Azimuth Error Research Articles

Rotational Risley prisms: Fast and high-accuracy inverse solution and application based on back propagation neural networks

In the application of rotational Risley prism systems, there is a conflict between inverse solution time and accuracy. This paper proposes an inverse solution method based on back propagation neural networks to solve this problem. The training set data for prism rotation, azimuth, and elevation angles are produced based on the beam deflection model of the actual application. After that, two independent networks are trained individually. One network is used to calculate the angular difference, while the other network calculates the synchronous rotation angle to satisfy the solutions of elevation and azimuth angles of target. The azimuth and elevation root mean square errors for the inverse solution of the spiral trajectory using the trained network were 8.04e-04 arcsec and 2.60e-3 arcsec, respectively. At a solution time of 80 µs, the pointing accuracy in the experiment was less than 1 arcsec. The experimental results demonstrate that the proposed inverse solution method can obtain high-accuracy analytical solutions with low time consumption.

Two-stage spatiotemporal cooperative reentry guidance strategy using transformer and improved beluga whale optimization

This research addresses the challenge of insufficient control margin caused by the coupling of multiple constraints in the cooperative precise reentry guidance of hypersonic vehicles. Drawing inspiration from the concept of spatiotemporal decoupling control, a rapid guidance strategy is developed to ensure precise handling of all constraints, including attack time, attack angle, and trajectory constraints. Initially, during the early phase of gliding flight, the adjustment of the heading angle is conceptualized as a single variable root-solving problem, in relation to the entrance width of the lateral azimuth error corridor. Subsequently, a lateral azimuth error corridor with adaptively narrowing entrance width, coupled with a Transformer network-based bank angle predictor, is incorporated to achieve precise fine-tuning of the heading angle under the soft constraint of velocity. In the later phase of gliding flight, the design of a cooperative guidance law under complex multiple constraints is transformed into a nonlinear rapid optimization problem of control commands. An enhanced beluga whale optimization suited to this guidance task is proposed. Finally, numerical simulations are carried out to validate the effectiveness of the proposed strategy under both nominal and uncertain conditions.

Cosmology Large Angular Scale Surveyor (CLASS): 90 GHz Telescope Pointing, Beam Profile, Window Function, and Polarization Performance

The Cosmology Large Angular Scale Surveyor (CLASS) is a telescope array that observes the cosmic microwave background (CMB) over ∼75% of the sky from the Atacama Desert, Chile, at frequency bands centered near 40, 90, 150, and 220 GHz. CLASS measures the large angular scale CMB polarization to constrain the tensor-to-scalar ratio and the optical depth to last scattering. This paper presents the optical characterization of the 90 GHz telescope. Observations of the Moon establish the pointing while dedicated observations of Jupiter are used for beam calibration. The standard deviations of the pointing error in azimuth, elevation, and boresight angle are 1.′3, 2.′1, and 2.′0, respectively, over the first 3 yr of observations. This corresponds to a pointing uncertainty ∼7% of the beam’s full width at half-maximum (FWHM). The effective azimuthally symmetrized instrument 1D beam estimated at 90 GHz has an FWHM of 0.°620 ± 0.°003 and a solid angle of 138.7 ± 0.6(stats.) ± 1.1(sys.) μsr integrated to a radius of 4°. The corresponding beam window function drops to bℓ2=0.93,0.71,0.14 at ℓ = 30, 100, 300, respectively. Far-sidelobes are studied using detector-centered intensity maps of the Moon and measured to be at a level of 10−3 or below relative to the peak. The polarization angle of Tau A estimated from preliminary survey maps is 149°.6 ± 0°.2(stats.) in equatorial coordinates. The instrumental temperature-to-polarization (T → P) leakage fraction, inferred from per-detector demodulated Jupiter scan data, has a monopole component at the level of 1.7 × 10−3, a dipole component with an amplitude of 4.3 × 10−3, with no evidence of quadrupolar leakage.

