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Consumer-grade range cameras such as the Kinect sensor have the potential to be used in mapping applications where accuracy requirements are less strict. To realize this potential insight into the geometric quality of the data acquired by the sensor is essential. In this paper we discuss the calibration of the Kinect sensor, and provide an analysis of the accuracy and resolution of its depth data. Based on a mathematical model of depth measurement from disparity a theoretical error analysis is presented, which provides an insight into the factors influencing the accuracy of the data. Experimental results show that the random error of depth measurement increases with increasing distance to the sensor, and ranges from a few millimeters up to about 4 cm at the maximum range of the sensor. The quality of the data is also found to be influenced by the low resolution of the depth measurements.

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 Surface Water and Ocean Topography (SWOT) mission will be affected by various sources of systematic errors, which are correlated in space and in time. Their amplitude before calibration might be as large as tens of centimeters, i.e., able to dominate the mission error budget. To reduce their magnitude, we developed so-called data-driven (or empirical) calibration algorithms. This paper provided a summary of the overall problem, and then presented the calibration framework used for SWOT, as well as the pre-launch performance simulations. We presented two complete algorithm sequences that use ocean measurements to calibrate KaRIN globally. The simple and robust Level-2 algorithm was implemented in the ground segment to control the main source of error of SWOT’s hydrology products. In contrast, the more sophisticated Level-3 (multi-mission) algorithm was developed to improve the accuracy of ocean products, as well as the one-day orbit of the SWOT mission. The Level-2 algorithm yielded a mean inland error of 3–6 cm, i.e., a margin of 25–80% (of the signal variance) with respect to the error budget requirements. The Level-3 algorithm yielded ocean residuals of 1 cm, i.e., a variance reduction of 60–80% with respect to the Level-2 algorithm.

The aim of the new generation of Global Geodetic Observing System is a millimeter-level accuracy in positioning, with a crucial role to be played by Global Navigation Satellites Systems (GNSS) in the Precise Point Positioning (PPP) mode. This is of course because GNSS constellations and receivers provide an efficient stand-alone technique with a homogeneous performance over large areas (positions, navigation and meteorology) when used in conjunction with the PPP mode, with also an ever-increasing data flow and different satellite line-of-sights. The requirement of accuracies reaching the millimeter or sub-millimeter implies a knowledge at this level of each line in the GNSS-PPP error budget, including, but not restricted to: clock biases, troposphere and ionosphere delays, multipath and ground deformations. In this review study, we consider this millimeter-/submillimeter level GNSS-PPP error budget, and possible mitigations and improvements in the frame of the existing global constellations: GPS, Galileo, GLONASS and BDS, in view of augmented constellations and/or Low Earth Orbit constellations, which will be available in the near future. We also pay a special attention to systematic biases that can/could exist between constellations.

Machining accuracy reliability is considered to be one of the most important indexes in the process of performance evaluation and optimization design of the machine tools. Geometric errors, thermal errors and tool wear are the main factors to affect the machining accuracy and so affect the machining accuracy reliability of machine tools. This paper proposed a geometric error budget method that simultaneously considers geometric errors, thermal errors and tool wear to improve the machining accuracy reliability of machine tools. Homogeneous transformation matrices, neural fuzzy control theory and a tool wear predictive approach were employed to develop a comprehensive error model, which shows the influence of the geometric, thermal errors and tool wear to the machining accuracy of a machine tool. Based on Rackwite–Fiessler and Advanced First Order and Second Moment, a reliability model and a sensitivity model were put forward, which can deal with the errors of a machine tool drawn from any distribution. Then, a geometric error budget method of multi-axis NC machine tool was developed and formed into a mathematical model. In such method, the minimum cost of machine tool was the optimization objective, the reliability of the machining accuracy was the constraint, and the sensitivity was to identify the geometric errors to be optimized. An example conducted on a five-axis NC machine tool was used to explain and validate the proposed method.

Underwater photogrammetry is increasingly being used by marine ecologists because of its ability to produce accurate, spatially detailed, non-destructive measurements of benthic communities, coupled with affordability and ease of use. However, independent quality control, rigorous imaging system set-up, optimal geometry design and a strict modeling of the imaging process are essential to achieving a high degree of measurable accuracy and resolution. If a proper photogrammetric approach that enables the formal description of the propagation of measurement error and modeling uncertainties is not undertaken, statements regarding the statistical significance of the results are limited. In this paper, we tackle these critical topics, based on the experience gained in the Moorea Island Digital Ecosystem Avatar (IDEA) project, where we have developed a rigorous underwater photogrammetric pipeline for coral reef monitoring and change detection. Here, we discuss the need for a permanent, underwater geodetic network, which serves to define a temporally stable reference datum and a check for the time series of photogrammetrically derived three-dimensional (3D) models of the reef structure. We present a methodology to evaluate the suitability of several underwater camera systems for photogrammetric and multi-temporal monitoring purposes and stress the importance of camera network geometry to minimize the deformations of photogrammetrically derived 3D reef models. Finally, we incorporate the measurement and modeling uncertainties of the full photogrammetric process into a simple and flexible framework for detecting statistically significant changes among a time series of models.

