High Relative Accuracy Research Articles

Improving UAV-SfM time-series accuracy by co-alignment and contributions of ground control or RTK positioning

Unmanned Aerial Vehicle Structure from Motion (UAV-SfM) photogrammetry is increasingly applied to topographic change detection, which requires multitemporal Digital Surface Models (DSMs) with high relative accuracy. Of these tools, Ground Control Points (GCPs) and an image processing method called co-alignment have so far shown promising results for change detection studies. However, there is still insufficient research on the extent of improving 3D model accuracy by combining these tools. In our study we assess absolute and relative accuracy of 120 DSMs generated through 24 workflows of UAV-SfM photogrammetry. Surveys were acquired with two different UAVs with Real Time Kinematic (RTK) or generic Global Navigation Satellite System (GNSS) positioning, and processed with varying combinations of survey co-alignment and GCPs. We show that co-alignment reduces relative errors to below 2 cm regardless of positioning quality. A single RTK survey in a co-aligned project is sufficient to obtain high absolute xy accuracy, but GCPs for at least one survey are still required to reduce absolute z error. We demonstrate that co-aligning RTK surveys with generic GNSS surveys results in RTK class accuracy for all surveys, even when mixed sensor grades are used. Our findings enable high-accuracy change detection with lower accuracy archived images when combined with RTK surveys. For future UAV-SfM change detection studies, we recommend to apply co-alignment for all studies, and where possible to include GCPs and RTK image coordinates in one survey to optimize absolute accuracy. Collecting and digitizing GCPs in multiple surveys has shown little additional benefit when co-alignment is applied and therefore may be omitted to save time, especially in challenging field conditions.

Accurate computations with Wronskian matrices of Bessel and Laguerre polynomials

This paper provides an accurate method to obtain the bidiagonal factorization of Wronskian matrices of Bessel polynomials and of Laguerre polynomials. This method can be used to compute with high relative accuracy their singular values, the inverse of these matrices, as well as the solution of some related systems of linear equations. Numerical examples illustrating the theoretical results are included.

Experimental Bayesian estimation of quantum state preparation, measurement, and gate errors in multiqubit devices

We introduce a Bayesian method for the estimation of single qubit errors in quantum devices, and use it to characterize these errors on three 27-qubit superconducting qubit devices. We self-consistently estimate up to seven parameters of each qubit's state preparation, readout, and gate errors, analyze the stability of these errors as a function of time, and demonstrate easily implemented approaches for mitigating different errors before a quantum computation experiment. On the investigated devices we find non-negligible qubit reset errors that cannot be parametrized as a diagonal mixed state, but manifest as a coherent phase of a superposition with a small contribution from the qubit's excited state. We are able to mitigate such errors by applying pre-rotations on the initialized qubits, which we demonstrate with multi-qubit entangled states. Our results demonstrate that Bayesian estimation can resolve small parameters - including those pertaining to quantum gate errors - with a high relative accuracy, at a lower measurement cost as compared with standard characterization approaches.

Generation of Large-Scale Orthophoto Mosaics Using MEX HRSC Images for the Candidate Landing Regions of China’s First Mars Mission

Planetary mapping products play a significant role in landing site selection, surface operations, and scientific investigations. This paper describes the techniques and processes used to create geometrically controlled image mosaics for the candidate landing regions of China’s first Mars exploration mission (i.e., Tianwen-1) using Mars Express (MEX) High-Resolution Stereo Camera (HRSC) images. In order to deal with the extremely complex situations due to large data volumes (hundreds of images), various imaging conditions (e.g., 5–80° incidence angles), and long time spans (>10 years), we developed corresponding methods and in-house software for the photogrammetric processing of MEX HRSC images. According to the characteristics of planetary images and multi-line pushbroom imaging, we optimized the algorithms of establishing control network, eliminating blunders, setting weights and processing abnormal images. The generated MEX HRSC image mosaics with a resolution of 12.5 m delivered a high relative accuracy (<1 pixel). Compared with the existing Mars global image mosaics, the generated image mosaics exhibit significantly better spatial resolution. The techniques and methods that we developed to solve the complicated photogrammetric processing problems can also be applied to produce global or large-scale Mars mapping products using existing and new returned orbital images.

