Error Propagation Scheme Research Articles

Towards high‐definition vector map construction based on multi‐sensor integration for intelligent vehicles: Systems and error quantification

AbstractA lightweight, high‐definition vector map (HDVM) enables fully autonomous vehicles. However, the generation of HDVM remains a challenging problem, especially in complex urban scenarios. Moreover, numerous factors in the urban environment can degrade the accuracy of HDVM, necessitating a reliable error quantification. To address these challenges, this paper presents an open‐source and generic HDVM generation pipeline that integrates the global navigation satellite system (GNSS), inertial navigation system (INS), light detection and ranging (LiDAR), and camera. The pipeline begins by extracting semantic information from raw images using the Swin Transformer. The absolute 3D information of semantic objects is then retrieved using depth from the 3D LiDAR, and pose estimation from GNSS/INS integrated navigation system. Vector information (VI), such as lane lines, is extracted from the semantic information to construct the HDVM. To assess the potential error of the HDVM, this paper systematically quantifies the impacts of two key error sources, segmentation and LiDAR‐camera extrinsic parameter error. An error propagation scheme is first formed to illustrate how these errors fundamentally influence the accuracy of the HDVM. The effectiveness of the proposed pipeline is demonstrated through our codeavailable at https://github.com/ebhrz/HDMap. The performance is verified using typical datasets, including indoor garages and complex urban scenarios.

Conversion of Induced Polarization Data and Their Uncertainty from Time Domain to Frequency Domain Using Debye Decomposition

The time-domain (TD) induced polarization (IP) method is used as an extension of direct current (DC) resistivity measurements to capture information on the ability of the subsurface to develop electrical polarization. In the TD, the transient voltage decay is measured after the termination of the current injection. To invert tomographic TD IP data sets into frequency-domain (FD) models of complex electrical resistivity, a suitable approach for converting TD IP transients and their corresponding uncertainties into the FD is essential. To apply existing FD inversion algorithms to TD IP measurements, a conversion scheme must transform the measured decay curves into FD impedances and also propagate the corresponding measurement uncertainty from the TD to the FD. Here, we present such an approach based on a Debye decomposition (DD) of the decay curve into a relaxation-time distribution and the calculation of the equivalent spectrum. The corresponding FD data error can be obtained by applying error propagation through all of these steps. To accomplish the DD we implement a non-linear Gauss–Newton inversion scheme. We test the conversion scheme in a synthetic study and demonstrate its application to field data on a tomographic TD IP data set measured on the Maletoyvaemskoie ore field (Kamchatka, Russia). The proposed conversion scheme yields accurate impedance data for relaxation processes, which are resolved by the TD measurements. The error propagation scheme provides a reasonable FD uncertainty estimate, as confirmed by a Monte Carlo analysis of the underlying parameter distributions.

A map of African humid tropical forest aboveground biomass derived from management inventories

Forest biomass is key in Earth carbon cycle and climate system, and thus under intense scrutiny in the context of international climate change mitigation initiatives (e.g. REDD+). In tropical forests, the spatial distribution of aboveground biomass (AGB) remains, however, highly uncertain. There is increasing recognition that progress is strongly limited by the lack of field observations over large and remote areas. Here, we introduce the Congo basin Forests AGB (CoFor-AGB) dataset that contains AGB estimations and associated uncertainty for 59,857 1-km pixels aggregated from nearly 100,000 ha of in situ forest management inventories for the 2000 – early 2010s period in five central African countries. A comprehensive error propagation scheme suggests that the uncertainty on AGB estimations derived from c. 0.5-ha inventory plots (8.6–15.0%) is only moderately higher than the error obtained from scientific sampling plots (8.3%). CoFor-AGB provides the first large scale view of forest AGB spatial variation from field data in central Africa, the second largest continuous tropical forest domain of the world.

Subpixel Edge Localization Based on Adaptive Weighting of Gradients.

This paper presents a subpixel edge localization method based on the adaptive weighting of gradients (AWG). The method first finds the optimal power factors to be used by the AWG through an error propagation scheme. Then, with the goal of fast implementation of the method, a process that directly relates the edge width to the optimal powers is proposed. A method that uses the squared weighting of gradients (SWG) is also proposed, which applies a power of 2 to the gradients of an edge profile to calculate the edge location with subpixel accuracy. Next, an enhanced version of the AWG that combines the SWG and AWG selectively is proposed to obtain the best localization. At present, a fitting method based on the error function (Erf) is considered to be the most accurate method among current state-of-the-art methods, but it has a very high computational cost. The experimental results show that the proposed method is computationally much less expensive and more accurate than the Erf-fitting method.

