Azimuth Error Research Articles

InSAR Baseline Estimation for Gaofen-3 Real-Time DEM Generation.

For Interferometry Synthetic Aperture Radar (InSAR), the normal baseline is one of the main factors that affects the accuracy of the ground elevation. For Gaofen-3 (GF-3) InSAR processing, the poor accuracy of the real-time orbit determination results in a large baseline error, leads to a modulation error in azimuth and a slope error in the range for timely Digital Elevation Model (DEM) generation. In order to address this problem, a novel baseline estimation approach based on Shuttle Radar Topography Mission (SRTM) DEM is proposed in this paper. Firstly, the orbit fitting is executed to remove the non-linear error factor, which is different from traditional methods. Secondly, the height errors are obtained in a slant-range plane between SRTM DEM and the GF-3 generated DEM, which can be used to estimate the baseline error with a linear variation. Then, the real-time orbit can be calibrated by the baseline error. Finally, the DEM generation is performed by using the modified baseline and orbit. This approach has the merit of spatial and precise orbital free ability. Based on the results of GF-3 interferometric SAR data for Hebei, the effectiveness of the proposed algorithm is verified and the accuracy of GF-3 real-time DEM products can be improved extensively.

Performance Characterization of Four-Arm MAW Spiral Antennas for Digital Direction-of-Arrival Sensing

The characterization of four-arm modulated arm width (MAW) spiral antennas for linearly polarized direction-of-arrival (DOA) sensing with a directly connected coherent receiver and digital backend is discussed. The performance is assessed from the system level, with the achievable field of view (FOV) is used as the metric for the antenna, evaluated by means of the Cramer–Rao Lower Bound. The resulting antenna deviates from the previous MAW spiral designs, emphasizing system DOA performance over previous metrics, such as pattern quality. Simulation and measurement of this MAW spiral show that the antenna can sense the DOA with 1° rms error in azimuth and elevation over a ±30° elevation and 360° azimuth FOV across a 4.6:1 bandwidth. This antenna is then compared with a traditional MAW spiral and a conventional spiral, which in contrast achieve bandwidth less than 2:1.

A modified rapid alignment method of SINS based on measurement augmentation

The precision and convergence time of initial alignment are two most important indicators for inertial navigation system, but they are usually contradictory. It is necessary to achieve considerable accuracy in a very short period for the launching of weapons such as artillery, torpedo and so on. However, the conventional methods need several minutes to complete the initial alignment. In this case, a Kalman filter method based on measurement augmentation (MAKF) is proposed to speed up convergence, and theoretical analysis of observability verifies the feasibility of the proposed method. Furthermore, a large misalignment angle model and a dimensionality reduction Cubature Kalman Filter using measurement augmentation (MACKF) are also employed to solve the invalidity of the linear model under the large misalignment angle. Finally, simulations and turntable experiment results show that the proposed method can speed up the convergence substantially. Even with initial misalignment angle of 70°, the azimuth error angle can be reduced within 1° in 5 s and 0.5° in 10 s. It has important engineering application value.

Hybrid Transverse Polar Navigation for High-Precision and Long-Term INSs.

Transverse navigation has been proposed to help inertial navigation systems (INSs) fill the gap of polar navigation ability. However, as the transverse system does not have the ability of navigate globally, a complicated switch between the transverse and the traditional algorithms is necessary when the system moves across the polar circles. To maintain the inner continuity and consistency of the core algorithm, a hybrid transverse polar navigation is proposed in this research based on a combination of Earth-fixed-frame mechanization and transverse-frame outputs. Furthermore, a thorough analysis of kinematic error characteristics, proper damping technology and corresponding long-term contributions of main error sources is conducted for the high-precision INSs. According to the analytical expressions of the long-term navigation errors in polar areas, the 24-h period symmetrical oscillation with a slowly divergent amplitude dominates the transverse horizontal position errors, and the first-order drift dominates the transverse azimuth error, which results from the gyro drift coefficients that occur in corresponding directions. Simulations are conducted to validate the theoretical analysis and the deduced analytical expressions. The results show that the proposed hybrid transverse navigation can ensure the same accuracy and oscillation characteristics in polar areas as the traditional algorithm in low and mid latitude regions.