Computing eigenvalues of quasi-generalized Vandermonde matrices to high relative accuracy

In this paper, the eigenvalue problem for the class of quasi-generalized Vandermonde (q-gV) matrices is considered. In order to parameterize q-gV matrices, the explicit expressions of minors of such matrices are presented. We develop an algorithm to accurately compute the parameterization for q-gV matrices. Relying on the accurate parameterization, all the eigenvalues of q-gV matrices are computed to high relative accuracy. Error analysis and numerical experiments are provided to confirm the high relative accuracy.

Accurate and efficient computations with Wronskian matrices of Bernstein and related bases

AbstractIn this article, we provide a bidiagonal decomposition of the Wronskian matrices of Bernstein bases of polynomials and other related bases such as the Bernstein basis of negative degree or the negative binomial basis. The mentioned bidiagonal decompositions are used to achieve algebraic computations with high relative accuracy for these Wronskian matrices. The numerical experiments illustrate the accuracy obtained using the proposed decomposition when computing inverse matrices, eigenvalues or singular values, and the solution of some related linear systems.

Computing eigenvalues of quasi‐rational Bernstein–Vandermonde matrices to high relative accuracy

AbstractIn this article, we consider how to accurately solve the eigenvalue problem for a class of quasi‐rational Bernstein–Vandermonde (q‐RBV) matrices. This class of matrices belongs to generalized sign regular matrices with signature . An algorithm is developed to accurately compute the parameter matrix for q‐RBV matrices. Based on the parameter matrix, all the eigenvalues of q‐RBV matrices have been computed to high relative accuracy. The perturbation theory for the eigenvalues of q‐RBV matrices and the error analysis of our proposed algorithm are provided. Numerical experiments are performed to confirm the claimed high relative accuracy.

Semi-analytical assessment of the relative accuracy of the GNSS/INS in railway track irregularity measurements

An aided Inertial Navigation System (INS) is increasingly exploited in precise engineering surveying, such as railway track irregularity measurement, where a high relative measurement accuracy rather than absolute accuracy is emphasized. However, how to evaluate the relative measurement accuracy of the aided INS has rarely been studied. We address this problem with a semi-analytical method to analyze the relative measurement error propagation of the Global Navigation Satellite System (GNSS) and INS integrated system, specifically for the railway track irregularity measurement application. The GNSS/INS integration in this application is simplified as a linear time-invariant stochastic system driven only by white Gaussian noise, and an analytical solution for the navigation errors in the Laplace domain is obtained by analyzing the resulting steady-state Kalman filter. Then, a time series of the error is obtained through a subsequent Monte Carlo simulation based on the derived error propagation model. The proposed analysis method is then validated through data simulation and field tests. The results indicate that a 1 mm accuracy in measuring the track irregularity is achievable for the GNSS/INS integrated system. Meanwhile, the influences of the dominant inertial sensor errors on the final measurement accuracy are analyzed quantitatively and discussed comprehensively.

Variable Coefficient Terminal-Phase Guidance Design for Deep Space High-Speed Impact

Asteroid impact poses a major threat to human survival. High-speed direct impact is a feasible and effective means to change the orbit of an asteroid. This paper takes Bennu, a potentially hazardous asteroid , as object to design the terminal guidance law of deep space high-speed impact. In view of the characteristics of high relative speed and high impact accuracy, the acceleration command is derived based on the Augmented Proportional Navigation Guidance law (APNG), considering the acceleration of the target. Moreover, the proportional coefficient is designed as a function of the relative distance to meet both the requirements of reducing fuel consumption and improving impact accuracy. An ignition strategy is designed to convert the continuous command into impulse command, without the need to give maneuvering time in advance. The simulation results show the effectiveness of the proposed algorithm. The miss distance constraint is satisfied, and the ignition times and fuel consumption are less than those of the constant proportional coefficient algorithm.

Accurate determinants of some classes of matrices

We present parametrizations of B-matrices, Nekrasov matrices and B-Nekrasov matrices that allow us to compute their determinants with high relative accuracy. Numerical examples confirm the accuracy of the method.