A Near-Vertical Well Attitude Measurement Method with Redundant Accelerometers and MEMS IMU/Magnetometers

Vertical drilling is the first stage of petroleum exploitation and directional well technology. The near-vertical attitude at each survey station directly determines the whole direction accuracy of the borehole trajectory. However, the attitude measurement for near-vertical wells has poor azimuth accuracy because the poor signal-to-noise ratio of radial accelerometers hardly obtains the correct horizontal attitude, especially the roll angle. In this paper, a novel near-vertical attitude measurement method was proposed to address this issue. The redundant micro-electromechanical system (MEMS) accelerometers were employed to replace the original accelerometers from MEMS inertial measurement unit (IMU)/magnetometers for calculating horizontal attitude under near-vertical conditions. In addition, a simplified four-position calibration method for the redundant accelerometers was proposed to compensate for the installation and non-orthogonal error. We found that the redundant accelerometers enhanced the signal-to-noise ratio to upgrade the azimuth accuracy at the near-vertical well section. Compared with the traditional method, the experiment results show that the average azimuth errors and roll errors are reduced from 34.45° and 27.09° to 5.7° and 0.61°, respectively. The designed configuration scheme is conducive to the miniaturized design and low-cost requirements of wellbore measuring tools. The proposed attitude measurement method can effectively improve the attitude accuracy of near-vertical wells.

Multiple ultrasonic partial discharge DOA estimation performance of KPCA Pseudo-Whitening mnc-FastICA

Empirical studies into partial discharge (PD) localization face the difficulty of signal contamination from external noise and interference. To extract relevant information from PD signals collected by acoustic sensor array, Kernel Principal Component Analysis (KPCA) pseudo-whitening with modified noncircular Fast Independent Component Analysis (mnc-FastICA) were used. By this approach, separated matrix and observed signals can be achieved. The reconstructed array manifold matrix created from the separated matrix generated by KPCA-mnc-FastICA may be used in the Direction of Arrival (DOA) estimation approach. An angle error correction matrix is designed to compensate for the sensor's phase inaccuracy. The simulation results show that angle identification accuracy is outstanding, with mistakes limited to a small margin of 2°. Furthermore, the results of trials show that this technique can efficiently isolate individual target signals even when they are polluted with significant noise and interference. The average errors in azimuth and pitch angle are less than 2° and 1.1°, respectively. These data support the effectiveness of the approach for effectively separating signals and estimating DOA of numerous signal sources.

Investigation of navigation information correction techniques for master-slave AUV formations in unstable communication environments

Cooperative navigation within master–slave Autonomous Underwater Vehicles (AUVs) necessitates the periodic transmission of high-precision positional data from the master AUV, endowed with advanced navigational instrumentation, to the slave AUV characterized by limited positional accuracy. This data exchange is facilitated through an acoustic sensor mechanism, enabling the quantification of relative spatial separation between the two vehicles. Employing an Extended Kalman Filter (EKF), the positioning error of the slave AUV can be estimated and corrected, enhancing its positional accuracy. However, this collaborative navigation methodology encounters dual challenges. Firstly, the intricate underwater acoustic environment introduces the potential for data loss or outlier measurements in submarine acoustic communication, thereby jeopardizing the efficacy of collaborative navigation. Secondly, the current approach solely rectifies the slave AUV's positional error upon the receipt of data from the master AUV, neglecting the fundamental divergence in positional error that accrues between successive data receptions, stemming from the inherent imprecision in the dead reckoning process. To contend with these complexities, this study presents a novel approach to rectifying navigation data within master–slave AUV formations, particularly within the context of unstable communication conditions. The proposed method harnesses an outlier adaptive discriminant EKF framework, proficiently addressing the slave AUV's positional error while simultaneously estimating and compensating for azimuthal angular errors during underwater acoustic communication between the master and slave AUVs. This method establishes a pivotal groundwork for heightening the accuracy of independent autonomous navigation within the slave AUV during subsequent operational phases. The accuracy and applicability of the proposed method are rigorously validated through simulation-based verification and lake-water field experiments. The empirical results unequivocally highlight the efficacy of the underwater acoustic communication approach put forth in this study, with an outlier recognition rate exceeding 80%. Furthermore, the method adeptly rectifies azimuthal angular errors and positional inaccuracies within the AUV, thus effecting a comprehensive enhancement of overall positioning precision. This research bears significant implications for advancing autonomous underwater navigation, providing a robust framework to bolster the precision and reliability of master–slave AUV formations, particularly under challenging communication circumstances.