A hybrid error modeling for MEMS IMU in integrated GPS/INS navigation system

Continuity of accurate navigational data for intelligent transportation applications has been widely provided by utilizing low-cost navigation systems through integrating GPS with micro-electro-mechanical-system (MEMS) inertial sensors. To achieve the required accuracy, augmentation of Kalman filter (KF) with nonlinear error modeling techniques such as fast orthogonal search (FOS) was introduced to enhance the navigational solution by estimating and eliminating a great part of both linear and nonlinear errors of azimuth angle sensed by MEMS gyro. Although this augmented approach enhanced the overall navigational accuracy to some extent, it still suffers from some drawbacks that diverge the system accuracy during GPS long outage periods. These drawbacks stem from the wide-variational behavior and high nonlinearities of the errors in MEMS gyros which make it difficult to depend on the non-adaptive linear error model provided by KF to model the two types of MEMS azimuth errors.In this paper we tried to minimize the effect of uncertainties associated with the KF azimuth prediction during the absence of GPS by introducing a hybrid error model which employs support vector machine (SVM) to model the KF output and FOS, based on autoregressive (AR) concept, to model the nonlinear azimuth errors. The performance of the proposed hybrid SVM-FOS approach is evaluated for GPS/ RISS (Reduced inertial sensor system integrated system) and the results were compared with the conventional KF and augmented KF-FOS approaches.

Coherent Auto-Calibration of APE and NsRCM under Fast Back-Projection Image Formation for Airborne SAR Imaging in Highly-Squint Angle

Synthetic Aperture Radar (SAR) imaging with a non-zero (forward) squint angle is capable of providing a longer time for reaction than that of the broadside mode. However, due to the large squint angle, there will be severe coupling between range and azimuth samples in the echoed data, which is known as the problematic Range Cell Migration (RCM) in the SAR community. Especially when the SAR sensor mounted on an airborne platform encounters unexpected motion deviations/errors, the coupling becomes more complicated, and it is difficult to differentiate the systematic RCM for the SAR Image Formation Processing (IFP) and the non-systematic RCM error to be compensated. To this end, a novel and accurate SAR imaging algorithm is proposed in this paper to facilitate the processing of airborne SAR data collected at a high-squint angle. Firstly, the proposed algorithm is established under a Fast Time-Domain Back-Projection (FTDBP) framework for the SAR IFP. FTDBP paves the way to avoid the complicated processing for the systematic RCM as for the conventional SAR IFP in the Doppler processing manner. It is capable of generating a high-resolution SAR image efficiently under more general geometries and configurations. Secondly, regarding the non-systematic RCM errors, the proposed algorithm realizes the compensation by correcting both the Non-systematic Range Cell Migration (NsRCM), as well as Azimuthal Phase Error (APE) in a coherent manner. It is consequently capable of auto-calibrating the effects of the motion error completely without being dependent on the airborne navigation unit. Finally, both simulated and raw data collected by the airborne squinted SAR are applied to evaluate the proposed algorithm. Comparisons with conventional algorithms are carried out to reveal the superiority of the proposed algorithm.

Fast Alignment of SINS for Marching Vehicles Based on Multi-Vectors of Velocity Aided by GPS and Odometer.

In the strap-down inertial navigation system (SINS), the initial attitude matrix is acquired through alignment. Though there were multiple valid methods, alignment time and accuracy are still core issues, especially regarding the condition of the motion carrier. Inspired by the idea of constructing nonlinear vectors by velocity in a different coordinate frame, this paper proposes an innovative alignment method for a vehicle-mounted SINS in motion. In this method, the core issue of acquiring the attitude matrix is to calculate the matrix between the inertial frame and the initial body frame, which can be constructed through the nonlinear velocity vectors’ information from the GPS and the odometer at different moments, which denominate the multi-vector attitude determination. The possibility of collinearity can easily be avoided by a turning movement. The characteristic of propagation of error is analyzed in detail, based on which an improved method is put forward to depress the effect of random noise. Compared with the existing alignment methods, this method does not use the measurement information of accelerometers. In order to demonstrate its performance, the method is compared with the two-position alignment method and the traditional two-stage alignment method. Simulation and vehicle-based experiment results show that the proposed alignment method can establish an attitude reference in 100 s with an azimuth error of less than 0.06°, and that the accuracy does not have a strong correlation with the accelerometer.

