Simple Error Model Research Articles

Simple linear functional Errors–In–Variables models with correlated errors

This paper establishes a new estimator for simple linear measurement error models with correlated errors. Under a small-noise asymptotic regime and using perturbation theory, an unbiased estimator has been developed. The consistency and the asymptotic normality of the new estimator have been established and then validated by using synthetic data. Moreover, the confidence intervals of the slope have been revisited. Simulation results show that our estimator is certainly the most stable of existing methods and its performance exceeds that of other existing methods in terms of coverage and interval length.

Realization of quantum signal processing on a noisy quantum computer

Quantum signal processing (QSP) is a powerful toolbox for the design of quantum algorithms and can lead to asymptotically optimal computational costs. Its realization on noisy quantum computers without fault tolerance, however, is challenging because it requires a deep quantum circuit in general. We propose a strategy to run an entire QSP protocol on noisy quantum hardware by carefully reducing overhead costs at each step. To illustrate the approach, we consider the application of Hamiltonian simulation for which QSP implements a polynomial approximation of the time evolution operator. We test the protocol by running the algorithm on the Quantinuum H1-1 trapped-ion quantum computer powered by Honeywell. In particular, we compute the time dependence of bipartite entanglement entropies for Ising spin chains and find good agreements with exact numerical simulations. To make the best use of the device, we determine optimal experimental parameters by using a simplified error model for the hardware and numerically studying the trade-off between Hamiltonian simulation time, polynomial degree, and total accuracy. Our results are the first step in the experimental realization of QSP-based quantum algorithms.

A flexible calibration method with multi-stage optimization for the axial error of mobile mapping systems

Mobile mapping systems, which are equipped with a laser scanner, panoramic camera, and inertial navigation system, can flexibly and efficiently obtain precision point clouds. However, these systems require re-installation for each mission, which causes displacement errors in the instruments, resulting in discrepancies between multiple collections of data. The existing calibration methods usually require additional control targets settled in a managed field survey. Furthermore, the point clouds obtained with mobile mapping systems do not follow the common assumption of rigid transformation. To alleviate the above problems, we propose a flexible in-situ calibration method that only requires data collected in a round-trip survey pattern and conducts a self-calibration of the placement parameters with meticulously designed exact point matching. Specifically, because the accuracy of the existing feature-based registration method is not sufficient to acquire the exact correspondences of point clouds and to prune the outliers in correspondence searching. We propose novel pruning and refining approaches to obtain exact point-to-point correspondences between the round-trip point clouds. From systematic analyses of the coupling between different factors, we then construct a simplified error model that takes into account the a priori rotation- and translation-weighted observations. Finally, to alleviate the correlation effects between different parameters, we decouple the least-squares solver into several stages and obtain robust self-calibration parameters. Surveying experiments show that the flexible calibration method proposed in this paper is both effective and feasible in improving the accuracy of point clouds in overlapping areas, and can reduce the inconsistency of the calibrated point clouds by 37.02%.

Application of stochastic time dependent parameters to improve the characterization of uncertainty in conceptual hydrological models

• We test stochastic processes to improve modeling of uncertainty in a real case study. • Bayesian inference and cross-validation are used to calibrate and assess performances. • Results highlight clear benefits for appropriate modeling choices. • We make recommendations to uncover/avoid issues due to overparameterization. • We test a novel parallel framework that simplifies access to HPC resources. The traditional description of a hydrological system with a deterministic, conceptual model and a lumped output error term does not explicitly consider the main mechanisms of uncertainty generation due to approximate process representation, unobserved variability in processes and influence factors, and input uncertainty. In this study, we test the description of such intrinsic uncertainty in conceptual models by making process rates stochastic through stochastic, time-dependent rate parameters. We analyze the advantages and challenges of this approach by using Bayesian inference to jointly estimate model parameters, parameters of the stochastic processes, and the time series of the stochastic parameters. Numerically, we use a particle filter to infer the stochastic time series and to approximate the marginal likelihood for Markov chain sampling of the constant parameters. Compared to the lumped error formulation, we achieve a more realistic description of uncertainty, as we obtain larger errors in intrinsic states, larger uncertainty during prediction than calibration periods (a feature missing for simple lumped error models), and autocorrelated model outputs. However, the additional degrees of freedom introduced with stochastic parameters can lead to an unintentional compensation for model deficits or input errors. This problem is symptomatic of model structure inadequacy or poor selection of the parameters that are made stochastic, and can be diagnosed through cross-validation and careful posterior analysis. The proposed approach is computationally more demanding and its implementation more challenging than the traditional description of hydrological systems using a deterministic model with a lumped error term. However, its advantages both in providing a more realistic representation of uncertainties and in diagnosing model deficiencies suggest its adoption and further development in future studies.

