, and the solar rotation Doppler difference error. The area overlap rate and the spread effects of the TDOA can be utilized to assess the overlap degree of the direct source and the reflected source in both space and time. Theoretical analyses and simulation results demonstrate that the direct and the reflected light sources can be accurately approximated as the same source. The solar rotation Doppler difference error is explored using a velocity error model. This model forms a hemi-ellipsoid that can be utilized to compensate the Doppler error caused by the solar rotation. The three errors decline with the deep space explorer approaching Mars, which means that the performance of the solar Doppler difference navigation method continuously improves in the critical capture period. These results can offer a reference for the system design of the solar Doppler difference navigation.

The performance of vehicle detection system is often affected by both internal and external noise. In this paper, a novel vehicle detection scheme called vehicle detector based on EMD-HT and multichannel GLRT (V-EHMG) is proposed, which composed of signal denoising part based on empirical mode decomposition (EMD) and signal detection part which takes advantage of the spatial–temporal relationship acquired by multiple sensors. In the first part, we propose a new denoising algorithm null-hypothesis interval threshold EMD denoising (EMD-HT) to check the similarity between the probability density function of the decomposed intrinsic mode functions (IMFs) from input signal and the generalized Gaussian distribution to determine relevant IMFs for signal reconstruction. Combined the interval threshold method, the denoised signals are acquired. In the second part, we use multichannel generalized likelihood ratio test (GLRT) detector to judge the presence of other vehicles with the denoised signals as the input. Simulation and physical experimental results show that with V-EHMG, the signal-to-noise ratio of the signal is doubled and the detection range is improved more than 40% compared with the traditional methods.

Current Motion Compensation (MOCO) methods using Inertial Navigation System (INS)/Global Positioning System (GPS) integrated systems have provided an important advance in Synthetic Aperture Radar (SAR) imagery, but most of these methods only work well over a short imaging period. With the development of high-resolution SAR that provides image gathering over long periods, the need for higher levels of INS/GPS performance than normally available is desired. The higher requirement of INS/GPS for SAR MOCO is two-fold: (1) the accurate knowledge of location information, and (2) the smoothness of relative change in navigation error. In this paper, we design an INS/GPS architecture with dual-filter correction to obtain accurate absolute velocity and position measurement information with smooth low relative error noise over a long image gathering period. Real SAR data experimental results show that the proposed method effectively improves the MOCO performance of INS/GPS with long SAR imaging periods, in which the SAR azimuth resolution reaches 1·45 m, which is very close to the design value of 1 m.

Optical rotation for atomic precession is detected using a superluminescent diode (SLD). The feasibility of the optical rotation detection using the SLD as a probe light source is theoretically and experimentally studied. The SLD has a more uniform Gauss configuration without additional beam shaping with a relatively high power, which has potential in the application of gradient magnetic field measurements. In addition, the robustness and compactness enables a new way for optical rotation detections, especially for applications in magnetoencephalography systems.

An improved target field method is proposed for the cylindrical coil design to meet the constraint of limited coil volume. It realizes the design of uniform magnetic field coil by predetermining the coil configuration and optimizing the coordinate positions of the target field points. Compared with conventional methods, this current density distribution is divided into two symmetric subregions to solve the problem of reserving a gap in the coil center for setting the light-passing holes. Therefore, this method is more applicable in the miniature atomic devices with optical paths. Moreover, the overall coil performance can be significantly improved using the optimized configuration of coil design parameters. The numerical evaluation shows that the coil designed by this method has remarkable advantages over the nested saddle coil, whose uniformity performance can be improved by about one order of magnitude. The measurements show that the relative magnetic field uniformities of the proposed coils reach 4 × 10-4 and 3 × 10-4 along the z-axis in the range of ±0.24 R. The measurement results match well with the theoretical simulation.

Spin-exchange relaxation-free atomic spin gyroscope (SERF gyro) has ultrahigh theoretical sensitivity and is regarded as one of the most potential atomic gyroscopes. To investigate its rotation response, a high linear atomic spin precession detection module was developed firstly by modifying the fiber reflective Sagnac interferometer for atomic spin precession detection and operating it in closed-loop mode. The SERF gyro based on K-Rb-21Ne comagnetometer was built and tested and appeared obvious nonlinear response feature. The nonlinear rotation response model was deduced by assuming the rotation-induced nuclei spin procession detecting as an in-situ magnetometer inside the SERF gyro and the fitting curves are in good agreement with the experimental results. The optimized pump power for maximum sensitivity and measurable dynamic range were analyzed theoretically and demonstrated experimentally. The investigation results show that the nonlinear rotation response is an intrinsic property of SERF gyro and its measurable dynamic range is limited due to the saturation characteristic of the sum of pumping and relaxation rate. This indicates that SERF gyro is propitious to a position gyroscope with high sensitivity.

When stellar refraction occurs, the refraction apparent rays contain two kinds of refraction information, stellar refraction angle and stellar refraction direction. The refraction apparent height and the stellar refraction angle are two typical measurements used in stellar refraction navigation, which essentially only uses stellar refraction angle, and does not use stellar refraction direction. In fact, the stellar refraction direction is a function of the satellite position vector, which is useful in determining the satellite position. In this paper, a new stellar refraction navigation method using the star pixel coordinates as a measurement is proposed to improve navigation accuracy by using two kinds of refraction information at the same time. The corresponding measurement model for the star pixel coordinates is established. Simulations show that the proposed method's navigation performance is better than that of refraction apparent height and stellar refraction angle.