Effect of Tracking Error of Double-Axis Tracking Device on the Optical Performance of Solar Dish Concentrator

In this paper, a flux distribution model of the focal plane in dish concentrator system has been established based on ray tracking method. This model was adopted for researching the influence of the mirror slope error, solar direct normal irradiance, and tracking error of elevation-azimuth tracking device (EATD) on the focal spot characteristics (i.e., flux distribution, geometrical shape, centroid position, and intercept factor). The tracking error transmission law of the EATD transferred to dish concentrator was also studied. The results show that the azimuth tracking error of the concentrator decreases with the increase of the concentrator elevation angle and it decreases to 0 mrad when the elevation angle is 90°. The centroid position of focal spot along x-axis and y-axis has linear relationship with azimuth and elevation tracking error of EATD, respectively, which could be used to evaluate and calibrate the tracking error of the dish concentrator. Finally, the transmission law of the EATD azimuth tracking error in solar heliostats is analyzed, and a dish concentrator using a spin-elevation tracking device is proposed, which can reduce the effect of spin tracking error on the dish concentrator. This work could provide fundamental for manufacturing precision allocation of tracking devices and developing a new type of tracking device.

Performance Evaluation of Dual-axis Tracking System of Parabolic Trough Solar Collector

A parabolic trough solar collector with the concentration ratio of 24 was developed in the College of Engineering; Nanjing Agricultural University, China with the using of the TracePro software an optical model built. Effects of single-axis and dual-axis tracking modes, azimuth and elevating angle tracking errors on the optical performance were investigated and the thermal performance of the solar collector was experimentally measured. The results showed that the optical efficiency of the dual-axis tracking was 0.813% and its year average value was 14.3% and 40.9% higher than that of the eat-west tracking mode and north-south tracking mode respectively. Further, form the results of the experiment, it was concluded that the optical efficiency was affected significantly by the elevation angle tracking errors which should be kept below 0.6o. High optical efficiency could be attained by using dual-tracking mode even though the tracking precision of one axis was degraded. The real-time instantaneous thermal efficiency of the collector reached to 0.775%. In addition, the linearity of the normalized efficiency was favorable. The curve of the calculated thermal efficiency agreed well with the normalized instantaneous efficiency curve derived from the experimental data and the maximum difference between them was 10.3%. This type of solar collector should be applied in middle-scale thermal collection systems.

Phase Error Analysis of Modified Conoscopic Holography

The modified conoscopic holography consists of a uniaxial crystal, a wave plate, and a linear polarizer. In this paper, the phase error due to imperfections of wave plate, azimuthal error of wave plate, and azimuthal error of linear polarizer are derived theoretically in modified conoscopic holography. Since the phase retardation error of a commercially available wave plate is very small, the resulting change in the phase error of the hologram is considered to be very small.BR Therefore, the phase error of the modified conoscopic holography is mainly attributed to the azimuthal error of the wave plate and the linear polarizer. The derived equations show that the azimuthal errors of the linear polarizer and the wave plate have similar effects on the phase error of the hologram.

Vibration Noise Modeling for Measurement While Drilling System Based on FOGs.

Aiming to improve survey accuracy of Measurement While Drilling (MWD) based on Fiber Optic Gyroscopes (FOGs) in the long period, the external aiding sources are fused into the inertial navigation by the Kalman filter (KF) method. The KF method needs to model the inertial sensors’ noise as the system noise model. The system noise is modeled as white Gaussian noise conventionally. However, because of the vibration while drilling, the noise in gyros isn’t white Gaussian noise any more. Moreover, an incorrect noise model will degrade the accuracy of KF. This paper developed a new approach for noise modeling on the basis of dynamic Allan variance (DAVAR). In contrast to conventional white noise models, the new noise model contains both the white noise and the color noise. With this new noise model, the KF for the MWD was designed. Finally, two vibration experiments have been performed. Experimental results showed that the proposed vibration noise modeling approach significantly improved the estimated accuracies of the inertial sensor drifts. Compared the navigation results based on different noise model, with the DAVAR noise model, the position error and the toolface angle error are reduced more than 90%. The velocity error is reduced more than 65%. The azimuth error is reduced more than 50%.