The Effect of Error Non-Orthogonality on Triple Collocation Analyses

Triple collocation analysis is an established technique for calculating the relative linear intercalibration coefficients and observation error variances for physical quantities measured simultaneously in space and time by three different observation systems. A simple parameterized error model is used. It relies on a few assumptions, one of which is that the observation errors are independent of the magnitude of the observed quantities. This is referred to as error orthogonality. Using an ocean surface vector winds data set of 44,948 collocations, this study shows that the violation of error orthogonality does affect the calibration coefficients but has only a small second-order effect on the observation error variances of the calibrated data.

Geometric error identification of five-axis machine tools using dual quaternion

A universal identification method for position independent geometric errors (PIGEs) of dual rotary axes of five-axis machine tools with arbitrary rotary axis position structures is proposed based on the unit dual quaternion (UDQ). The PIGEs of translational/rotary axes are redefined based on UDQ transformation, which effectively reduces the transformation parameters and avoids the unitization process of UDQ compared with the existing UDQ kinematics model. Based on the redefined PIGEs, a kinematic error model of a five-axis machine tool is established for error identification. Taking the cradle-type five-axis machine too with non-intersecting rotary axes as the research objective, a novel method for identifying PIGEs through the synchronous motion of dual rotary axes using a double ball bar (DBB) is proposed. Compared with BK1 and BK2 in ISO10791-6 and other existing methods, the advantage of the proposed method is that it can greatly reduce the complexity of the experiment and the operation steps by directly constructing the relative kinematic relationship between the tool and the workpiece based on the error model. Only one installation and one measurement trajectory are needed to simultaneously identify the eight PIGEs of the dual rotary axes. In addition, a trajectory equalization algorithm is proposed to effectively solve the asynchronous problem of motion and data sampling in DBB trajectory operation. By combining the simplified error model with the sampling data of DBB, the pseudo-inverse matrix is used for decoupling. The effectiveness of the proposed method is verified by DBB compensation comparison experiment. The proposed error identification method can be applied to other types of five-axis machine tools with a few changes in the configural parameters, which is ideal for periodic checks and calibration to ensure the machining accuracy.

Crossing a topological phase transition with a quantum computer

Quantum computers promise to perform computations beyond the reach of modern computers with profound implications for scientific research. Due to remarkable technological advances, small scale devices are now becoming available for use. One of the most apparent applications for such a device is the study of complex many-body quantum systems, where classical computers are unable to deal with the generic exponential complexity of quantum states. Even zero-temperature equilibrium phases of matter and the transitions between them have yet to be fully classified, with topologically protected phases presenting major difficulties. We construct and measure a continuously parametrized family of states crossing a symmetry protected topological phase transition on the IBM Q quantum computers. We present two complementary methods for measuring string order parameters that reveal the transition, and additionally analyse the effects of noise in the device using simple error models. The simulation that we perform is easily scalable and is a practical demonstration of the utility of near-term quantum computers for the study of quantum phases of matter and their transitions.

Calibration of Collaborative Robots Based on Position Information and Local Product of Exponentials

To improve the positioning accuracy of collaborative robots, a novel modeling and calibration method for collaborative robots is proposed based on position information and modified local product of exponentials (LPoE). The kinematic error model is derived from the kinematic model through differential transformation. To solve the problem of the high redundancy and complexity of the error model that is difficult to identify, the errors of the kinematic parameters are all transferred to the initial position and posture matrix of the local coordinate system, which simplifies the error model and improves the speed and accuracy of the identification calculation. However, the simplified error model still requires posture data which are very difficult to acquire in practice. For this reason, the position error is separated from the kinematic model, and an error model based on position data is established. Then, a kinematic calibration method of the collaborative robot based on position data is proposed, which simplifies the measurement process and improves the efficiency of calibration. The effectiveness of the method is verified by simulations and experiments on a six degree-of-freedom collaborative robot.

