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Interferometric synthetic aperture radar (InSAR) processing techniques have been widely used to derive surface deformation or retrieve terrain elevation. Over the development of the past few decades, most research has mainly focused on its application, new techniques for improved accuracy, or the investigation of a particular error source and its correction method. Therefore, a thorough discussion about each error source and its influence on InSAR-derived products is rarely addressed. Additionally, InSAR is a challenging topic for beginners to learn due to the intricate mathematics and the necessary signal processing knowledge required to grasp the core concepts. This results in the fact that existing papers about InSAR are easy to understand for those with a technical background but difficult for those without. To cope with the two issues, this paper aims to provide an organized, comprehensive, and easily understandable review of the InSAR error budget. In order to assist readers of various backgrounds in comprehending the concepts, we describe the error sources in plain language, use the most fundamental math, offer clear examples, and exhibit numerical and visual comparisons. In this paper, InSAR-related errors are categorized as intrinsic height errors or location-induced errors. Intrinsic height errors are further divided into two subcategories (i.e., systematic and random error). These errors can result in an incorrect number of phase fringes and introduce unwanted phase noise into the output interferograms, respectively. Location-induced errors are the projection errors caused by the slant-ranging attribute of the SAR systems and include foreshortening, layover, and shadow effects. The main focus of this work is on systematic and random error, as well as their effects on InSAR-derived topographic and deformation products. Furthermore, because the effects of systematic and random errors are greatly dependent on radar wavelengths, different bands are utilized for comparison, including L-band, S-band, C-band, and X-band scenarios. As examples, we used the parameters of the upcoming NISAR operation to represent L-band and S-band, ERS-1 and Sentinel-1 to represent C-band, and TerraSAR-X to represent X-band. This paper seeks to bridge this knowledge gap by presenting an approachable exploration of InSAR error sources and their implications. This robust and accessible analysis of the InSAR error budget is especially pertinent as more SAR data products are made available (e.g., NISAR, ICEYE, Capella, Umbra, etc.) and the SAR user-base continues to expand. Finally, a commentary is offered to explore the error sources that were not included in this work, as well as to present our thoughts and conclusions.

The Integrated Multisatellite Retrievals for GPM (IMERG) is designed to derive precipitation by merging data from all the passive microwave (PMW) and infrared (IR) sensors. While the input source errors originating from the PMW and IR sensors are important, their structure, characteristics, and algorithm improvement remain unclear. Our study utilized a four-component error decomposition (4CED) method and a systematic and random error decomposition method to evaluate the detectability of IMERG dataset and identify the precipitation errors based on the multi-sensors. The 30 min data from 30 precipitation stations in the Tunxi Watershed were used to evaluate the IMERG data from 2018 to 2020. The input source includes five types of PMW sensors and IR instruments. The results show that the sample ratio for IR (Morph, IR + Morph, and IR only) is much higher than that for PMW (AMSR2, SSMIS, GMI, MHS, and ATMS), with a ratio of 72.8% for IR sources and a ratio of 27.2% for PMW sources. The high false ratio of the IR sensor leads to poor detectability performance of the false alarm ratio (FAR, 0.5854), critical success index (CSI, 0.3014), and Brier score (BS, 0.1126). As for the 4CED, Morph and Morph + IR have a large magnitude of high total bias (TB), hit overestimate bias (HOB), hit underestimate bias (HUB), false bias (FB), and miss bias (MB), which is related to the prediction ability and sample size. In addition, systematic error is the prominent component for AMSR2, SSMIS, GMI, and Morph + IR, indicating some inherent error (retrieval algorithm) that needs to be removed. These findings can support improving the retrieval algorithm and reducing errors in the IMERG dataset.

The TanDEM-X Digital Elevation Model (DEM) is limited by the radar side-view imaging mode, which still has gaps and anomalies that directly affect the application potential of the data. Many methods have been used to improve the accuracy of TanDEM-X DEM, but these algorithms primarily focus on eliminating systematic errors trending over a large area in the DEM, rather than random errors. Therefore, this paper presents the least-squares collocation-based error correction algorithm (LSC-TXC) for TanDEM-X DEM, which effectively eliminates both systematic and random errors, to enhance the accuracy of TanDEM-X DEM. The experimental results demonstrate that TanDEM-X DEM corrected by the LSC-TXC algorithm reduces the root mean square error (RMSE) from 6.141 m to 3.851 m, resulting in a significant improvement in accuracy (by 37.3%). Compared to three conventional algorithms, namely Random Forest, Height Difference Fitting Neural Network and Back Propagation in Neural Network, the presented algorithm demonstrates a reduction in the RMSEs of the corrected TanDEM-X DEMs by 6.5%, 7.6%, and 18.1%, respectively. This algorithm provides an efficient tool for correcting DEMs such as TanDEM-X for a wide range of areas.