Astronomical position without observed altitude of the celestial body

The basis of all recommended methods for obtaining position by using celestial bodies is the known altitude of the celestial body being observed. Accordingly, it is necessary to have a sextant, classic or with an artificial horizon, or some other device that can measure altitude. However, there is a way to obtain position using astronomical navigation without determining the altitude of a celestial body, and this method will be analysed in this paper. The introduced method requires only precise measurement of the azimuth, and is based on determining two positions close to the dead reckoning position and lying on the isoazimuthal curve, i.e. a curve of the same great circle azimuths of a celestial body. Furthermore, the model assumes that a part of this curve, between the selected positions, can be replaced by a straight line. Special attention will be given to the analysis of errors of the line of position for various azimuth errors and various dead reckoning (assumed) positions. It will also be shown how a modern Electronic Chart Display and Information System (ECDIS) can help in approximate position determination, knowing only the azimuths of celestial bodies.

A Solar Position Sensor Based on Image Vision.

Solar collector technologies operate with better performance when the Sun beam direction is normal to the capturing surface, and for that to happen despite the relative movement of the Sun, solar tracking systems are used, therefore, there are rules and standards that need minimum accuracy for these tracking systems to be used in solar collectors’ evaluation. Obtaining accuracy is not an easy job, hence in this document the design, construction and characterization of a sensor based on a visual system that finds the relative azimuth error and height of the solar surface of interest, is presented. With these characteristics, the sensor can be used as a reference in control systems and their evaluation. The proposed sensor is based on a microcontroller with a real-time clock, inertial measurement sensors, geolocation and a vision sensor, that obtains the angle of incidence from the sunrays’ direction as well as the tilt and sensor position. The sensor’s characterization proved how a measurement of a focus error or a Sun position can be made, with an accuracy of 0.0426° and an uncertainty of 0.986%, which can be modified to reach an accuracy under 0.01°. The validation of this sensor was determined showing the focus error on one of the best commercial solar tracking systems, a Kipp & Zonen SOLYS 2. To conclude, the solar tracking sensor based on a vision system meets the Sun detection requirements and components that meet the accuracy conditions to be used in solar tracking systems and their evaluation or, as a tracking and orientation tool, on photovoltaic installations and solar collectors.

Enhanced MEMS SINS Aided Pipeline Surveying System by Pipeline Junction Detection in Small Diameter Pipeline

Pipeline is one of the most important tools to transport gases or liquid substances from the starting point to the destination. There are large numbers of small diameter pipelines under urban areas, which require to be inspected regularly to prevent their leakage. Pipeline Inspection Gauge (PIG) carries the pipeline defects detection sensors and localization sensors to discover the pipeline defects and the corresponding positions by its spiral motion inside the inspected pipeline. The low-accuracy property of Micro-Electro-Mechanical System (MEMS) based inertial sensors is the main limitation that influences the positioning precision of pipeline defects. This paper studies a method to enhance the positioning precision of MEMS Strap-down Inertial Navigation System (SINS) aided pipeline surveying system by pipeline junction detection to correct the azimuth and pitch errors induced PIG positioning error. The verification experiment results show that the positioning precision of MEMS SINS aided pipeline surveying system would improve about 54.42% after adding azimuth and pitch errors correction in each straight pipeline segment with the pipeline junction detection result.

Exploiting kinematic constraints to compensate magnetic disturbances when calculating joint angles of approximate hinge joints from orientation estimates of inertial sensors.

Inertial Measurement Units (IMUs) have become a widely used tool for rehabilitation and other application domains in which human motion is analyzed using an ambulatory or wearable setup. Since the magnetic field is inhomogeneous in indoor environments and in the proximity of ferromagnetic material, standard orientation estimation and joint angle calculation algorithms often lead to inaccurate or even completely wrong results. One approach to circumvent this is to exploit the kinematic constraint that is induced by mechanical hinge joints and also by approximate hinge joints such as the knee joint and the finger (interphalangeal) joints of the human body. We propose a quaternion-based method for joint angle measurement for approximate hinge joints moving through inhomogeneous magnetic fields. The method exploits the kinematic constraint to compensate the error that the magnetic disturbances induce in the IMU orientation estimates. This is achieved by realtime estimation and correction of the relative heading (azimuth) error that is caused by the disturbance. Since the kinematic constraint does not allow heading correction when the joint axis is vertical, we extend the proposed method such that it improves accuracy and robustness when the joint is close to that singularity. We evaluate the method by simulations of a quick hand motion and study the effect of inaccurate sensor-to-segment (anatomical) calibration and joint constraint relaxations. As a main result, the proposed method is found to reduce the root-mean-square error of the joint angle from 25.8° to 2.6° in the presence of large magnetic disturbances.