Universal hardware-efficient topological measurement-based quantum computation via color-code-based cluster states

Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit Pauli measurements with a family of large entangled states called cluster states as resources. Raussendorf's three-dimensional cluster states (RTCSs) based on the surface codes are mainly considered for topological MBQC. In such schemes, however, the fault-tolerant implementation of the logical Hadamard, phase ($Z^{1/2}$), and $T$ ($Z^{1/4}$) gates which are essential for building up arbitrary logical gates has not been achieved to date without using state distillation, while the controlled-NOT (CNOT) gate does not require it, to best of our knowledge. State distillation generally consumes many ancillary logical qubits, thus it is a severe obstacle against practical quantum computing. To solve this problem, we suggest an MBQC scheme via a family of cluster states called color-code-based cluster states (CCCSs) based on the two-dimensional color codes instead of the surface codes. We define logical qubits, construct elementary logical gates, and describe error correction schemes. We show that all the logical Clifford gates including the CNOT, Hadamard, and phase gates can be implemented fault-tolerantly without state distillation, although the fault-tolerant $T$ gate still requires it. We further prove that the minimal number of physical qubits per logical qubit in a CCCS is at most approximately 1.8 times smaller than the case of an RTCS. We lastly show that the error threshold of MBQC via CCCSs for logical-$Z$ errors is 2.7-2.8%, which is comparable to the value for RTCSs, assuming a simple error model where physical qubits have $X$-measurement or $Z$ errors independently with the same probability.

Accelerating uncertainty quantification of groundwater flow modelling using a deep neural network proxy

Quantifying the uncertainty in model parameters and output is a critical component in model-driven decision support systems for groundwater management. This paper presents a novel algorithmic approach which fuses Markov Chain Monte Carlo (MCMC) and Machine Learning methods to accelerate uncertainty quantification for groundwater flow models. We formulate the governing mathematical model as a Bayesian inverse problem, considering model parameters as a random process with an underlying probability distribution. MCMC allows us to sample from this distribution, but it comes with some limitations: it can be prohibitively expensive when dealing with costly likelihood functions, subsequent samples are often highly correlated, and the standard Metropolis–Hastings algorithm suffers from the curse of dimensionality. This paper designs a Metropolis–Hastings proposal which exploits a deep neural network (DNN) approximation of a groundwater flow model, to significantly accelerate MCMC sampling. We modify a delayed acceptance (DA) model hierarchy, whereby proposals are generated by running short subchains using an inexpensive DNN approximation, resulting in a decorrelation of subsequent fine model proposals. Using a simple adaptive error model, we estimate and correct the bias of the DNN approximation with respect to the posterior distribution on-the-fly. The approach is tested on two synthetic examples; a isotropic two-dimensional problem, and an anisotropic three-dimensional problem. The results show that the cost of uncertainty quantification can be reduced by up to 50% compared to single-level MCMC, depending on the precomputation cost and accuracy of the employed DNN.

Cooperative control method of multi-missile formation under uncontrollable speed

Under the missile speed is uncontrollable, a design method of multi-missile formation flight controller based on the sliding mode variable structure control theory and adaptive dynamic surface control theory is proposed. Firstly, according to the relative position of the leader and the follower in the inertial frame, the tracking error model for the relative position and the expected relative position between the leader and the follower is obtained, and the multi-missile formation control system in the inertial coordinate system is obtained. Secondly, in order to obtain the expression of the formation control system in the ballistic coordinate system, the acceleration of the missile in the ballistic coordinate system is converted to the inertial coordinate system. Combining with the tracking of the relative position and the desired relative position of the leader and the followers, we can obtain the simplified error model for the formation control system. Then the sliding mode variable structure control theory and the adaptive dynamic surface control theory are used to design the formation controllers for the leader and follower missiles respectively, and the stability of the present controller is analysed via the Lyapunov stability theory. Finally, the designed formation controllers are used for the leader and follower missiles to simulate the parameters. The results verify the feasibility and effectiveness of the present method.

Experimental Characterization of Fault-Tolerant Circuits in Small-Scale Quantum Processors

Experiments conducted on open-access cloud-based IBM Quantum devices are presented for characterizing their fault tolerance using [4,2,2]-encoded gate sequences. Up to 100 logical gates are activated in the Ibmq_Bogota and Ibmq_Santiago devices and we found that a [4,2,2] code’s logical gate set may be deemed fault-tolerant for gate sequences larger than 10 gates. However, certain circuits did not satisfy the fault tolerance criterion. In some cases the encoded-gate sequences show a high error rate that is lower bounded at ≈ 0.1, whereby the error inherent in these circuits cannot be mitigated by classical post-selection. A comparison of the experimental results to a simple error model reveal that the dominant gate errors cannot be readily represented by the popular Pauli error model. Finally, it is most accurate to assess the fault tolerance criterion when the circuits tested are restricted to those that give rise to an output state with a low dimension.