Distributed position and orientation system (POS) uses transfer alignment to accurately measure multi-node time-spatial reference information, which is urgently demanded to compensate motion error of imaging sensors for aerial survey. The lever-arm deformation in transfer alignment will result in nonlinear error and time-varying measurement noise covariance, which decreases the accuracy of real-time estimation. In order to solve this problem, a nonlinear transfer alignment method of distributed POS based on an adaptive second-order divided difference filter (ADDF2) is proposed. First, a transfer alignment model for distributed POS is established. Furthermore, an ADDF2 based on adaptive innovation estimation is proposed to solve the nonlinear problem and adaptively adjust the measurement noise covariance matrix of transfer alignment in real time. The flight experiment results show that the proposed method is effective to improve the precision of distributed POS.

Many studies have been conducted about angular velocity estimation using star sensors, and fairly good performance is achieved when the spacecraft is working at low-dynamic environments. However, when the spacecraft rotates at a large angular velocity, the star image will become blurred, which makes it difficult to identify and recognize star centroids, which, in turn, reduces the accuracy of angular velocity estimation. Therefore, to solve the problem with angular velocity estimation in highly dynamic situations, this research studies a method of angular velocity estimation using blurred star images. The length and ending point coordinates of star trails obtained from these blurred star images are used for a series of processes, which includes the pre-processing of blurred star images, determination of starting and ending points, thinning and selection of star trails, and calculation of trail lengths. Simulations show that the effectiveness of the proposed method in highly dynamic situations and the angular velocity estimation errors in constant and sinusoidal variation are reduced by at least 66% and 62%, respectively, compared with those of the traditional method.

The strap-down inertial navigation system/celestial navigation system (SINS/CNS)-integrated system can be divided into the loosely coupled integrated mode and the tightly coupled integrated mode. Because the loosely coupled integrated mode requires the star sensor to observe at least three stars at the same time to obtain the attitude matrix, the tightly coupled integrated mode, which can still work with only one star, is more practical in reality, especially for the aircraft that need to work in the daytime. The star sensor is a vital part of the CNS, while its installation error impacts the navigation accuracy seriously in both the modes. Therefore, the star sensor installation error of the SINS/CNS-integrated navigation system must be corrected. The installation error calibration has been settled for the loosely coupled SINS/CNS-integrated navigation system when the attitude matrix is available. However, it is still a problem for the tightly coupled mode. This paper proposes a fast calibration method of the star sensor installation error for the tightly coupled SINS/CNS-integrated navigation system based on maneuvers and observability analysis. Simulations indicate that the proposed method is feasible and effective when only one star is visible at a time. The mean position error of the tightly coupled SINS/CNS-integrated navigation decreases by about 63.23% after compensation for the star sensor installation error.

Markley variables have advantages of slow variation, easy numerical integration and high precision in describing the attitude of spinning spacecraft. Previous attitude estimation methods based on Markley variables for spinning spacecraft usually employ a sun vector from the sun sensor, a magnetic vector from the magnetometer, or the angular rate from the gyro as the measurement. This paper proposes a Markley variables-based attitude estimation method using optical flow and a star vector from a star sensor as the measurement, where optical flow provides rate information and the star vector provides direction information. This method can estimate the direction of the spin axis and spin angular rate very well by using only one star sensor. In addition, the star sensor has higher accuracy than the traditional sun sensor and magnetometer, and the star sensor can also replace the gyro in case the gyro is out of action. The impact factors of this method are also analysed, which include spin angular rate, spin axis orientation and spacecraft moment of inertia tensor error.

We investigate the effects of pump laser power density on the hybrid optically pumped comagnetometer operated in the spin-exchange relaxation-free (SERF) regime. The analytic steady-state output model for the comagnetometer considering two alkali metal species and one nuclear species is presented for the first time. And the effects of pump laser power density on the rotation sensitivity, suppression of low-frequency magnetic noise and long-term stability of the comagnetometer are studied experimentally. The results indicate that when the product of pumping rate and density ratio of pumped atom to probed atom is equal to the spin relaxation rate of the probed atom, the maximum response and highest sensitivity of the comagnetometer are achieved. However, the suppression of low-frequency magnetic noise and long-term stability improve with the increasing of pump laser power density due to the increasing of nuclear spin polarization. Our focus is to optimize the performance of the comagnetometer for rotation sensing, but the theory and method presented here are relevant to all applications of the hybrid optical pumping technique.

In order to receive ground signals efficiently, doubly salient permanent magnet (DSPM) motor which is applied in communication satellites as a drive needs to be activated frequently to adjust the attitude of communication satellites. Then, the initial rotor position of the motor must be estimated accurately at standstill for producing a steady and sufficient starting torque. If the rotor rotates during the estimation process, the pointing accuracy of the satellite pointing mechanism will be affected. To solve this problem, this paper proposes a novel rotor initial position estimation scheme based on the principle that different initial rotor positions can cause the variations of stator winding inductances. The identification signals, which do not cause the rotor to rotate during the identification process, are injected into the motor windings to identify the stator inductances. Thus, the variations of the winding inductances can be detected, and the initial rotor position can be estimated accurately by these variations. The proposed method is verified through experimental platform. The experimental results show that the initial rotor position is accurately estimated, and the starting performance of the DSPM is improved.