The selection of an appropriate measurement system for an inertial navigation system requires an analysis of the impact of sensor errors on the position and orientation determination accuracy to ensure that the selected solution is cost-effective and complies with the requirements. In the current literature, this problem is solved based on the navigation duration only by considering the time-dependent errors due to sensor bias and random walk parameters or by conducting numerous simulations. In the former case, oversimplifying the analysis will not allow accurate values to be determined, while the latter method does not provide direct insight into the emerging dependencies. In contrast, this article introduces an analytic approach with a detailed model. This article presents general formulas, also written in detail for the measurement system model adopted and various manoeuvres. Although general equations are complicated, the use of piecewise constant motion variables allow us to discern fragments of equations corresponding to individual error sources. The results confirm the effect the carouseling has on the reduction of navigation errors. The general formulas presented extend the potential to analyse the influence of the entire host vehicle motion, while the detailed formulas make dependencies between motion and navigational errors evident.

This paper describes a calibration technique aimed at combined estimation of onboard and external magnetic disturbances for small Unmanned Aerial Systems (UAS). In particular, the objective is to estimate the onboard horizontal bias components and the external magnetic declination, thus improving heading estimation accuracy. This result is important to support flight autonomy, even in environments characterized by significant magnetic disturbances. Moreover, in general, more accurate attitude estimates provide benefits for georeferencing and mapping applications. The approach exploits cooperation with one or more “deputy” UAVs and combines drone-to-drone carrier phase differential GNSS and visual measurements to attain magnetic-independent attitude information. Specifically, visual and GNSS information is acquired at different heading angles, and bias estimation is modelled as a non-linear least squares problem solved by means of the Levenberg–Marquardt method. An analytical error budget is derived to predict the achievable accuracy. The method is then demonstrated in flight using two customized quadrotors. A pointing analysis based on ground and airborne control points demonstrates that the calibrated heading estimate allows obtaining an angular error below 1°, thus resulting in a substantial improvement against the use of either the non-calibrated magnetic heading or the multi-sensor-based solution of the DJI onboard navigation filter, which determine angular errors of the order of several degrees.

Several organizations, including NASA and the European Space Agency, have initiated plans for establishing lunar navigation satellite systems (LNSSs). This effort is driven by surging interest in the Moon as a platform for scientific discovery and staging area for future missions beyond Earth orbit. Near-Earth missions benefit from GNSSs, which have been refined over decades and are capable of real-time, sub-meter level positioning. For GNSS systems, the navigation community and managing organizations, such as the U.S. Department of Defense (in the case of GPS), have precisely characterized the error sources inherent in pseudorange and range-rate measurements in Earth’s vicinity. Here, we draw parallels between errors in current GNSSs and those expected in future cislunar navigation systems. We identify key differences between the terrestrial and lunar environments and propose methods to accurately quantify the resulting measurement errors. Specifically, we develop techniques for constructing a time-varying error budget for pseudorange and pseudorange-rate measurements near the Moon and then test these techniques using arbitrary system and signal configurations.

The HyperSpectral Imager for Climate Science (HySICS) is the core instrument of the Climate Absolute Refractivity and Reflectance Observatory (CLARREO) Pathfinder (CPF) mission and is currently scheduled to be launched to the International Space Station (ISS) in 2023. HySICS is an Offner–Chrisp imaging spectrometer designed to meet an unprecedented radiometric uncertainty requirement of 0.3% (k = 1) over its entire spectral range of 350–2300 nm. The approach represents the need for significant improvement over the Radiometric Calibration (RadCal) of existing space-borne spectrometers. One strategy to demonstrate that HySICS achieves this level of accuracy is through an Independent Calibration (IndCal) effort that can provide an alternative referencing RadCal, which follows a traceability chain independent of the operational RadCal of ratioing approach. The IndCal relies on a pre-launch detector-based absolute RadCal of HySICS, using a tunable laser system as source, and the system planned for the HySICS absolute RadCal is the Goddard Laser for Absolute Measurement of Radiance (GLAMR). GLAMR was developed at NASA’s Goddard Space Flight Center and has been used to calibrate multiple operational remote sensing instruments, as well as the SOlar, Lunar Absolute Reflectance Imaging Spectroradiometer (SOLARIS), a calibration demonstration system developed for the CLARREO mission. In this work, the data of SOLARIS GLAMR RadCal conducted in 2019 are processed to derive the Absolute Spectral Response (ASR) functions and other key characterization parameters of SOLARIS detectors. The results are further analyzed with the goals to plan the HySICS GLAMR RadCal, in particular to optimize its configuration, to demonstrate the traceability route to the NIST standard, and to develop the error budget of the calibration approach. The SOLARIS calibration is also compared with other source- and detector-based calibrations to validate the absolute radiometric accuracy achieved.