A Parameter Dimension Reduction-Based Estimation Approach to Enhance the Kinematic Accuracy of a Parallel Hardware-in-the-Loop Docking Simulator

SUMMARYThe docking simulators are significant ground test equipment for aerospace projects. The fidelity of docking simulation highly depends on the accuracy performance. This paper investigates the kinematic accuracy for the developed docking simulator. A novel kinematic calibration method which can reduce the number of parameters for error modeling is presented. The principle of parameters separation is studied. A simplified error model is derived based on Taylor series. This method can contribute to the simplification of the error model, fewer measurements, and easier convergence during the parameters identification. The calibration experiment validates this method for further accuracy enhancement.

Linking Gy’s Formula to QA/QC Duplicates Statistics

Obtaining representative samples is of the uttermost importance for modelling mineral deposits. On one hand, Gy’s formula makes it possible to compute relative error variance for a specified target grade on the stringent assumption of perfect homogenization. On the other hand, duplicates (field, rejects and pulp) are now routinely used in QA/QC. No direct links have been established between Gy’s relative variance and the main duplicates statistics used in QA/QC. This paper presents a simple multiplicative error model that makes it possible to predict from Gy’s formula the standard deviation of duplicates differences and duplicates correlation for any distribution. Assuming lognormality, a test is derived to predict whether the sample preparation procedure is likely to meet the target proportion of duplicates with half absolute relative difference (HARD) of less than 10%. The test and the predicted statistics can be used to predict duplicates’ QA/QC results and make necessary adjustments early, before any QA/QC data is acquired. The relationships are tested and validated by simulations and a series of deposit data extracted from NI43-101 published reports.

Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory

Based on numerically-optimized real-device gates and parameters we study the performance of the phase-flip (repetition) code on a linear array of Gallium Arsenide (GaAs) quantum dots hosting singlet-triplet qubits. We first examine the expected performance of the code using simple error models of circuit-level and phenomenological noise, reporting, for example, a circuit-level depolarizing noise threshold of approximately 3%. We then perform density-matrix simulations using a maximum-likelihood and minimum-weight matching decoder to study the effect of real-device dephasing, read-out error, quasi-static as well as fast gate noise. Considering the trade-off between qubit read-out error and dephasing time (T2) over measurement time, we identify a sub-threshold region for the phase-flip code which lies within experimental reach.

Geometric- and force-induced errors compensation and uncertainty analysis of rotary axis in 5-axis ultra-precision machine tool

In machining of a microstructure on a free form surface, a five-axis ultra-precision machine tool has a great advantage in its flexibility and efficiency compared to a conventional machine tool. However, rotary axes in the five-axis machine tool are sensitive to position errors due to low rigidity. In addition, micro-tools, which are utilized in micro-machining, have low stiffness. The low rigidity and stiffness of the rotary axes and tool introduce geometric errors in machining. Therefore, the position and orientation errors of the rotary axes and the micro-tool must be identified and compensated. Many components contribute to uncertainty of the measurements which will inevitably reduce the reliability of the results. Therefore, it is necessary to analyze the uncertainty of each component. This paper proposed a method to comprehensively identify position-independent geometric errors (PIGEs) and force-induced errors (FIEs) of a system from the rotary axis on the machine to the micro-tool. A simple and practical error model to represent the tool position with respect to the angle of the rotary axis was built. Uncertainty was analyzed to validate the reliability of the proposed method. Cutting experiments were carried out on an AISI 1018 steel and an Al6061 workpiece, and the results were analyzed to verify the proposed model.