Accurate Computations with Collocation and Wronskian Matrices of Jacobi Polynomials

In this paper an accurate method to construct the bidiagonal factorization of collocation and Wronskian matrices of Jacobi polynomials is obtained and used to compute with high relative accuracy their eigenvalues, singular values and inverses. The particular cases of collocation and Wronskian matrices of Legendre polynomials, Gegenbauer polynomials, Chebyshev polynomials of the first and second kind and rational Jacobi polynomials are considered. Numerical examples are included.

High relative accuracy with matrices of q‐integers

AbstractThis article shows that the bidiagonal decomposition of many important matrices of q‐integers can be constructed to high relative accuracy (HRA). This fact can be used to compute with HRA the eigenvalues, singular values, and inverses of these matrices. These results can be applied to collocation matrices of q‐Laguerre polynomials, q‐Pascal matrices, and matrices formed by q‐Stirling numbers. Numerical examples illustrate the theoretical results.

Ga-modified YAG:Pr3+ dual-mode tunable luminescence thermometers

• Dual-mode thermometry is executed in YAG:Pr 3+ -YGG:Pr 3+ systems. • Bandgap engineering allows enhancing the performance of the thermometers. • YAG:Pr-YGG:Pr present manageable high relative sensitivity and high accuracy. • Garnet-based luminescence thermometers work effectively in the range 17–700 K. • Relative temperature errors are calculated and compared for all the garnets. The temperature determination using luminescent materials is nowadays considered the perspective remote technique for temperature gauging, despite the few examples reported so far combining wide operating temperature range with satisfying relative thermal sensitivity and temperature uncertainty values. In this paper, we study the Y 3 (Al,Ga) 5 O 12 :0.1%Pr phosphors with controlled Ga:Al composition to deliberately affect their luminescent properties. We demonstrate that the energy barrier for thermal quenching of the 5d-4f luminescence can be effectively tailored, yielding the fine tune of the thermometric parameters of these phosphors. By exploiting time-resolved and time-integrated approaches we show that the thermometers can cover the 17–700 K temperature range with a maximum relative sensitivity up to 3.6%·K −1 and a temperature uncertainty as lower as 0.02 K. For each sample, the temperature readout of the distinct thermometric parameters is compared illustrating that the performance of the thermometers should also consider the relative temperature error between the calculated and the measured temperatures, besides relative thermal sensitivity and temperature uncertainty.

Accurate computations of eigenvalues of quasi-Cauchy-Vandermonde matrices

In this paper, we consider the eigenvalue problem for the class of quasi-Cauchy-Vandermonde (qCV) matrices belonging to the class of generalized sign regular matrices with signature (1,…,1,−1). We present the explicit expressions of minors of qCV matrices. An algorithm is designed to accurately compute the parameterization matrix for qCV matrices. Based on the parameterization matrix, all the eigenvalues of such matrices are computed to high relative accuracy. Error analysis and numerical experiments are presented to confirm the high relative accuracy.

Characterizations and accurate computations for tridiagonal Toeplitz matrices

ABSTRACT Tridiagonal Toeplitz P-matrices, M-matrices and totally positive matrices are characterized. For some classes of tridiagonal matrices and tridiagonal Toeplitz matrices, it is shown that many algebraic computations can be performed with high relative accuracy.

Accurate bidiagonal decomposition and computations with generalized Pascal matrices

This paper provides an accurate method to obtain the bidiagonal factorization of many generalized Pascal matrices, which in turn can be used to compute with high relative accuracy the eigenvalues, singular values and inverses of these matrices. Numerical examples are included.