Opcode vector: An efficient scheme to detect soft errors in instructions

Bit flips on instructions may affect the execution of the processor depending on the Instruction Set Architecture (ISA) and the location of the flipped bits. Intrinsically, ISAs may detect bit upsets if the errors on the instructions produce exceptions that halt the execution. In this paper, we explore a dynamic checking of the instructions to detect errors before execution. The scheme is based on loading an approximate representation of the instructions based on a vector that identifies the opcodes used in the program in a special purpose register. During execution, instructions are first checked on the register and on a negative an error is detected as the instruction has an opcode that does not correspond to any of the ones used in the program. Since we use an approximate representation, a small number of false positives can occur for erroneous instructions which may still be detected if they lead to a system crash. The proposed opcode vector scheme is compared with the use of a Bloom filter (BF) that has been previously proposed to detect errors on instructions. In both cases, a check can produce false positives but not false negatives. The Bloom filter is built using all the bits in the instruction. On the other hand, the opcode vector uses only a few bits of the instruction. In both cases, the check is combined with a previous error propagation scheme. In the opcode case, this ensures that all errors corrupt the opcode bits while for the BF, the error propagation reduces the number of false positives. The proposed approach has two main benefits. The first one is an increase in the error detection rate as the set of valid instructions is restricted to those used in the program allowing the detection of invalid instructions even if they do not lead to a system crash. The second one is that errors are detected before the crash. This is done at the cost of adding a small register for the vector of opcodes and some control logic. This is significantly simpler than in the case of the BF that needs to compute several hash functions and access several bits on the register to perform the check. We evaluated this approach on binary files of the ARM Cortex M0 core. According to our findings, the proposed vector of opcodes is more effective to detect errors than the BF and its detection rate is less dependent on the program size. Based on those results, it seems that the proposed method can be an interesting option to detect errors in instructions for systems on which a small overhead can be introduced if it improves reliability.

Accuracy improvement of volumetric error modeling in CNC machine tools

Three-axis structures are widely used as the main body of multi-axis CNC machine tools and coordinate measuring machines. As an open-loop mechanism, the cumulative effects of position-dependent/position-independent geometric errors of the moving axes cause significant volumetric deviation of the functional point. Such effect is more tangible for angular error motions, where they can considerably be magnified by long Abbe offsets. An appropriate volumetric error modeling approach should estimate the total effect of individual error motions accurately. Accuracy of the model depends on applied error propagation scheme and correctness of the error identification procedure. In this paper, both issues are investigated in order to enhance the practical validity of the model in presence of rigid-body and steady thermal assumptions. Regarding mechanical design of the sliding system, the linear axes are categorized in two different extruding type and sliding type with different error-mapping functions. Based on the homogeneous transformation matrix method, the overall consequence of error motions of each axis is calculated separately within entire working volume. The new approach explicitly contributes the axis design and structural configuration in error propagation procedure and facilitates the root cause identification for volumetric deviations of the functional point. The modeling scheme is verified experimentally on a three-axis CNC machine tool via comparison of the estimations with measured error values on circular and diagonal tool paths.

A quality assessment of the soil water index by the propagation of ASCAT soil moisture error estimates through an exponential filter

ABSTRACTSoil moisture data from remote-sensing measurements are used extensively and error characterization is critical in assessing their utility for specific applications. In hydrological monitoring and forecast applications, an estimate of the root-zone soil moisture is often required, and the exponential filter constitutes a common approach to obtaining a soil water index (SWI), i.e. the profile soil moisture from the remotely-sensed surface states. Advanced Scatterometer (ASCAT) surface soil moisture (SSM) time series include error estimates as ancillary data, however their effects are rarely considered in SWI computations. In this study, we introduced a simple error propagation scheme in parallel to exponential filter computation, aimed at estimating a SWI noise, which implicitly takes into account both errors and availability of the input SSM data actually used for each single SWI estimation. Integrating a control on SWI noise within quality check procedures was analysed by comparing in situ measurements available at different depths, up to 60 cm, for the period 2007–2014 in 10 stations located in Italy. The capacity of ASCAT-derived SWI to capture the same processes observed in the root-zone by in situ sensors, was evaluated by computing standard statistics (the correlation coefficient r and the root mean square difference [RMSD]) for different ‘a priori’ data masking procedures on SSM data, based on several indicators (processing flag, orbit direction, SSM noise) available for the ASCAT product. The effects of using the information contained in SSM noise and in the proposed SWI noise were also investigated. Removing data according to ‘a posteriori’ control on SWI noise rather than a priori masking SSM data, with the exponential filter T value and the percentage of removed data being equal, was found to generally improve the statistics of the resulting SWI time series. In addition, evaluating T on the SWI time series screened according to the SWI noise, outperforms other approaches analysed in almost every test case.