Horizontal sound localization in presence of noise in normal-hearing young adults

Objective: This study investigates the effect of signal-to-noise ratio (SNR), frequency, and bandwidth on horizontal sound localization accuracy in normal-hearing young adults. Methods: From August 2022 to December 2022, a total of 20 normal-hearing young adults, including 7 males and 13 females, with an age range of 20 to 35 years and a mean age of 25.4 years, were selected to participate in horizontal azimuth recognition tests under both quiet and noisy conditions. Six narrowband filtered noise stimuli were used with central frequencies (CF) of 250, 2 000, and 4 000 Hz and bandwidths of 1/6 and 1 octave. Continuous broadband white noise was used as the background masker, and the signal-to-noise ratio (SNR) was 0, -3, and -12 dB. The root-mean-square error (RMS error) was used to measure sound localization accuracy, with smaller values indicating higher accuracy. Friedman test was used to compare the effects of SNR and CF on sound localization accuracy, and Wilcoxon signed-rank test was used to compare the impact of the two bandwidths on sound localization accuracy in noise. Results: In a quiet environment, the RMS error in horizontal azimuth in normal-hearing young adults ranged from 4.3 to 8.1 degrees. Sound localization accuracy decreased with decreasing SNR: at 0 dB SNR (range: 5.3-12.9 degrees), the difference from the quiet condition was not significant (P>0.05); however, at -3 dB (range: 7.3-16.8 degrees) and -12 dB SNR (range: 9.4-41.2 degrees), sound localization accuracy significantly decreased compared to the quiet condition (all P<0.01). Under noisy conditions, there were differences in sound localization accuracy among stimuli with different frequencies and bandwidths, with higher frequencies performing the worst, followed by middle frequencies, and lower frequencies performing the best, with significant differences (all P<0.01). Sound localization accuracy for 1/6 octave stimuli was more susceptible to noise interference than 1 octave stimuli (all P<0.01). Conclusions: The ability of normal-hearing young adults to localize sound in the horizontal plane in the presence of noise is influenced by SNR, CF, and bandwidth. Noise with SNRs of ≥-3 dB can lead to decreased accuracy in narrowband sound localization. Higher CF signals and narrower bandwidths are more susceptible to noise interference.

Ultrafast polarization characterization with Mueller matrix based on optical time-stretch and spectral encoding.

High-speed optical polarization characterization is highly desirable for a wide range of applications, including remote sensing, telecommunication, and medical diagnosis. The utilization of the Mueller matrix provides a superior systematic and comprehensive approach to represent polarization attributes when matter interacts with optical beams. However, the current measurement speed of Mueller matrix is limited to only seconds or milliseconds. In this study, we present an ultrafast Mueller matrix polarimetry (MMP) technique based on optical time-stretch and spectral encoding that enables us to achieve an impressive temporal resolution of 4.83 nanoseconds for accurate Mueller matrix measurements. The unique feature of optical time-stretch technology enables continuous, ultrafast single-shot spectroscopy, resulting in a remarkable speed of up to 207 MHz for spectral encoding Mueller matrix measurement. We have employed an effective Mueller linear reconstruction algorithm based on the measured modulation matrix, accounting for all potential non-ideal effects of polarization components like retardance error and azimuth error. To ensure high precision, prior to the actual measurement, high-order dispersion induced by time-stretch requires adjustment through proper modulation matrix design. Upon such correction, both the results of static and rapid dynamic samples measurements exhibit exceptional accuracy with root-mean-square error (RMSE) approximately equal to 0.04 and 0.07 respectively. This presented ultrafast MMP provides a significant advance over preceding endeavors, enabling superior accuracy and increased speed concurrently.