The random error of fiber optic gyros is a critical factor affecting their measurement accuracy. However, the statistical characteristics of these errors exhibit time-varying properties, which degrade model fidelity and consequently impair the performance of random error suppression algorithms. To address these issues, this study first proposes a recursive dynamic Allan variance calculation method that effectively mitigates the poor real-time performance and spectral leakage inherent in conventional dynamic Allan variance techniques. Subsequently, the recursive dynamic Allan variance is integrated with the process variance estimation of Kalman filtering to construct a dual-adaptive Kalman filter capable of autonomously switching and adjusting between model parameters and noise variance. Finally, both static and dynamic validation experiments were conducted to evaluate the proposed method. The experimental results demonstrate that, compared to existing algorithms, the proposed approach significantly enhances the suppression of angular random walk errors in fiber optic gyros.

NOABSTRACTThe focus of this study was to determine the set-up errors so as to estimate the margin between the Clinical Target Volume (CTV) and the Planning Target Volume (PTV) and to suggest optimum margins for planning target volume (PTV) coverage in thorax cancers.In the present study data from 51 patients was incorporated. A total of 1308 portal images were examined. Set up errors were estimated by superimposing a digitally reconstructed radiograph (DRR), using an electronic portal image device (EPID) as a reference image. The Medio-Lateral (ML), Cranio-Caudal (CC), and Antero-Posterior (AP) directions were subsequently evaluated. According to the shifts obtained, systematic and random errors were computed. The van Herk formula was employed to determine the values for the clinical-to-planning target volume (CTV-PTV) margins.The systematic error was found to be between 1.0 mm and 1.7 mm, 1.0 mm and 1.8 mm, and 2.1 mm and 3.1 mm along the x, y, and z axis. In the x, y, and z axis, the random error varied from 0.5 mm to 0.7 mm, 0.4 mm to 0.8 mm, and 0.7 mm to 1.7 mm, respectively. Based on the Van Herk equation, the PTV margin following our findings was estimated to be 4.7 mm, 3.3 mm, 8.8 mm for lung, 3.6 mm, 2.7 mm, and 5.7 mm for oesophagus, and 3.0 mm, 4.9 mm, and 8.6 mm for breast in the x, y, and z dimensions respectively.This study demonstrates that an 8.8 mm extension of CTV to PTV margin for the lung, 5.7 mm for the oesophagus, and 8.6 mm for the breast, serving as an upper limit, is sufficient to guarantee that 90% of patients diagnosed with thoracic cancers will receive a cumulative CTV dose that is at least 95% of the prescribed dose.

Research and industrial studies have indicated that small size, low cost, high precision, and ease of integration are vital features that characterize microelectromechanical systems (MEMS) inertial sensors for mass production and diverse applications. In recent times, sensors like MEMS accelerometers and MEMS gyroscopes have been sought in an increased application range such as medical devices for health care to defense and military weapons. An important limitation of MEMS inertial sensors is repeatedly documented as the ease of being influenced by environmental noise from random sources, along with mechanical and electronic artifacts in the underlying systems, and other random noise. Thus, random error processing is essential for proper elimination of artifact signals and improvement of the accuracy and reliability from such sensors. In this paper, a systematic review is carried out by investigating different random error signal processing models that have been recently developed for MEMS inertial sensor precision improvement. For this purpose, an in-depth literature search was performed on several databases viz., Web of Science, IEEE Xplore, Science Direct, and Association for Computing Machinery Digital Library. Forty-nine representative papers that focused on the processing of signals from MEMS accelerometers, MEMS gyroscopes, and MEMS inertial measuring units, published in journal or conference formats, and indexed on the databases within the last 10 years, were downloaded and carefully reviewed. From this literature overview, 30 mainstream algorithms were extracted and categorized into seven groups, which were analyzed to present the contributions, strengths, and weaknesses of the literature. Additionally, a summary of the models developed in the studies was presented, along with their working principles viz., application domain, and the conclusions made in the studies. Finally, the development trend of MEMS inertial sensor technology and its application prospects were presented.

The Precision of radiotherapy is checked based on the matching of pre-treatment 2D portal imaging/CBCT to the reference image. The objective of this study is to find inter-fractional systematic and random setup errors (mm) for head and Neck cancer patients and also find setup margin for Planning Target Volume (PTV) at Mohan Dai Oswal Cancer Hospital Ludhiana Punjab. Inter-fractional motion errors were quantified for 10 Head and neck cancer patients who underwent image guided helical intensity modulated radiation therapy with Radixact X9 machine. One hundred fan beam computed tomography scans of 2mm slice thickness, 3.5 MV average energy and flattening filter free beam has been used to collect the data for the calculation of systematic and random errors. After patient immobilization, patient accuracy is checked with registration of pre-treatment image with reference planning image with the help of Accuray Precision image guidance protocol. For every patient 10 fan beam computed tomography images has been taken. Translational errors have been calculated in X, Y and Z direction to find systematic error (∑) and random error (σ). The final PTV margin is calculated by van Herk’s equation (2.5∑ + 0.7σ). The results of this study shows that mean translational errors varies from -2.3 mm to 3.3 mm in lateral direction (X), -3.6 mm to 1.7 mm in longitudinal direction (Y), -2.7 mm to 1.5 mm in vertical direction (Z). The mean and standard deviation (SD) for systematic errors are 1.467, 0.8, 0.923 and random error 0.0595, 0.02266, 0.03824 in X, Y and Z direction has been calculated. The Total Margin for CTV to PTV which include setup margin (mm) in X, Y and Z direction are 3.7 mm, 2.02 mm and 2.33 mm. In addition to that, a PTV margin of 5.00 mm is the appropriate margin for Mohan Dai Oswal Cancer Hospital’s patients. This work conclude that CTV to PTV margin of 5.00 mm is suitable for image guided helical intensity modulated radiation therapy for Head and neck patients to ensure the minimum 95% coverage of dose to target