The active surge suppression is a challenging topic in the industrial compressor systems. This paper addresses the two issues on the surge detection approach for magnetically suspended centrifugal compressors (MSCCs) utilizing the signal monitoring capabilities of magnetic bearings. An adaptive frequency estimator is proposed to extract the surge signal, and a judgment criterion is establish to the surge state. First, the derivation of a surge disturbance transfer model for the fluctuating pressure and rotor displacement was presented, and the characteristics of surge signal in the MSCC system is analyzed. Then, a conventional notch filter (NF) is used to eliminate the synchronous disturbance in the surge signal, and a modified adaptive notch filter (ANF) method is used to estimate the frequency of surge signal. The convergence analysis of the modified ANF shows that the linearized system is asymptotically stable. The mild surge detection technology and judgement criterion are also discussed. Experimental results on both the 100 kW and 315 kW MSCC systems show that the proposed method can rapidly detect the surge before the MSCC systems develops into the modified surge.

Solar oscillations cause significant variations in sunlight spectral wavelength and intensity over short time periods. These oscillations have been studied in detail over the years, both theoretically and using actual observations. Through detecting the sunlight spectral central wavelengths and intensity and recording the moment when solar oscillation occurs, the time delay between the sunlight coming from the Sun directly and the sunlight reflected by a celestial body such as the satellite of a planet or asteroid can be obtained. Because the solar oscillation time delay is determined by the relative positions of the spacecraft, the reflective celestial body, and the Sun, it can be adopted as the navigation measurement to provide the spacecraft's position information. In this paper, a novel celestial navigation method using the solar oscillation time delay measurement is proposed. The implicit measurement model of time delay is built, and the implicit unscented Kalman filter is applied. Simulation results indicate that the position error and velocity error of the proposed method for the transfer orbit are about 3.55 km and 0.077 m/s, respectively, and those for the surrounding orbit are about 1.76 km and 1.57 m/s, respectively. The impact of four factors on the navigation performance is also investigated.

Airborne distributed position and orientation system (POS) is playing an important role in the high-resolution aerial survey and a remote sensing system. It is composed of a master inertial navigation system (INS), the global navigation satellite system, and several slave INSs. However, the high-frequency vibration disturbance of aircraft engine and the flexure deformation disturbance of lever arm could lead to serious initial alignment errors of slave INSs. In order to solve the problem, an anti-disturbance initial alignment method based on quadratic integral for airborne distributed POS is proposed. A coarse alignment based on quadratic integral in inertial frame is proposed to reduce the disturbances of high-frequency vibration and flexure deformation. Furthermore, the disturbance of flexure deformation is considered as the first-order Markov process, and is added into the fine transfer alignment model. The experimental results verified that the proposed method can effectively improve the initial alignment of the distributed POS, especially the azimuth precision of two slave INSs which are improved by 0.0260° and 0.0167°, respectively.

The array antenna SAR or integrated multi-task imaging sensors are the most attractive development directions of aerial survey and remote sensing system, and urgently demand an airborne distributed position and orientation system (ADPOS), which depends on transfer alignment to accurately measure multi-node motion information. In this paper, an adaptive unscented two-filter smoother (AUTFS) is proposed for the offline transfer alignment of ADPOS, which deals with the problem of time-varying measurement noise covariance. The proposed smoother adopts a forward–backward approach, which includes an adaptive unscented Kalman filter tuned by fading factors in the forward direction and a backward filter using the weighted statistical linear regression formulation. A semi-physical simulation based on a flight experiment with ADPOS shows that the proposed AUTFS can achieve higher accuracy than the standard unscented two-filter smoother.

Position and orientation system (POS), which typically integrates strapdown inertial navigation system (SINS) and global navigation satellite system (GNSS), serves as a key sensor in airborne remote sensing, mobile mapping, and vehicle localization. POS can provide reliable, high-frequency and high-precision motion parameters using nonlinear Kalman Filter models based on fusion methods, such as extended Kalman filter, unscented Kalman filter, central difference Kalman filter (CDKF), and square root CDKF (SR-CDKF). Although the nonlinear parametric models are of high efficiency, there are also limitation on their capabilities of prediction and estimation, as it is often impossible to model all aspects of POS. In this paper, Gaussian processes (GP)-based is presented to enhance the capabilities of prediction and estimation for parametric CDKF. On one hand, it can estimate the state vector of POS with the nonlinear parametric CDKF on condition that trained data is limited; on the other hand, GP can take both the noise and the uncertainty in the nonlinear parametric CDKF into consideration. Consequently, the incorporation of GP into CDKF can result in further performance improvement. The proposed approach is verified in the real experiment, and shows that large performance benefits are achieved through applying the enhanced GP-CDKF(EGP-CDKF) into the SINS/GNSS integrated system.

This paper presents an elaborate scheme, which is different from the traditional parameter identification method, to estimate the parameters precisely for high-speed magnetic suspension motor. It is well known that the inductance and resistance of each winding play an important role in ensuring the stability of the controller for motor. There have been sufficient research works on equivalent circuit model, where the input and output data are assumed to be true value, and unknown circuit parameters are obtained by solving the equivalent circuit equations of motor. However, the output data are often interfered with noises, such as measurement error, the high-frequency components from pulse width modulation signals and sampling errors. The system response output data are reconstructed through applying in stochastic theory, which is different from the traditional filter techniques, to eliminate effectively the above-mentioned noises. Thus, the parameters can be estimated precisely. As an experimental verification, parameters estimated by the proposed method are applied in calculation of switching point between pulse width modulation mode and pulse amplitude modulation mode for magnetic suspension motor. The experimental results validate the effectiveness of the proposed method.