Experimental demonstration of indoor 3D optical wireless positioning and azimuth estimation using steerable line lasers

We present an indoor three-dimensional (3D) optical wireless positioning and azimuth estimation (OWPAE) scheme that utilizes steerable line lasers. This approach enables the simultaneous acquisition of precise 3D coordinate and azimuth of a mobile receiver without requiring a priori knowledge of the radiation pattern of the light source and photo-detector (PD) characteristics. Our work begins with an analysis of the feasibility of using line lasers for OWPAE. Subsequently, by leveraging the geometric relationship between two line lasers and a pair of PDs, we establish the OWPAE model, considering receiver tilt, and design the frame structure for conveying essential information. To evaluate the effectiveness of our proposed OWPAE scheme, we set up an experimental platform. Experimental results confirm that when the receiver is oriented upwards, the system accurately determines the receiver's location with a mean 3D positioning error of 6.3 cm and its azimuth with a mean azimuthal error of 2.8°. When the receiver tilts at a polar angle of 30°, the system remains effective, yielding a mean 3D positioning error of 8.3 cm and a mean azimuthal error of 5.6°.

SAL vibration estimation and compensation based on triangular interferometric signals.

Synthetic aperture Ladar (SAL) is an extension of synthetic aperture technology in the optical frequency band. Owing to the short wavelength of lasers, the system has high-resolution, high-data-rate, and refined imaging capabilities, which has potential in high-resolution observation fields such as ground observation and space target observation. However, the short wavelength of lasers also makes SAL severely sensitive to vibrations even on the micron order which cause azimuth defocusing and range cell migration. To address this problem, we establish a de-chirp signal model under vibration environment, and propose a vibration error estimation and compensation method using triangular interferometric signals. According to the symmetrical characteristics of triangular frequency modulated continuous wave (T-FMCW) and the time-frequency information introduced by the azimuthal vibration phase, we use a two-stage interferometry method to estimate instantaneous frequency introduced by the vibration errors that cause range cell migration. For the scenarios without obvious range cell migration, we use a one-stage interferometry method to estimate the instantaneous frequency. Subsequently, we establish a vibration compensation filter using the estimated instantaneous frequency to compensate for the vibration errors. We use two experiments to verify the effectiveness and superiority of the proposed method. The results show that the proposed method effectively eliminates range cell migration and azimuthal phase errors introduced by vibration errors, producing SAL imaging results with higher resolution than the conventional spectral correlation method.

ACCURACY ANALYSIS OF AIRCRAFT POSITION PARAMETERS PROVIDED BY GCA 2000 AIRPORT SURVEILLANCE RADAR

The aim of this article was to investigate the accuracy of determining the position parameters of an aircraft by the GCA 2000 airport control radar located at Deblin Airport (EPDE). In order to analyse the accuracy of determining the position of an aircraft by the GCA 2000 radar, a research flight was carried out. The position of the aircraft was recorded by the GCA 2000 radar and the Thales Mobile Mapper Pro GPS receiver on board the aircraft. The resulting position parameters were compared with each other to investigate the accuracy of the radar’s coordinate determination. In addition, a number of analyses and comparisons were performed to determine the reasons for the interruptions in the radar detection of the aircraft. Based on the study, it can be concluded that the GCA 2000 radar located at Deblin airport meets the requirements set by the International Civil Aviation Organisation (ICAO) for radar performance. According to ICAO, the standard deviation of the distance error should be 70–130 metres and the azimuth error for primary radars should be 0.15–0.2°, and for secondary radars 0.2–0.3°. The standard deviation of the distance error during a research flight by the GCA 2000 radar is 81.1 metres and the standard deviation of the azimuth error is 0.19°.

ACCURACY ANALYSIS OF AIRCRAFT POSITIONING USING NAVIGATIONAL DATA FROM AVIA-W RADAR

The paper presents an analysis of the accuracy of determination of parameters of the position of aircraft using data from the AVIA-W radar. In the first place, the authors determined the position of the aircraft as well as the range and azimuth parameters by the AVIA-W radar, located in Dęblin. This was followed by a determination of the absolute position error of the aircraft and the determination of the range and azimuth measurement error by the AVIA-W radar. The research test was carried out using a Diamond DA40 NG aircraft on which a GPS satellite receiver was mounted in order to determine the flight reference position. In addition, the range and azimuth measurements for the aircraft were acquired from the AVIA-W radar. Navigational calculations were conducted for polar and rectangular planar coordinates. Based on the performed research, the azimuth error was found to be –1.4o, while the radar range measurement error was equal to –0.04 km. The conducted research is experimental in its character. In the future it will be repeated and extended to the GCA-2000 radar, which is also located at Dęblin military airfield.