A Novel Method for Very-high Frequency Omni Range (VOR) Azimuth Error Correction using Kalman Filter for the Improvement of Aircraft Density

A Novel Method for Very-high Frequency Omni Range (VOR) Azimuth Error Correction using Kalman Filter for the Improvement of Aircraft Density

Multiple sound source localization using gammatone auditory filtering and direct sound componence detection

In order to research multiple sound source localization with room reverberation and background noise, we analyze the shortcomings of traditional broadband MUSIC and ordinary auditory filtering based broadband MUSIC method, then a new broadband MUSIC algorithm with gammatone auditory filtering of frequency component selection control and detection of ascending segment of direct sound componence is proposed. The proposed algorithm controls frequency component within the interested frequency band in multichannel bandpass filter stage. Detecting the direct sound componence of the sound source for suppressing room reverberation interference is also proposed, whose merits are fast calculation and avoiding using more complex de-reverberation processing algorithm. Besides, the pseudo-spectrum of different frequency channels is weighted by their maximum amplitude for every speech frame. Through the simulation and real room reverberation environment experiments, the proposed method has good performance. Dynamic multiple sound source localization experimental results indicate that the average absolute error of azimuth estimated by the proposed algorithm is less and the histogram result has higher angle resolution.

Generalised two target localisation using passive monopulse radar

The simultaneous lobing technique, also known as monopulse technique, has been widely used for fast target localisation and tracking purposes. Many works focused on accurately localising one or two targets lying within a narrow beam centred around the monopulse antenna boresight. In this study, a new approach is proposed, which uses the outputs of four antennas to rapidly localise two point targets present in the hemisphere. If both targets have the same elevation angle, the proposed scheme cannot detect them. To detect such targets, a second set of antennas is required. In this study, to detect two targets at generalised locations, the antenna array is divided into multiple overlapping sets each of four antennas. Two algorithms are proposed to combine the outputs from multiple sets and improve the detection performance. Simulation results show that the algorithm is able to localise both targets with <;2° mean square error in azimuth and elevation.

Error Estimation on Wander Frame for SINS Ground Alignment Through Observability Analysis

This paper presents a novel alignment method based on wander frame for SINS (strap down inertial navigation system) whose initial attitude information is completely unknown. During the course mode, the cosine and sine of the wander angle is defined as the filter states, and modeled as the velocity/position error in the geographic frame. Azimuth errorstate in the fine mode of the filter is defined as wander angle error to provide continuous estimation of navigation states. A systematic analysis of the Observability of a strap down inertial navigation system (SINS) in ground alignment with Bar-Itzhack and Berman’s error model is presented. It is shown that the unobservable states are separately contained in twode-coupled subspaces. The constraints on the selection of unobservable states are discussed. An estimation algorithm, which is derived fully from the horizontal velocity outputs for computing the misalignment angles, is provided. It reveals that the azimuth error can be entirely estimated from the estimates of leveling error and leveling error rate, without usinggyro output signals explicitly. This paper also, estimates the errors of a strap down inertial navigation systems by using appropriate Kalman filter design.

Maximum likelihood estimators and Cramér-Rao bound for estimating azimuth and elevation angles using compact arrays.

The problem of estimating the azimuth and elevation angle of a sound source using a compact array of hydrophones is addressed. The closed-form representations for several time-difference of arrival (TDOA) based estimators are given, and their accuracies are evaluated using both statistical simulations and in situ tests. Simulations demonstrated that the accuracy provided by the estimators is close to the Cramér-Rao bounds. In real conditions, the main cause of azimuth and elevation errors can be refraction, surface and bottom reflections and other unpredictable sound propagation effects resulting in large and slowly changing errors.