In the traditional observability analysis methods, much attention is paid to the accuracy of the condition number. However, the authors find the fact that besides the accuracy, the structure of condition numbers is important, such as their range and sequence. A structured condition number method is proposed, which includes the double-reciprocal condition number and the compensation based on the continuous period. As the condition number is in non-linear relation with the navigation error, the mean of condition numbers does not reflect the navigation performance accurately. To solve this problem, the double-reciprocal condition number is proposed, where the impact of a large condition number is small. Considering the fact that the longer the continuous period is, the worse the navigation performance is, the authors develop the compensation method based on the continuous period. Amending the double-reciprocal condition number with the continuous period-based compensation, the authors propose the structured condition number which possesses the advantages of them, and apply it into the celestial direction measurement-based integrated navigation systems which have sharply variable observability degree. The simulation results demonstrate that the structured condition number can reflect the navigation performance and select a proper navigation star effectively.

In the Venus capture period, it is difficult for celestial autonomous navigation to satisfy the requirement of high precision. To improve autonomous navigation performance, a Direction, Distance and Velocity (DDV) measurements deeply integrated navigation method is proposed. The “deeply” integrated navigation reflects the fact that the direction and velocity measurements suppress the Doppler effects in the pulsar signals. In the pulsar observation period, the direction and velocity measurements are utilised to compensate for Doppler effects in the pulsar signals. By these means, the residual effects can be ignored. When the direction, distance or velocity measurements are obtained, they are fused to improve the navigation performance. Simulation results demonstrate that the DDV measurements deeply integrated navigation filter converges very well, and provides highly accurate position estimation without a high quality requirement on navigation sensors.

Distributed array antenna synthetic aperture radar (SAR), flexible baseline interferometric SAR (InSAR) or integrated multi-task imaging sensors are the most attractive development directions of aerial survey and remote sensing system, and urgently demand a distributed Position and Orientation System (DPOS) to accurately measure multi-nodes time-spatial reference information. However, the traditional transfer alignment (TA) method can't meet the requirements of some high precision interferometric imaging task. To solve the problem, a dual-filter TA method based on position-velocity-attitude matching (PVAM) was proposed. Firstly, the TA method based on attitude matching (AM) is conducted in filter-1 to estimate the flexible angles and the derivatives. Then the TA method based on position-velocity matching (PVM) is conducted in filter-2, and the position and velocity measurements are compensated by the flexible angles and the derivatives estimated by filter-1. Finally, the strapdown solutions of slave IMU are corrected by the corrections from both filter-1 and filter-2. A semi-physical simulation based on airborne DPOS flight experiment has been conducted, verifying that the baseline error has been reduced from 0.0240 m to 0.0083 m and the computation time has been decrease by 3.41%.

Celestial navigation system (CNS) and X-ray pulsar-based navigation (XNAV) are two kinds of autonomous navigation methods for spacecraft. Because these two methods are complementary, CNS/XNAV integrated navigation is a feasible solution to improve the navigation accuracy and reliability. However, the pulsar's direction has a great impact on the navigation accuracy of CNS/XNAV integrated navigation because of the existence of measurement errors. In this paper, the analytic expression of the estimation errors of CNS/XNAV integrated navigation is deduced, based on which the impact of the pulsar's direction on the estimation errors is analyzed. A modified observability analysis method on the basis of the unscented Kalman filter is presented and applied to give the quantitative index of the pulsar's direction, whose observability matrix is constructed by the equivalent state transition matrix and measurement matrix. The equivalent state transition matrix is obtained through sigma points, and the equivalent measurement matrix is acquired with the help of the cross-covariance matrix and the predicted covariance matrix. Simulations demonstrate that the position and velocity estimation errors of CNS/XNAV integrated navigation increase exponentially with the angle between the pulsar's direction and the target body's direction. Both the error analysis method and the observability analysis method have been verified as suitable and effective for the analysis of the best choice for a pulsar in the CNS/XNAV integrated navigation system.

A Position and Orientation System (POS) integrating an Inertial Navigation Systems (INS) and the Global Positioning System (GPS) is a key component of remote sensing motion compensation. It can provide reliable and high-frequency high-precision motion information using a Kalman Filter (KF) during GPS availability. However, the performance of a POS significantly degrades during GPS outages. To maintain reliable POS outputs, this paper proposes a new hybrid predictor based on modelling the nonlinear time-series data-driven INS-errors using Noisy Input Gaussian Process Regression (NIGPR), which takes the input noise into account. The proposed approach is used to learn the nonlinear INS-errors model when GPS signals are available. When GPS outages occur, it starts to predict the observation measurement, and then feeds it to a KF as a virtual update to estimate all the INS errors. The proposed approach is verified in a real airplane, which combines a POS and Synthetic Aperture Radar (SAR). Experimental results show that the proposed approach significantly improves the performance of the POS, with improvements more than 90% better than a KF and 10% better than a Gaussian Process Regression (GPR/KF) combination during various GPS outages.

Reliable knowledge of the complete navigation states is a key requirement for the mobile mapping and land localization applications. And it is the system integrating strapdown inertial navigation system (SINS) and global navigation satellite system (GNSS) that can seamlessly provide the position, velocity and orientation. In the SINS/GNSS integration, GNSS serves as the accurate reference, however, it is susceptible to the multipath propagations in the dense urban environment where GNSS signals may be reflected by buildings or bridges. When multipath situations occur, the positioning quality of GNSS is dramatically degraded, which also has a negative effect on the stable performance of the integration. Therefore, in order to degrade the negative effect caused by GNSS multipath errors, this paper proposes an intelligent identification and mitigation of GNSS multipath errors method, which employs adaptive bayesian online change point detection (BOCPD) based on the high-precision characteristics of the SINS in the short sampling period. The real tests are conducted, which demonstrate that the proposed approach can effectively identify and mitigate GNSS multipath errors, and then improve the accuracy and reliability of the integration.