Phase Estimation for Distributed Scatterers in InSAR Stacks Using Integer Least Squares Estimation

In recent years, new algorithms have been proposed to retrieve maximum available information in synthetic aperture radar (SAR) interferometric stacks with focus on distributed scatterers. The key step in these algorithms is to optimally estimate single-master (SM) wrapped phases for each pixel from all possible interferometric combinations, preserving useful information and filtering noise. In this paper, we propose a new method for SM-phase estimation based on the integer least squares principle. We model the SM-phase estimation problem in a linear form by introducing additional integer ambiguities and use a bootstrap estimator for joint estimation of SM-phases and the integer unknowns. In addition, a full error propagation scheme is introduced in order to evaluate the precision of the final SM-phase estimates. The main advantages of the proposed method are the flexibility to be applied on any (connected) subset of interferograms and the quality description via the provision of a full covariance matrix of the estimates. Results from both synthetic experiments and a case study over the Torfajokull volcano in Iceland demonstrate that the proposed method can efficiently filter noise from wrapped multibaseline interferometric stacks, resulting in doubling the number of detected coherent pixels with respect to conventional persistent scatterer interferometry.

Calibration of 3-D wind measurements on a single-engine research aircraft

Abstract. An innovative calibration method for the wind speed measurement using a boom-mounted Rosemount model 858 AJ air velocity probe is introduced. The method is demonstrated for a sensor system installed on a medium-size research aircraft which is used for measurements in the atmospheric boundary layer. The method encounters a series of coordinated flight manoeuvres to directly estimate the aerodynamic influences on the probe and to calculate the measurement uncertainties. The introduction of a differential Global Positioning System (DGPS) combined with a high-accuracy inertial reference system (IRS) has brought major advances to airborne measurement techniques. The exact determination of geometrical height allows the use of the pressure signal as an independent parameter. Furthermore, the exact height information and the stepwise calibration process lead to maximum accuracy. The results show a measurement uncertainty for the aerodynamic influence of the dynamic and static pressures of 0.1 hPa. The applied parametrisation does not require any height dependencies or time shifts. After extensive flight tests a correction for the flow angles (attack and sideslip angles) was found, which is necessary for a successful wind calculation. A new method is demonstrated to correct for the aerodynamic influence on the sideslip angle. For the three-dimensional (3-D) wind vector (with 100 Hz resolution) a novel error propagation scheme is tested, which determines the measurement uncertainties to be 0.3 m s−1 for the horizontal and 0.2 m s−1 for the vertical wind components.

Uncertainties in Plot‐Scale Mass Balance Measurements Using Aeolian Sediment Traps

Modified Wilson and Cooke (MWAC) sediment catchers are commonly used for quantifying aeolian sediment transport in the saltation layer. The accuracy of aeolian mass flux and mass balance estimates using MWAC catchers has, however, not been reported in detail so far. By combining analytical error propagation equations and Monte Carlo simulation, this study tested a random error propagation scheme that incorporates six sources of uncertainty: sediment mass, MWAC inlet diameter, vertical position of the catchers, trapping efficiency, horizontal spacing between catcher arrays, and wind direction. For a weighing uncertainty of 0.01 g, the relative uncertainty in the cumulative mass flux of sediment reached up to 140%, but this generally affected only the highest catchers. The relative error in the measured unit mass transport was much less, ranging between 2 and 20%, with an average of 10%. The relative uncertainty in the corrected cumulative unit sediment mass transport, however, was found to be 32%, on average, because of the high relative uncertainty in the trapping efficiency of 31%. The relative uncertainty in the plot‐scale mass balances ranged between 32 and 80%. Uncertainty in the trapping efficiency and the measured unit mass transport contributed most to the mass balance uncertainty, but the uncertainty in the wind direction sometimes also contributed substantially. The high uncertainties that potentially affect the sediment mass transport and mass balances highlight the need for their systematic reporting in future studies. We also investigated possible pathways for reducing the uncertainty.