Manufacturing errors of cable length, external node coordinates and tension force by the passive tension method are inevitable, which will inevitably affect the prestressing of cable bearing-grid structures, while existing studies lack the error analysis of error influences in this area. This paper proposes a method for analyzing random errors in constructing annular cable bearing-grid structures. An error control index and a normal distribution-based random error model, considering the impact of cable and ring beam length errors on cable force, were established afterwards. Taking the roof of the Qatar Education City Stadium as an example, the influence of the length errors of the radial cable, ring cable, and outer pressure ring beam on the structural cable force and stress level was analyzed, and the coupling error effect analysis was carried out. The results show that ring cable force and radial cable force are less affected by the length error of each other’s cables, while they are more affected by the length error of the outer ring beam. Stress levels exhibit greater sensitivity to outer ring beam errors compared to cable length errors. As the error limits of outer ring beam increase, radial and ring cable error ratios and outer ring beam stress errors also rise.

Background For accurate thoracic and abdominal radiotherapy, inter- and intrafractional geometrical uncertainties need to be considered to enable accurate margin sizes. We aim to quantify interfractional diaphragm and abdominal organ position variations, and intrafractional diaphragm motion in a large multicenter cohort of pediatric cancer patients (< 18 years). We investigated the correlation of interfractional position variations and intrafractional motion with age, and with general anesthesia (GA). Methods In 189 children (mean age 8.1; range 0.4–17.9 years) from six institutes, interfractional position variation of both hemidiaphragms, spleen, liver, left and right kidneys was quantified using a two-step registration. CBCTs were registered to the reference CT relative to the bony anatomy, followed by organ registration. We calculated the group mean, systematic and random errors (standard deviations Σ and σ, respectively) in cranial-caudal (CC), left-right and anterior-posterior directions. Intrafractional right hemidiaphragm motion was quantified using CBCTs on which the breathing amplitude, defined as the difference between end-inspiration and end-expiration peaks, was assessed (N = 79). We investigated correlations with age (Spearman’s ρ), and differences in motion between patients treated with and without GA (N = 75; all < 5.5 years). Results Interfractional group means were largest in CC direction and varied widely between patients, with largest variations in the right hemidiaphragm (range -13.0–17.5 mm). Interfractional group mean of the left kidney showed a borderline significant correlation with age (p = 0.047; ρ = 0.17). Intrafractional right hemidiaphragm motion in patients ≥ 5.5 years (mean 10.3 mm) was significantly larger compared to patients < 5.5 years treated without GA (mean 8.3 mm) (p = 0.02), with smaller Σ and σ values. We found a significant correlation between breathing amplitude and age (p < 0.001; ρ = 0.43). Interfractional right hemidiaphragm position variations were significantly smaller in patients < 5.5 years treated with GA than without GA (p = 0.004), but intrafractional motion showed no significant difference. Conclusion In this large multicenter cohort of children undergoing thoracic and abdominal radiotherapy, we found that interfractional position variation does not depend on age, but the use of GA in patients < 5.5 years showed smaller systematic and random errors. Furthermore, our results showed that breathing amplitude increases with age. Moreover, variations between patients advocate the need for a patient-specific margin approach.

In high-precision inertial navigation systems, suppressing the random errors of a fiber-optic gyroscope is of great importance. However, the traditional rule-based autoregressive moving average modeling method, when applied in Kalman filtering considering colored noise, presents inherent disadvantages in principle, including inaccurate state equations and difficulties in state dimension expansion. To this end, the noise characteristics in the fiber-optic gyroscope signal are first deeply analyzed, a random error model form is clarified, and a new model-order determination criterion is proposed to achieve the high-precision modeling of random errors. Then, based on the effective suppression of the angle random walk error of the fiber-optic gyroscope, and combined with the linear system equation of its colored noise, an adaptive Kalman filter based on noise-spectrum information decoupling is designed. This breaks through the principled limitations of traditional methods in suppressing colored noise and provides a scheme for modeling and suppressing fiber-optic gyroscope random errors under static conditions. Experimental results show that, compared with existing methods, the initial alignment accuracy of the proposed method based on 5 min data of fiber-strapdown inertial navigation is improved by an average of 48%.