In the traditional compressive sensing methods, to realize highly-accurate pulsar time-of-arrival (TOA) estimation, a large-size measurement matrix has to be adopted due to the low radiation flux of X-ray pulsars. However, a large-size measurement matrix results in a large computational load. To estimate the pulsar TOA fast and accurately, an observation range-based compressive sensing (ORCS) method with a small-size measurement matrix is proposed in this paper. In this method, the observation range (OR) of a measurement vector is developed, which is defined as the variation range of the corresponding observation values that are equal to the inner products between the measurement vector and each atom in the dictionary. The larger the observation range is, the smaller the number of atoms corresponding with the same measurement value is, and vice versa. We also find that the observation ranges of only a few measurement vectors are large. Using several measurement vectors with large observation ranges, we can construct the OR-based measurement matrix with a small size, and then obtain the most matching atom in the dictionary. Besides, according to the heuristic knowledge, the size of the dictionary and the bin number of the accumulated pulsar profile can decrease, which results in a small computational load. The simulation results demonstrate that even though the size of the measurement matrix is very small, the observation range-based compressive sensing method provides highly-accurate and real-time TOA estimation with low-flux pulsars.

In the traditional observability analysis methods, only current and a few historical measurement values are considered. For the linear systems, the satisfactory analysis results can be obtained. However, for the nonlinear systems, the analysis results are not completely in accordance with the navigation errors since the high-order nonlinearity of the navigation system is not embodied on the observability matrix. In order to solve this problem, a fractional differentiation-based observability analysis method is developed. Considering the fact that the fractional differentiation with respect to time is characterized by long-term memory effects, the fractional derivative of the measurement model with respect to time is considered. By this means, more historical measurement data can be exploited. And then the fractional differentiation-based observability matrix, which reflects the high-order nonlinearity of the navigation system, is constructed. Finally, as the condition number is not directly proportional to the positioning error, to evaluate the navigation performance, the exponent weighted condition number is developed, where small condition numbers have large weight. The simulation results demonstrate that the fractional differentiation-based observability analysis method is sensitive to the orbital elements in the nonlinear X-ray pulsar navigation system, and has small calculation load. In addition, compared to the traditional observability analysis methods, it is observed that its analysis result matches well with the X-ray pulsar navigation performance.

For the atomic gyroscope (AG) operated in spin-exchange relaxation-free (SERF) regime, the sensitivity to external magnetic fields has been suppressed while the ability to sense inertial rotations has been kept. Here, a theoretical relationship between the magnetic fields and the AG response is given, and the influence of field fluctuations on the systematic stability is also shown. The spin-exchange rate of the electron spins R se en and the relaxation rate of the nuclear spins R tot n aggravate the influence of the field component B x . Experimental results indicate that the contributions of long-term fluctuations in the fields, approximately 2.4 pT/h for B x and 0.9 pT/h for B y , to the bias stability are 2.19 × 10 −2 deg/h and 5.29 × 10 −4 deg/h. This work is not only valuable for understanding the field-suppression effect in SERF AG, but also provides a useful tool for identifying the influence of fields on the systematic stability.

Active magnetic bearings (AMBs) have achieved great advantages in the high-speed and high-power-density rotating machine. Various vibration control strategies based on the notch filter have been reported to reduce the rotor imbalance vibration. But, the study is still insufficient to determine why the vibration gets reduced. This paper addresses a concise and direct explanation of the effects of notch filter on the rotor imbalance vibration with AMBs. An analytic solution for the synchronous response of rotor imbalance is introduced using the simple planar rotor model and general notch filter method. Then, combined with practical matters, the amplifier of a heteropolar radial AMB is further specified to uncover the effect of motion induced voltage to rotor self-centering, as a comparison with the homopolar radial AMB. Since the developed motor is equipped with both types of radial AMBs, a detailed control design is exhibited based on the dynamics of rigid body motion. The traditional simplification of two-plane separate control is improved, and a centralized controller is constructed. The effects of the rotor imbalance vibration rejection are demonstrated by the simulation results and experiments in a 30-kW 60000-r/min permanent magnet motor.

In the capture period of deep space exploration, three traditional celestial navigation methods including the direction, velocity, and distance measurements cannot completely meet the requirement of navigation accuracy due to ephemeris errors. To solve this problem, considering the fact that some impulses exist in solar light irradiance profile due to solar flares, we propose the solar flare time difference of arrival (TDOA) measurement method, which exploits these impulses to measure the position of the spacecraft. As the time of arrival (TOA) of solar flare cannot be predicted, we cannot use the solar flare TOA directly. The Mars light irradiance variation is related to the solar one, as the Mars light is the solar light filtered by the Martian atmosphere absorption filter. Based on this theory, the solar flare TDOA measurement method using direct and reflected light is developed. In this method, two solar flare TOAs are obtained by the spacecraft. One is from the sun directly. The other is the corresponding TOA reflected by Mars. Their difference is the TDOA measurement. In addition, we also propose two alternative schemes. One uses the solar light instead of flare if solar flares do not occur in the capture period, and the other adopts Phobos as the reflected point instead of Mars to solve the Martian atmospheric absorption. The traditional direction measurement-based navigation method can provide highly accurate navigation information at the tangential direction in the capture period. However, its accuracy at the radial direction is very low. Fortunately, the solar flare TDOA measurement method offsets this problem. To get highly accurate navigation information, the solar flare TDOA measurement and the Mars direction measurement are coupled into the solar flare TDOA/Mars direction integrated navigation system. We present simulation results that demonstrate the feasibility and effectiveness of the solar flare TDOA measurement method. Compared to the traditional direction measurement-based navigation method, the solar flare TDOA/Mars direction integrated navigation can provide higher positioning accuracy, especially the radial component.