A Novel Forward-Looking Target Reconstruction Method With Electromagnetic Vortex Interferometry

For the target in the radar forward-looking sight, only the range-history phase information can be exhibited when the plane electromagnetic (EM) wave illuminating. For traditional approaches, the reconstruction of target azimuthal information requires antennas configured at both ends of the long baseline to implement multi-angle observation, usually leading to a baseline length burden. In contrast, the target’s azimuth information, related to the orbital angular momentum (OAM), is directly modulated in the new-dimensional echo phase by the antenna radiating the vortex EM wave, which provides a new foundation for target azimuth reconstruction. In this article, a novel forward-looking target reconstruction methodology with EM vortex interferometry is proposed, and the target 3-D imaging with different OAM modes interferometry strategies is achieved as well. The developed approach can improve the target azimuthal reconstruction error performance without increasing the length of short baseline and image registration. Comprehensive results of simulated data and real-world measured data are performed to validate the effectiveness and anti-noise robustness of the proposals.

Azimuth calibration based on equal angle balance correction algorithm for measurement-while-drilling system

The precision of azimuth calculation in measurement-while-drilling systems is heavily reliant on the triaxial magnetometer, necessitating proper calibration to minimize azimuth errors. To address the need for high-precision calibration of systematic errors such as sensor scale factors, bias, and non-orthogonality, a relationship between the error model and the correction matrix is derived and a novel equal angle balance correction method to calibrate azimuth is proposed. Experimental results demonstrate that the mean azimuth error generated by this algorithm is less than 0.00624°, which is at least 28 times lower than that of the ellipsoid fitting correction method. The algorithm effectively eliminates systematic errors and meets the practical engineering requirements for azimuth calibration in measurement-while-drilling systems.

Design and testing of star tracker algorithms for autonomous optical line-of-sight deep-space navigation.

This paper aims to investigate the capabilities of exploiting optical line-of-sight navigation using star trackers. First, a synthetic image simulator is developed to generate realistic images, which is later exploited to test the star tracker's performance. Then, generic considerations regarding attitude estimation are drawn, highlighting how the camera's characteristics influence the accuracy of the estimation. The full attitude estimation chain is designed and analyzed in order to maximize the performance in a deep-space cruising scenario. After that, the focus is shifted to the actual planet-centroiding algorithm, with particular emphasis on the illumination compensation routine, which is shown to be fundamental to achieving the required navigation accuracy. The influence of the center of the planet within the singular pixel is investigated, showing how this uncontrollable parameter can lower performance. Finally, the complete algorithm chain is tested with the synthetic image simulator in a wide range of scenarios. The final promising results show that with the selected hardware, even in the higher noise condition, it is possible to achieve a direction's azimuth and elevation angle error in the order of 1-2arc sec for Venus, and below 1arc sec for Jupiter, for a spacecraft placed at 1AU from the Sun. These values finally allow for a positioning error below 1000km, which is in line with the current non-autonomous navigation state-of-the-art.

A multi-sensor cooperative detection target tracking method based on radar-optical linkage control

Radar is a common means of tracking a target, and with active enemy interference, it often causes the target to lose its track, thus causing the radar to lose continuous tracking of the target. To improve the tracking effect, a multi-sensor cooperative detection target tracking method based on radar photoelectric linkage control was established. The study is based on radar photoelectric linkage, constant velocity (CV), constant acceleration (CA) and current statistical model (CSM) as the mathematical model of moving targets for this study. Improved interactive multi-model (IMM) and standard IMM were compared for targets in different motion states, as well as single sensor electronic support measures (ESM) and multi-sensor electronic support measures (ESM), infrared search and track (IRST). The research results show that in variable speed motion, the improved IMM algorithm and multiple sensors are used for target tracking. The azimuth and elevation tracking errors of the target are low, which can effectively solve the problem of model mismatch during the conversion of motion modes such as CV and CA. The azimuth and elevation image curves fluctuate smoothly, and have high stability. This method can achieve better tracking results.