Comparison of Single-Valued Forecasts in a User-Oriented Framework

Abstract We compare single-valued forecasts from a consensus of numerical weather prediction models to forecasts from a single model across a range of user decision thresholds and sensitivities, using the relative economic value framework, and present this comparison in a new graphical format. With the help of a simple linear error model, we obtain theoretical results and perform synthetic calculations to gain insights into how the results relate to the characteristics of the different forecast systems. We find that multimodel consensus forecasts are more beneficial for users interested in decisions near the climatological mean, due to their reduced spread of errors compared to the constituent models. Single model forecasts may present greater benefit for users sensitive to extreme events if the forecasts have smaller conditional biases than the consensus forecasts and hence better resolution of such events. The results support use of consensus averaging approaches for single-valued forecast services in typical conditions. However, it is hard to cater for all user sensitivities in more extreme conditions. This underscores the importance of providing probability-based services for unusual conditions.

Synthetic Gaia Surveys from the FIRE Cosmological Simulations of Milky Way-mass Galaxies

Abstract With Gaia Data Release 2, the astronomical community is entering a new era of multidimensional surveys of the Milky Way. This new phase-space view of our Galaxy demands new tools for comparing observations to simulations of Milky Way-mass galaxies in a cosmological context, to test the physics of both dark matter and galaxy formation. We present ananke, a framework for generating synthetic phase-space surveys from high-resolution baryonic simulations, and use it to generate a suite of synthetic surveys resembling Gaia DR2 in data structure, magnitude limits, and observational errors. We use three cosmological simulations of Milky Way-mass galaxies from the Latte suite of the Feedback In Realistic Environments project, which feature self-consistent clustering of star formation in dense molecular clouds and thin stellar/gaseous disks in live cosmological halos with satellite dwarf galaxies and stellar halos. We select three solar viewpoints from each simulation to generate nine synthetic Gaia-like surveys. We sample synthetic stars by assuming each star particle (of mass 7070 M ⊙) represents a single stellar population. At each viewpoint, we compute dust extinction from the simulated gas metallicity distribution and apply a simple error model to produce a synthetic Gaia-like survey that includes both observational properties and a pointer to the generating star particle. We provide the complete simulation snapshot at z = 0 for each simulated galaxy. We describe data access points, the data model, and plans for future upgrades. These synthetic surveys provide a tool for the scientific community to test analysis methods and interpret Gaia data.

Online Optimization in Cloud Resource Provisioning

Due to mainstream adoption of cloud computing and its rapidly increasing usage of energy, the efficient management of cloud computing resources has become an important issue. A key challenge in managing the resources lies in the volatility of their demand. While there have been a wide variety of online algorithms (e.g. Receding Horizon Control, Online Balanced Descent) designed, it is hard for cloud operators to pick the right algorithm. In particular, these algorithms vary greatly on their usage of predictions and performance guarantees. This paper aims at studying an automatic algorithm selection scheme in real time. To do this, we empirically study the prediction errors from real-world cloud computing traces. Results show that prediction errors are distinct from different prediction algorithms, across virtual machines, and over the time horizon. Based on these observations, we propose a simple prediction error model and prove upper bounds on the dynamic regret of several online algorithms. We then apply the empirical and theoretical results to create a simple online meta-algorithm that chooses the best algorithm on the fly. Numerical simulations demonstrate that the performance of the designed policy is close to that of the best algorithm in hindsight.

Incorporating climate model similarities and hydrologic error models to quantify climate change impacts on future riverine flood risk

Quantifying uncertainty in projecting climate change impact on flood frequency analysis is particularly relevant for long-term water resources planning and management. This study examines uncertainties arising from (1) a climate model, with and without accounting of intermodel similarities, (2) a hydrological model with two different error model definitions, which have previously received less attention in studies propagating uncertainty through climate change impacts on flood response. Through a Bayesian modeling framework, a proposed statistical framework is utilized to explore various definitions of sources of uncertainty and to develop a series of nested formulations that can evaluate the leverage of specific uncertainty sources in quantiles of future streamflow. To be specific, climate model similarity, hydrologic prediction error, and frequency analysis are formally modeled with an appropriate likelihood function. The quantiles inferred by each formulation are compared in a case study of the Yongdam Basin in Korea. Results indicate that variance in hydrologic response is underestimated if climate model similarities are ignored, and in many cases, the inferred quantiles of streamflow projection are biased accordingly. Furthermore, a simple error model used in defining hydrologic uncertainty may create incorrect information in determining the quantiles in streamflow projection. The approach presented here of quantifying uncertainty has the potential to better depict overall multi-source uncertainties in projections of climate change impacts on hydrologic response. Finally, our results also indicate that careful flood planning management may be required for the Yongdam Basin in future summers.