To effectively suppress the synchronous vibration torques for a magnetically suspended rotor (MSR) with significant gyroscopic effects and serious coupling dynamics, a novel cross-feedback notch filter is proposed in this paper. First, the coupled multi-input-multi-output active magnetic bearing rotor system is converted into an equivalent complex single-input single-output (SISO) system. The equivalent transformation aims at easing the controller design and extending the classical stability criterion to the complex coefficient frequency domain. Then, the principle and implementation of the proposed scheme used for synchronous vibration suppression over an entire rotational speed range is analyzed in details. The performance compared with the conventional decentralized notch filter is investigated. Moreover, the closed-loop stability, which based on the equivalent complex SISO system and complex-coefficient stability criterion is given. Experimental results on a magnetically suspended flywheel demonstrate the significant effect of the proposed method on both synchronous vibration suppression and stability preservation.

The stellar refraction navigation is a type of autonomous celestial navigation method for satellites that uses high-accuracy star sensors to obtain the stellar refraction. The apparent height and the stellar refraction angle are two kinds of measurements for the satellite stellar refraction navigation system. A better navigation performance can be achieved by the stellar refraction angle rather than the refraction apparent height. However, the measurement model of the stellar refraction angle is an implicit function, which needs an implicit filter method. A new implicit unscented Kalman filter (UKF) method is proposed and applied to the satellite stellar refraction navigation system in this paper. The main difference between the classical UKF and the implicit UKF lies in the measurement update. First, since the implicit measurement model can be rearranged into an equation whose one side is zero, the vector of zeros is regarded as the equivalent measurement, and the difference between the predicted measurement and its true value is utilized for updating the predicted state and its covariance matrix. Second, the measurement noise and its covariance matrix are transformed based on the unscented transformation principle. In addition, the implicit UKF is compared with the implicit extended Kalman filter (IEKF), the iterative IEKF, and the UKF. Simulations show that the proposed implicit UKF method can obtain about 19.0% and 17.5% improvements in three-dimensional root mean square position estimation compared to the IEKF and the iterative IEKF, respectively. Although the navigation performance of the UKF is close to the implicit UKFs, the computational time of the implicit UKF is much shorter than the UKFs. In addition, the sensitivities of the four different Kalman filters to the star sensor's faults and the atmosphere perturbation are compared, respectively.

Solar oscillation, which causes the sunlight intensity and spectrum frequency change, has been studied in great detail, both observationally and theoretically. In this paper, owing to the existence of solar oscillation, the time delay between the sunlight coming from the Sun directly and the sunlight reflected by the other celestial body such as the satellite of planet or asteroid can be obtained with two optical power meters. Because the solar oscillation time delay is determined by the relative positions of the spacecraft, reflective celestial body and the Sun, it can be adopted as the navigation measurement to estimate the spacecraft's position. The navigation accuracy of single solar oscillation time delay navigation system depends on the time delay measurement accuracy, and is influenced by the distance between spacecraft and reflective celestial body. In this paper, we combine it with the star angle measurement and propose a solar oscillation time delay measurement assisted celestial navigation method for deep space exploration. Since the measurement model of time delay is an implicit function, the Implicit Unscented Kalman Filter (IUKF) is applied. Simulations demonstrate the effectiveness and superiority of this method.

The combination of celestial measurement and ground Doppler measurement has been successfully used for orbit determination in many deep-space exploration missions. However, one of the inherent drawbacks of ground tracking is the long communication delay. Using the Doppler measurement from the sun instead of the ground station is a feasible strategy for real-time navigation, but the accuracy of this Doppler measurement is affected by the frequency fluctuation of the solar spectrum. To solve this problem, a differential Doppler measurement-aided celestial navigation method is proposed in this paper, which uses the differential Doppler measurement to reduce the influence caused by instability of the solar spectrum frequency and improve the navigation accuracy. Simulations demonstrate the feasibility and effectiveness of this method.

Celestial navigation (CeleNav) has been successfully used for position determination in many Mars exploration missions. Traditional CeleNav usually uses star angle as measurement, which is a function of spacecraft's position. Its accuracy is affected by the distance between the spacecraft and the Mars. X-ray pulsar-based navigation (XNAV) is a feasible autonomous method which can provide highly accurate distance measurements. However, single pulsar navigation system is unobservable and its navigational performance is influenced by the corresponding systematic biases caused by the pulsar directional error and the spacecraft-borne clock error. For the complementary of the CeleNav and the XNAV, the differential X-ray pulsar aided CeleNav method is proposed, which adopts the time-differenced X-ray pulsar measurement to eliminate the major part of systematic biases and improve the navigation accuracy. Simulations demonstrate the feasibility and effectiveness of this method.