EVALUACIÓN DE PRODUCTOS FOTOGRAMÉTRICOS DE UNA UNIDAD KÁRSTICA OBTENIDOS CON UN DRON

&lt;p&gt;&lt;strong&gt;Background&lt;/strong&gt;. The rapid technological development of drones has been used in different disciplines as a new tool for the collection of geospatial data. Depending on the application of geospatial data, users may not require high absolute precision and therefore the measurement error within the model (relative precision) may be more important. &lt;strong&gt;Objective&lt;/strong&gt;. To determine the root mean square error and the relative precision of the orthomosaics and digital elevation models at different heights generated with the SfM photogrammetric technique and a drone, over a sinkhole located in the Cenote Ring in the state of Yucatán. &lt;strong&gt;Methodology&lt;/strong&gt;. Aerial images were acquired with a DJI Phantom 4 drone over a sinkhole at two heights, 80 and 100 m. Subsequently, the aerial images were processed obtaining digital elevation models (DEM) and orthomosaic with which the root mean squared error (RMSE) of the UTM coordinates (x, y) and elevations (z) was calculated. Finally, the relative precision was calculated by comparing the measurements in the field with those obtained in the DEMs and orthomosaics. &lt;strong&gt;Results&lt;/strong&gt;. Flights at 100 m altitude showed the least variation in coordinates and elevations compared to flights at 80 m. The highest relative precision was recorded at 100 m high in the orthomosaics and ranged from 0.03 to 0.36 m with an average value of 0.22 m. &lt;strong&gt;Implications&lt;/strong&gt;. With these results we can affirm that it is possible to carry out studies without control points in applications where a consistent and centimeter precision is not required. &lt;strong&gt;Conclusion&lt;/strong&gt;. The 100 m high flights had the lowest RMSE and the highest relative accuracy.&lt;/p&gt;

Rapid detection of Clostridium perfringens in food by loop-mediated isothermal amplification combined with a lateral flow biosensor.

Clostridium perfringens is a key anaerobic pathogen causing food poisoning. Definitive detection by standard culture method is time-consuming and labor intensive. Current rapid commercial test kits are prohibitively expensive. It is thus necessary to develop rapid and cost-effective detection tool. Here, loop-mediated isothermal amplification (LAMP) in combination with a lateral-flow biosensor (LFB) was developed for visual inspection of C. perfringens-specific cpa gene. The specificity of the developed test was evaluated against 40 C. perfringens and 35 other bacterial strains, which showed no cross-reactivity, indicating 100% inclusivity and exclusivity. LAMP-LFB detection limit for artificially contaminated samples after enrichment for 16 h was 1–10 CFU/g sample, which was comparable to the commercial real-time PCR kit. The detection performance of LAMP-LFB was also compared to culture-based method using 95 food samples, which revealed the sensitivity (SE), specificity (SP) and Cohen's kappa coefficient (κ) of 88.0% (95% CI, 75.6%-95.4%), 95.5% (95% CI, 84.8%-99.4%) and 0.832 (95% CI, 0.721–0.943), respectively. Area under the receiver operating characteristic (ROC) curve was 0.918 (95% CI, 0.854–0.981), indicating LAMP-LFB as high relative accuracy test. In conclusion, LAMP-LFB assay is a low-cost qualitative method and easily available for routine detection of C. perfringens in food samples, which could serve as an alternative to commercial test kit.

Accurate solutions of structured generalized Kronecker product linear systems

In this paper, we consider the generalized Kronecker product (GKP) linear system associated with a class of consecutive-rank-descending (CRD) matrices arising from bivariate interpolation problems. Relying on the sign sequences of CRD matrices, we show that the associated GKP linear system is accurately solved with an “ideal” componentwise forward error. In particular, a pleasantly small componentwise relative forward error is provided to illustrate that each component of the solution is computed to high relative accuracy. We then present the sign sequences of generalized Vandermonde matrices to show that the associated GKP linear system is accurately solved with the desired componentwise forward errors. Numerical experiments are performed to confirm the high relative accuracy.

Accurate Numerical Solution for Shifted M-Matrix Algebraic Riccati Equations

An algebraic Riccati equation (are) is called a shifted M-matrix algebraic Riccati equation (mare) if it can be turned into an mare after its matrix variable is partially shifted by a diagonal matrix. Such an are can arise from computing the invariant density of a Markov modulated Brownian motion. Sufficient and necessary conditions for an are to be a shifted mare are obtained. Based on the conditions, a highly accurate implementation of the alternating directional doubling algorithm (adda) is established to compute the extremal solution of a shifted mare, as well as a quantity needed for computing the invariant density in the application, with high entrywise relative accuracy. Numerical examples are presented to demonstrate the theory and algorithms.