Novel pseudo-linear Kalman filtering for 3D angle-only tracking in the presence of observer’s location errors

This paper presents novel pseudo-linear Kalman filtering algorithms for three-dimensional (3D) angle-only tracking (AOT) in the presence of observer’s locations perturbed by random noises. These random observer’s location errors (OLEs) seriously deteriorate the filtering precision, since the additional errors are introduced into the angle measurements when the noisy observer location is directly used to estimate the target state of interest. A new pseudo-linear measurement model is firstly constructed in the presence of OLEs, and the first two-order statistical moments of the pseudo-linear measurement noises are analyzed conditioned on the exact observer location. Then, on the premise of deriving the azimuth and elevation errors caused by OLEs and re-analyzing the first two-order statistical moments of the pseudo-linear measurement noises conditioned on the noisy observer location, a novel pseudo-linear Kalman filter in the presence of OLEs (abbreviated as OPKF) is put forward. A closed-form bias estimate of this proposed OPKF is further derived recursively, and the corresponding bias-compensated and instrumental variable-based pseudo-linear Kalman filters in the presence of OLEs are finally designed to improve filtering precision. The advantages of filtering precision of the proposed method over the existing pseudo-linear Kaman filter and its variants are demonstrated by an example of 3D AOT in the presence of OLEs, in terms of different levels of sensor accuracy and observer’s location errors.

Solar laser pumping approach for both simultaneous and stable multibeam operation under tracking error condition

A solar laser pumping approach to achieve both simultaneous and stable multibeam solar laser operation under solar tracking error condition is proposed here. By using a heliostat, solar radiation is firstly redirected to a parabolic mirror, secondarily concentrated by an aspheric lens, and finally absorbed by four Nd:YAG rods within a pump cavity using a homogenizer. Zemax® and LASCAD™ analysis demonstrate that four simultaneous and stable 1064-nm continuous-wave solar laser emissions with similar multimode power levels can be achieved even with azimuthal solar tracking errors up to ± 0.5 deg. The variation on the multimode solar laser power of the four rods is significantly reduced from 32.38% and 55.52% without the homogenizer to 0.00% and 0.21% with the homogenizer for ± 0.1 deg and ± 0.2 deg azimuthal solar tracking error, respectively. More importantly, simultaneous and stable TEM00 mode solar laser emissions from the four rods are also numerically attained under solar tracking error condition.

Pointing Error Correction for a Moving-Platform Electro-Optical Telescope Using an Optimized Parameter Model.

This paper proposes a new optimized parameter model that enhances the pointing accuracy of moving-platform electro-optical telescopes (MPEOTs). The study begins by comprehensively analyzing the error sources, including the telescope and the platform navigation system. Next, a linear pointing correction model is established based on the target positioning process. To eliminate multicollinearity, stepwise regression is applied to obtain the optimized parameter model. The experimental results show that the MPEOT corrected by this model outperforms the mount model, with pointing errors of less than 50 arcsec for approximately 23 h. In the three tests conducted, the modified azimuth error(s) (RMS) were 14.07″, 12.71″, and 28.93″, and the elevation error(s) (RMS) were 12.94″, 12.73″, and 28.30″, respectively.

Contribution to Uncertainty Propagation Associated with On-Site Calibration of Infrasound Monitoring Systems

To improve the confidence and quality of measurements produced by regional and international infrasound monitoring networks, this work investigates a methodology for propagating uncertainty associated with on-site measurement systems. We focus on the propagation of sensor calibration uncertainties. The proposed approach is applied to synthetic infrasound signals with known back azimuth and trace velocity, recorded at the array elements. Relevant input uncertainties are investigated for propagation targeting the incoming signals (noise), instrumentation (microbarometers, calibration system, wind noise reduction system), and the time-delay-of-arrival (TDOA) model (frequency band). Uncertainty propagation is performed using the Monte Carlo method to obtain the corresponding uncertainties of the relevant output quantities of interest, namely back azimuth and trace velocity. The results indicate that, at high frequencies, large sensor uncertainties are acceptable. However, at low frequencies (&lt;0.1 Hz), even a 2∘ sensor phase uncertainty can lead to errors in the back azimuth of up to 5∘ and errors in the trace velocity of 20 m/s.