To effectively reject the influence of moving gimbal effect and parameter variation on the control performance of the rotor-active magnetic bearings (AMBs) system in a double gimbal magnetically suspended control moment gyro (MSCMG), this paper proposes a feedback linearization and extended state observer (ESO) based control (FLESOBC) strategy, which can attenuate the matched and mismatched system uncertainties simultaneously. First, considering the voltage-type power amplifier used in the MSCMG for space applications, the rotor dynamics is modeled completely and then rearranged into translation and tilt motion subsystems according to modal separation control, where the lumped system uncertainties are adopted to represent the external disturbances and the parameter variations. Then, feedback linearization based on differential geometry theory is performed to transform the original system into the integral chain pseudo-linear system, making the mismatched uncertainties in the same channel as the new virtual input. Afterwards, the ESO is designed to estimate the lumped uncertainties. To combine the merits of compensation control and robust control, a PIDD controller (PID with second order differential) is designed to guarantee the closed loop stability and avoid the power amplifier saturation. Finally, simulations and experiments are carried out to demonstrate the effectiveness of the proposed method.

The rotating machinery suspended by an active magnetic bearing (AMB) system always suffers from rotor mass imbalance and sensor runout disturbances, which lead to the periodic fluctuations in control currents. This paper presents a novel multiple resonant controllers (MRC) for an AMB system to suppress the multifrequency current harmonics in the presence of variable rating speed. The principle and structure of the plug-in MRC used for current harmonics suppression in the AMB system is discussed. The design of the proposed MRC, using the progressively tuning and segmentation switch strategy, is given. The proposed design method for the MRC can achieve the balance between good stability and harmonics suppression precision. As well, the robustness of the overall system is systematically analyzed for the entire operational speed range. Simulation and experimental results for current fluctuations and multifrequency vibration forces on a magnetically suspended flywheel validate the effectiveness of the proposed method.

This paper presents a novel synchronous micro-vibration suppression method on the basis of the small gain theorem to reduce the frequency-varying synchronous micro-vibration forces for a magnetically suspended flywheel (MSFW). The proposed synchronous micro-vibration suppression method not only eliminates the synchronous current fluctuations to force the rotor spinning around the inertia axis, but also considers the compensation caused by the displacement stiffness in the permanent-magnet (PM)-biased magnetic bearings. Moreover, the stability of the proposed control system is exactly analyzed by using small gain theorem. The effectiveness of the proposed micro-vibration suppression method is demonstrated via the direct measurement of the disturbance forces for a MSFW. The main merit of the proposed method is that it provides a simple and practical method in suppressing the frequency varying micro-vibration forces and preserving the nominal performance of the baseline control system.

A Celestial Navigation System (CNS) is a feasible and economical autonomous navigation system for deep-space probes. Ephemeris errors have a great influence on the performance of CNSs during the Mars approach phase, but there are few research studies on this problem. In this paper, the analysis shows that the ephemeris error of Mars is slowly-varying, while the ephemeris error of Phobos and Deimos is periodical. The influence of the ephemeris errors of Mars and its satellites is analysed in relation to both the Sun-centred frame and the Mars-centred frame. The simulations show that the position error of a probe relative to the Sun caused by the Mars ephemeris error is almost equal to the ephemeris error itself, that the velocity error is affected slightly, and that the position and velocity relative to Mars are hardly affected. The navigation result of a Mars probe is also greatly affected by the quantities and periodicities of the ephemeris errors of Phobos and Deimos, especially that of Deimos.

We investigate the real-time closed-loop control of the compensation point in a K-Rb-21Ne comagnetometer operated in the spin-exchange relaxation-free regime. By locking the electron resonance, the alkali-metal electrons are free from the fluctuations of the longitudinal ambient magnetic field and nuclear magnetization, which could improve the systematic stability, enlarge the linear measuring range, and suppress the cross-talk error of the comagnetometer. The demonstration of closed-loop control of the magnetic field in the single nuclear species comagnetometer is of great significance for rotation sensing such as in gyroscopes and other high-precision metrology applications of the comagnetometer.

The distributed position and orientation system (POS) uses transfer alignment to accurately measure multi-node time-spatial reference information, which is necessary for compensating the motion error of imaging sensors used in aerial surveys. Lever-arm deformation in transfer alignment will result in time-varying covariance of measurement noise, which decreases the estimation accuracy. To address this problem, a second-order adaptive divided difference two-filter smoother (ADDTFS) is proposed for transfer alignment. The second-order adaptive divided difference filter (ADDF2) severs as the forward filter to address nonlinearity in the system. The ADDF2 can estimate the measurement noise covariance in real time based on adaptive estimation using innovation information. The weighted statistical linear regression formulation is used in the backward filter to independently estimate the states and error covariance matrices. Then the forward and backward results are combined, to obtain high-precision estimation results in post-processing. Finally, the vehicle experiment results show that the proposed method can improve the attitude precision of transfer alignment in a distributed POS by 27.84%, which has been successfully applied to motion compensation of airborne interferometric synthetic aperture radar (InSAR).

Switching power amplifier is an essential component for magnetic bearing system. However, the current ripple resulted from the conduction and shutoff operation of power switch component inevitably affects the performance of active magnetic bearing. To reduce the current ripple of switching power amplifier, the characteristics of current ripple are first analysed. In response to the spectrum character of current ripple, an online lifting wavelet transform de-noising algorithm, unlike the conventional power filter circuit, is proposed in this study. Moreover, the sliding data window and an improved threshold function are introduced to realise the feasibility of online processing and to improve the de-noising performance, respectively. Finally, plentiful comparative experiments, taking the magnetically suspended flywheel as subject, are implemented. The results illustrate that the proposed algorithm could dramatically reduce the current ripple and that the rotor displacement jitter and the vibration force are suppressed accordingly.

Imbalance vibration control for rotor is the main factor affecting attitude control performance for satellite using magnetically suspended control moment gyro (MSCMG). The method for adaptive imbalance vibration control for the rotor of variable-speed MSCMG with active-passive magnetic bearings is investigated in this paper. Firstly, on the basis of feedforward compensation, a rotor model for the imbalance vibration of variable-speed MSCMG with active-passive magnetic bearings is built, and the main factor affecting imbalance vibration compensation is also analyzed. Then, power amplifier parameter modifier with control switches is designed to eliminate the effects of time-varying parameters on the imbalance vibration compensation precision. The adaptive imbalance vibration control based on this modifier not only has high compensation precision, but also can control the frequency of parameter adjustment according to the compensation precision. Besides, since the passive magnetic bearing displacement stiffness of the rotor of variable-speed MSCMG with active-passive magnetic bearings cannot be obtained accurately, displacement stiffness modifier is employed. Finally, stability analysis is made on the imbalance vibration control system, and the range of rotation speed to ensure system stability is derived. Simulation results show that, imbalance vibration control method proposed in this paper can suppress the imbalance vibration of the rotor of variable-speed MSCMG with active-passive magnetic bearings effectively and has high precision.

Satellite autonomous navigation by stellar refraction is a type of autonomous celestial navigation method that uses high-accuracy star sensors instead of Earth sensors to provide information regarding Earth's horizon. There are two kinds of measurements of satellite stellar refraction navigation. They are the apparent height and the stellar refraction angle. A better navigation performance can be achieved by the stellar refraction angle rather than the refraction apparent height. However, the measurement model of the stellar refraction angle is an implicit function. The traditional UKF and observability analysis methods are not applicable to the system with an implicit measurement model. The implicit UKF (IUKF) and its observability analysis method are proposed in this paper. The equivalent observability matrix is constructed based on the IUKF algorithm. Furthermore, the best scheme for observation of the stellar refraction angle is studied using this new IUKF and its observability analysis. Both the observability analysis and simulation results show that a significant improvement in navigation performance can be achieved by the rotating observation of the stellar refraction angle.

Due to the high speed and the high power density, the blade strength and the rotor overheating of a turbomolecular pump (TMP) are strongly related to the safety and the stability of the pump operation. For magnetically levitated TMPs, which can obtain an ultra-clean and ultra-high vacuum in comparison to traditional TMPs with oil-lubricated bearings, the rotor strength and overheating are limiting their ultimate pumping speed, since the rotor is only cooled by thermal radiation. This paper focuses on the stress analysis of the pump and the rotor thermal performance evaluation to prevent the permanent magnets (PMs) from irreversible demagnetization at high temperature and to ensure the rotor integrity throughout the whole speed range. The influence of the thickness of the sleeve around the PMs of the rotor shaft on electromagnetic losses and stress is analyzed. Finally, the electromagnetic and thermal tests are implemented on a prototype to verify the theoretical methods and the design concept. The measured maximum pumping speed of the prototype can reach 4180 L/s.

In this paper, a high-speed permanent-magnet (PM) electrical machine is designed for centrifugal air blower application with consideration of the multiphysics constraints, including the mechanical strength, rotor dynamics, mechanical losses, and thermal field. In order to minimize the probabilities of mechanical failure and to realize the compact structure, the length and the outer diameter of rotor from mechanical point of view are designed and optimized. The optimization of sleeve thickness is performed by an accurate finite-element modeling which the interference is equivalent to the contact pressure. The optimization of rotor strength is based on the length–diameter ratio curve by using the finite-element method, which is followed behind the optimization of sleeve thickness. An assessment of machine cooling design from thermal point of view is performed by using the computational fluid dynamics modeling. Finally, in order to verify the accuracy of theoretical analysis, the prototype is fabricated with consideration of all critical values of the design parameters, and measured on the test bench.

To improve the performance of the surface permanent magnet synchronous motor drives, a sensorless control scheme based on the sliding-mode observer with an orthogonal phase-locked loop (PLL) incorporating two synchronous frequency-extract filters (SFFs) is proposed. The rotor position estimation errors are analyzed. The analysis results show that the harmonic errors of the estimated signal are hard to eliminate completely. Therefore, an improved adaptive notch filter - The SFF is proposed to extract the fundamental wave of the rotor position estimation before applying to the PLL. This method of the PLL combined SFFs can compensate the estimated back electromotive force harmonic error efficiently and adaptively. An experimental driveline system used for testing the electrical performance of the developed magnetically suspended motor is built. The effectiveness and the feasibility of the proposed method are validated with the experimental results.

This paper presents a novel method for position sensorless control of high-speed brushless DC motors with low inductance and nonideal back electromotive force (EMF) in order to improve the reliability of the motor system of a magnetically suspended control moment gyro for space application. The commutation angle error of the traditional line-to-line voltage zero-crossing points detection method is analyzed. Based on the characteristics measurement of the nonideal back EMF, a two-stage commutation error compensation method is proposed to achieve the high-reliable and high-accurate commutation in the operating speed region of the proposed sensorless control process. The commutation angle error is compensated by the transformative line voltages, the hysteresis comparators, and the appropriate design of the low-pass filters in the low-speed and high-speed region, respectively. High-precision commutations are achieved especially in the high-speed region to decrease the motor loss in steady state. The simulated and experimental results show that the proposed method can achieve an effective compensation effect in the whole operating speed region.